Created on Wed Sep 22 2010, 08:29:36 CEST GENUS: 4 NUMBER OF MAPS: 111 REFLEXIBLE MAPS: 77 CHIRAL MAPS: 34 #TYPE I: 76 #TYPE II: 35 CAYLEY MAPS: 109 NON-CAYLEY MAPS: 2 NON-CAYLEY REPRESENTATIVES: A4.656, A4.1874 MAP : A4.1 NOTES : type II, reflexible, isomorphic to DBar({3,12}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <72, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 432 R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432) L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 366)(74, 371)(75, 361)(76, 369)(77, 364)(78, 363)(79, 396)(80, 362)(81, 365)(82, 403)(83, 368)(84, 370)(85, 378)(86, 383)(87, 373)(88, 381)(89, 376)(90, 375)(91, 420)(92, 374)(93, 377)(94, 391)(95, 380)(96, 382)(97, 414)(98, 419)(99, 409)(100, 417)(101, 412)(102, 411)(103, 384)(104, 410)(105, 413)(106, 427)(107, 416)(108, 418)(109, 390)(110, 395)(111, 385)(112, 393)(113, 388)(114, 387)(115, 372)(116, 386)(117, 389)(118, 379)(119, 392)(120, 394)(121, 402)(122, 407)(123, 397)(124, 405)(125, 400)(126, 399)(127, 432)(128, 398)(129, 401)(130, 367)(131, 404)(132, 406)(133, 426)(134, 431)(135, 421)(136, 429)(137, 424)(138, 423)(139, 408)(140, 422)(141, 425)(142, 415)(143, 428)(144, 430)(145, 292)(146, 294)(147, 331)(148, 289)(149, 355)(150, 290)(151, 299)(152, 340)(153, 326)(154, 338)(155, 295)(156, 328)(157, 312)(158, 321)(159, 311)(160, 324)(161, 347)(162, 309)(163, 315)(164, 348)(165, 306)(166, 345)(167, 303)(168, 301)(169, 316)(170, 318)(171, 307)(172, 313)(173, 343)(174, 314)(175, 323)(176, 352)(177, 302)(178, 350)(179, 319)(180, 304)(181, 336)(182, 297)(183, 335)(184, 300)(185, 359)(186, 333)(187, 291)(188, 360)(189, 330)(190, 357)(191, 327)(192, 325)(193, 344)(194, 298)(195, 341)(196, 296)(197, 339)(198, 346)(199, 317)(200, 337)(201, 310)(202, 342)(203, 305)(204, 308)(205, 356)(206, 322)(207, 353)(208, 320)(209, 351)(210, 358)(211, 293)(212, 349)(213, 334)(214, 354)(215, 329)(216, 332) MAP : A4.7 NOTES : type II, reflexible, isomorphic to DBar({4,5}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {5, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^5 > CTG (small) : <120, 34> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, (x.2^-1 * x.3)^2, (x.3 * x.1^-1)^4, (x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^5, x.3^2 * x.2^-1 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-2 * x.2^-2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 10) #DARTS : 720 R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720) L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 604)(122, 605)(123, 602)(124, 641)(125, 640)(126, 601)(127, 719)(128, 718)(129, 677)(130, 705)(131, 708)(132, 676)(133, 612)(134, 609)(135, 636)(136, 607)(137, 608)(138, 633)(139, 716)(140, 715)(141, 703)(142, 710)(143, 709)(144, 704)(145, 717)(146, 720)(147, 712)(148, 684)(149, 681)(150, 713)(151, 686)(152, 685)(153, 673)(154, 680)(155, 679)(156, 674)(157, 687)(158, 690)(159, 682)(160, 654)(161, 651)(162, 683)(163, 689)(164, 688)(165, 647)(166, 675)(167, 678)(168, 646)(169, 702)(170, 699)(171, 606)(172, 697)(173, 698)(174, 603)(175, 694)(176, 695)(177, 692)(178, 611)(179, 610)(180, 691)(181, 657)(182, 660)(183, 652)(184, 624)(185, 621)(186, 653)(187, 672)(188, 669)(189, 696)(190, 667)(191, 668)(192, 693)(193, 656)(194, 655)(195, 643)(196, 650)(197, 649)(198, 644)(199, 664)(200, 665)(201, 662)(202, 701)(203, 700)(204, 661)(205, 659)(206, 658)(207, 617)(208, 645)(209, 648)(210, 616)(211, 629)(212, 628)(213, 707)(214, 615)(215, 618)(216, 706)(217, 626)(218, 625)(219, 613)(220, 620)(221, 619)(222, 614)(223, 634)(224, 635)(225, 632)(226, 671)(227, 670)(228, 631)(229, 627)(230, 630)(231, 622)(232, 714)(233, 711)(234, 623)(235, 642)(236, 639)(237, 666)(238, 637)(239, 638)(240, 663)(241, 563)(242, 562)(243, 533)(244, 567)(245, 570)(246, 532)(247, 560)(248, 559)(249, 565)(250, 548)(251, 547)(252, 566)(253, 592)(254, 593)(255, 590)(256, 503)(257, 502)(258, 589)(259, 561)(260, 564)(261, 550)(262, 516)(263, 513)(264, 551)(265, 600)(266, 597)(267, 492)(268, 595)(269, 596)(270, 489)(271, 556)(272, 557)(273, 554)(274, 599)(275, 598)(276, 553)(277, 521)(278, 520)(279, 485)(280, 531)(281, 534)(282, 484)(283, 546)(284, 543)(285, 594)(286, 541)(287, 542)(288, 591)(289, 518)(290, 517)(291, 529)(292, 512)(293, 511)(294, 530)(295, 519)(296, 522)(297, 514)(298, 510)(299, 507)(300, 515)(301, 494)(302, 493)(303, 481)(304, 506)(305, 505)(306, 482)(307, 495)(308, 498)(309, 508)(310, 588)(311, 585)(312, 509)(313, 497)(314, 496)(315, 581)(316, 483)(317, 486)(318, 580)(319, 528)(320, 525)(321, 558)(322, 523)(323, 524)(324, 555)(325, 538)(326, 539)(327, 536)(328, 545)(329, 544)(330, 535)(331, 573)(332, 576)(333, 586)(334, 552)(335, 549)(336, 587)(337, 504)(338, 501)(339, 540)(340, 499)(341, 500)(342, 537)(343, 572)(344, 571)(345, 577)(346, 584)(347, 583)(348, 578)(349, 490)(350, 491)(351, 488)(352, 527)(353, 526)(354, 487)(355, 575)(356, 574)(357, 569)(358, 579)(359, 582)(360, 568) MAP : A4.10 NOTES : type II, reflexible, isomorphic to DBar({4,6}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <72, 40> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3 * x.2 * x.3^2 * x.2 * x.3 * x.2^-2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 432 R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432) L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 362)(74, 365)(75, 368)(76, 363)(77, 426)(78, 369)(79, 416)(80, 419)(81, 422)(82, 417)(83, 372)(84, 423)(85, 420)(86, 411)(87, 414)(88, 425)(89, 406)(90, 377)(91, 366)(92, 393)(93, 396)(94, 371)(95, 388)(96, 431)(97, 364)(98, 391)(99, 394)(100, 379)(101, 392)(102, 385)(103, 382)(104, 373)(105, 376)(106, 361)(107, 374)(108, 367)(109, 402)(110, 429)(111, 432)(112, 407)(113, 424)(114, 395)(115, 400)(116, 427)(117, 430)(118, 415)(119, 428)(120, 421)(121, 418)(122, 409)(123, 412)(124, 397)(125, 410)(126, 403)(127, 398)(128, 401)(129, 404)(130, 399)(131, 390)(132, 405)(133, 380)(134, 383)(135, 386)(136, 381)(137, 408)(138, 387)(139, 384)(140, 375)(141, 378)(142, 389)(143, 370)(144, 413)(145, 330)(146, 357)(147, 360)(148, 335)(149, 352)(150, 323)(151, 328)(152, 355)(153, 358)(154, 343)(155, 356)(156, 349)(157, 346)(158, 337)(159, 340)(160, 325)(161, 338)(162, 331)(163, 326)(164, 329)(165, 332)(166, 327)(167, 318)(168, 333)(169, 308)(170, 311)(171, 314)(172, 309)(173, 336)(174, 315)(175, 312)(176, 303)(177, 306)(178, 317)(179, 298)(180, 341)(181, 290)(182, 293)(183, 296)(184, 291)(185, 354)(186, 297)(187, 344)(188, 347)(189, 350)(190, 345)(191, 300)(192, 351)(193, 348)(194, 339)(195, 342)(196, 353)(197, 334)(198, 305)(199, 294)(200, 321)(201, 324)(202, 299)(203, 316)(204, 359)(205, 292)(206, 319)(207, 322)(208, 307)(209, 320)(210, 313)(211, 310)(212, 301)(213, 304)(214, 289)(215, 302)(216, 295) MAP : A4.16 NOTES : type II, reflexible, isomorphic to DBar({4,10}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {10, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 10, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^10 > CTG (small) : <40, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^10 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 20) #DARTS : 240 R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198) MAP : A4.31 NOTES : type I, reflexible, isomorphic to Trun({4,5}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^5, (u.2 * u.3^-1)^5 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, x.2^5, (x.2^2 * x.3)^3, (x.2 * x.3)^5, (x.2^-2 * x.3 * x.2 * x.3)^2, (x.1 * x.2^-1)^5 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 10, 10) #DARTS : 360 R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360) L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 305)(62, 318)(63, 341)(64, 302)(65, 304)(66, 334)(67, 314)(68, 317)(69, 319)(70, 313)(71, 330)(72, 329)(73, 327)(74, 303)(75, 340)(76, 339)(77, 351)(78, 301)(79, 328)(80, 325)(81, 312)(82, 354)(83, 326)(84, 356)(85, 342)(86, 352)(87, 338)(88, 353)(89, 349)(90, 315)(91, 311)(92, 336)(93, 323)(94, 308)(95, 310)(96, 316)(97, 332)(98, 335)(99, 337)(100, 331)(101, 348)(102, 347)(103, 345)(104, 309)(105, 322)(106, 321)(107, 357)(108, 307)(109, 346)(110, 343)(111, 306)(112, 360)(113, 344)(114, 350)(115, 324)(116, 358)(117, 320)(118, 359)(119, 355)(120, 333)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 265)(140, 266)(141, 267)(142, 268)(143, 269)(144, 270)(145, 259)(146, 260)(147, 261)(148, 262)(149, 263)(150, 264)(151, 277)(152, 278)(153, 279)(154, 280)(155, 281)(156, 282)(157, 271)(158, 272)(159, 273)(160, 274)(161, 275)(162, 276)(163, 241)(164, 242)(165, 243)(166, 244)(167, 245)(168, 246)(169, 247)(170, 248)(171, 249)(172, 250)(173, 251)(174, 252)(175, 253)(176, 254)(177, 255)(178, 256)(179, 257)(180, 258) MAP : A4.44 NOTES : type I, reflexible, isomorphic to Trun({4,6}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^4, u.3^4, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^3 > CTG (small) : <36, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^4, x.3^4, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (4, 12, 12) #DARTS : 216 R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 75)(38, 94)(39, 79)(40, 89)(41, 108)(42, 98)(43, 81)(44, 88)(45, 73)(46, 95)(47, 102)(48, 104)(49, 96)(50, 87)(51, 92)(52, 74)(53, 82)(54, 85)(55, 90)(56, 93)(57, 86)(58, 80)(59, 76)(60, 91)(61, 106)(62, 84)(63, 107)(64, 97)(65, 99)(66, 77)(67, 100)(68, 78)(69, 101)(70, 103)(71, 105)(72, 83)(145, 198)(146, 201)(147, 194)(148, 188)(149, 184)(150, 199)(151, 214)(152, 192)(153, 215)(154, 205)(155, 207)(156, 185)(157, 208)(158, 186)(159, 209)(160, 211)(161, 213)(162, 191)(163, 183)(164, 202)(165, 187)(166, 197)(167, 216)(168, 206)(169, 189)(170, 196)(171, 181)(172, 203)(173, 210)(174, 212)(175, 204)(176, 195)(177, 200)(178, 182)(179, 190)(180, 193) MAP : A4.46 NOTES : type II, reflexible, isomorphic to DBar({6,6}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 > CTG (small) : <36, 12> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, (x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 12) #DARTS : 216 R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 207)(39, 212)(40, 189)(41, 181)(42, 206)(43, 205)(44, 191)(45, 211)(46, 210)(47, 182)(48, 185)(49, 199)(50, 198)(51, 194)(52, 216)(53, 213)(54, 202)(55, 201)(56, 195)(57, 209)(58, 215)(59, 214)(60, 208)(61, 197)(62, 203)(63, 190)(64, 193)(65, 204)(66, 188)(67, 192)(68, 186)(69, 196)(70, 183)(71, 200)(72, 187)(73, 171)(74, 148)(75, 145)(76, 170)(77, 176)(78, 153)(79, 154)(80, 149)(81, 174)(82, 175)(83, 180)(84, 155)(85, 147)(86, 160)(87, 157)(88, 146)(89, 152)(90, 165)(91, 166)(92, 161)(93, 150)(94, 151)(95, 156)(96, 167)(97, 159)(98, 172)(99, 169)(100, 158)(101, 164)(102, 177)(103, 178)(104, 173)(105, 162)(106, 163)(107, 168)(108, 179) MAP : A4.100 NOTES : type I, reflexible, isomorphic to TDual({4,5}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2, (x.3^-2 * x.2^2)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (5, 8, 8) #DARTS : 360 R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360) L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 125)(62, 138)(63, 161)(64, 122)(65, 124)(66, 154)(67, 134)(68, 137)(69, 139)(70, 133)(71, 150)(72, 149)(73, 147)(74, 123)(75, 160)(76, 159)(77, 171)(78, 121)(79, 148)(80, 145)(81, 132)(82, 174)(83, 146)(84, 176)(85, 162)(86, 172)(87, 158)(88, 173)(89, 169)(90, 135)(91, 131)(92, 156)(93, 143)(94, 128)(95, 130)(96, 136)(97, 152)(98, 155)(99, 157)(100, 151)(101, 168)(102, 167)(103, 165)(104, 129)(105, 142)(106, 141)(107, 177)(108, 127)(109, 166)(110, 163)(111, 126)(112, 180)(113, 164)(114, 170)(115, 144)(116, 178)(117, 140)(118, 179)(119, 175)(120, 153)(241, 309)(242, 357)(243, 346)(244, 345)(245, 333)(246, 355)(247, 310)(248, 307)(249, 330)(250, 336)(251, 308)(252, 302)(253, 348)(254, 334)(255, 344)(256, 335)(257, 331)(258, 321)(259, 318)(260, 304)(261, 314)(262, 305)(263, 301)(264, 351)(265, 340)(266, 337)(267, 360)(268, 306)(269, 338)(270, 332)(271, 320)(272, 323)(273, 313)(274, 319)(275, 312)(276, 311)(277, 359)(278, 324)(279, 347)(280, 356)(281, 358)(282, 352)(283, 329)(284, 354)(285, 317)(286, 326)(287, 328)(288, 322)(289, 350)(290, 353)(291, 343)(292, 349)(293, 342)(294, 341)(295, 339)(296, 327)(297, 316)(298, 315)(299, 303)(300, 325) MAP : A4.103 NOTES : type I, reflexible, isomorphic to Trun({5,5}), QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 5, 5 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^5, (u.1 * u.2^-1)^5 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2 | x.1^2, x.2^5, (x.1 * x.2^-2)^3, (x.2 * x.1 * x.2)^3, (x.1 * x.2^-1)^5, (x.2^2 * x.1 * x.2^-1 * x.1)^2, (x.2 * x.1 * x.2^-1 * x.1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (5, 10, 10) #DARTS : 180 R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180) L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 161)(62, 126)(63, 173)(64, 158)(65, 160)(66, 166)(67, 122)(68, 125)(69, 127)(70, 121)(71, 138)(72, 137)(73, 135)(74, 159)(75, 172)(76, 171)(77, 147)(78, 157)(79, 136)(80, 133)(81, 156)(82, 150)(83, 134)(84, 140)(85, 174)(86, 148)(87, 170)(88, 149)(89, 145)(90, 123)(91, 155)(92, 168)(93, 131)(94, 152)(95, 154)(96, 124)(97, 164)(98, 167)(99, 169)(100, 163)(101, 180)(102, 179)(103, 177)(104, 153)(105, 130)(106, 129)(107, 141)(108, 151)(109, 178)(110, 175)(111, 162)(112, 144)(113, 176)(114, 146)(115, 132)(116, 142)(117, 128)(118, 143)(119, 139)(120, 165) MAP : A4.105 NOTES : type I, reflexible, isomorphic to TDual({3,12}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^6 > CTG (small) : <36, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 216 R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 186)(38, 202)(39, 212)(40, 203)(41, 195)(42, 196)(43, 200)(44, 189)(45, 214)(46, 216)(47, 209)(48, 213)(49, 182)(50, 184)(51, 205)(52, 181)(53, 190)(54, 183)(55, 191)(56, 206)(57, 207)(58, 193)(59, 194)(60, 210)(61, 185)(62, 187)(63, 215)(64, 192)(65, 199)(66, 211)(67, 204)(68, 198)(69, 208)(70, 188)(71, 201)(72, 197)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163) MAP : A4.143 NOTES : type I, reflexible, isomorphic to TDual({4,6}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <36, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 8, 8) #DARTS : 216 R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 185)(39, 190)(40, 189)(41, 181)(42, 184)(43, 191)(44, 187)(45, 186)(46, 192)(47, 188)(48, 183)(49, 194)(50, 197)(51, 214)(52, 213)(53, 193)(54, 196)(55, 203)(56, 199)(57, 210)(58, 204)(59, 200)(60, 207)(61, 206)(62, 209)(63, 202)(64, 201)(65, 205)(66, 208)(67, 215)(68, 211)(69, 198)(70, 216)(71, 212)(72, 195)(73, 147)(74, 166)(75, 151)(76, 161)(77, 180)(78, 170)(79, 153)(80, 160)(81, 145)(82, 167)(83, 174)(84, 176)(85, 168)(86, 159)(87, 164)(88, 146)(89, 154)(90, 157)(91, 162)(92, 165)(93, 158)(94, 152)(95, 148)(96, 163)(97, 178)(98, 156)(99, 179)(100, 169)(101, 171)(102, 149)(103, 172)(104, 150)(105, 173)(106, 175)(107, 177)(108, 155) MAP : A4.161 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.2 * x.1)^2, (x.2 * x.4^-1 * x.1)^2, (x.4^-1 * x.1)^3, (x.4 * x.2)^3, x.3 * x.4^-1 * x.1 * x.4 * x.3 * x.1 * x.4^-1 * x.2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 98)(50, 100)(51, 97)(52, 99)(53, 103)(54, 101)(55, 104)(56, 102)(57, 112)(58, 111)(59, 110)(60, 109)(61, 118)(62, 120)(63, 117)(64, 119)(65, 107)(66, 105)(67, 108)(68, 106)(69, 116)(70, 115)(71, 114)(72, 113)(121, 133)(122, 134)(123, 135)(124, 136)(125, 137)(126, 138)(127, 139)(128, 140)(129, 141)(130, 142)(131, 143)(132, 144) MAP : A4.163 NOTES : type I, reflexible, isomorphic to Med2({3,12}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^6 > CTG (small) : <36, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 288 R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 83)(38, 102)(39, 76)(40, 82)(41, 98)(42, 101)(43, 100)(44, 73)(45, 78)(46, 75)(47, 80)(48, 97)(49, 96)(50, 89)(51, 79)(52, 91)(53, 90)(54, 86)(55, 106)(56, 84)(57, 74)(58, 103)(59, 108)(60, 107)(61, 92)(62, 105)(63, 94)(64, 87)(65, 81)(66, 93)(67, 99)(68, 95)(69, 77)(70, 88)(71, 85)(72, 104)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 270)(218, 286)(219, 260)(220, 287)(221, 279)(222, 280)(223, 284)(224, 273)(225, 262)(226, 264)(227, 257)(228, 261)(229, 266)(230, 268)(231, 253)(232, 265)(233, 274)(234, 267)(235, 275)(236, 254)(237, 255)(238, 277)(239, 278)(240, 258)(241, 269)(242, 271)(243, 263)(244, 276)(245, 283)(246, 259)(247, 288)(248, 282)(249, 256)(250, 272)(251, 285)(252, 281) MAP : A4.179 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^6, (u.1^-1 * u.2^-1)^3 > CTG (small) : <36, 11> CTG (fp) : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 144 R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144) L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142) MAP : A4.186 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4^3, u.5^3, u.3 * u.4^-1 * u.1 * u.3^-1 * u.2 * u.5^-1 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^3, x.5^3, x.5^-1 * x.1 * x.2 * x.4^-1, (x.4, x.5^-1), x.5^-1 * x.1 * x.4^-1 * x.1, x.3 * x.1 * x.5 * x.3^-1 * x.2 * x.5^-1 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)(109, 139)(110, 140)(111, 141)(112, 142)(113, 143)(114, 144)(115, 127)(116, 128)(117, 129)(118, 130)(119, 131)(120, 132)(121, 133)(122, 134)(123, 135)(124, 136)(125, 137)(126, 138) MAP : A4.205 NOTES : type I, reflexible, isomorphic to Med2({4,5}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^5, u.4^5 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.3 * x.2 * x.4, (x.3 * x.1^-1)^2, x.2^5, x.4^5, (x.4 * x.2^-1)^3, x.4 * x.2^2 * x.3 * x.2^-1 * x.4^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 5) #DARTS : 480 R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240)(241, 301, 361, 421)(242, 302, 362, 422)(243, 303, 363, 423)(244, 304, 364, 424)(245, 305, 365, 425)(246, 306, 366, 426)(247, 307, 367, 427)(248, 308, 368, 428)(249, 309, 369, 429)(250, 310, 370, 430)(251, 311, 371, 431)(252, 312, 372, 432)(253, 313, 373, 433)(254, 314, 374, 434)(255, 315, 375, 435)(256, 316, 376, 436)(257, 317, 377, 437)(258, 318, 378, 438)(259, 319, 379, 439)(260, 320, 380, 440)(261, 321, 381, 441)(262, 322, 382, 442)(263, 323, 383, 443)(264, 324, 384, 444)(265, 325, 385, 445)(266, 326, 386, 446)(267, 327, 387, 447)(268, 328, 388, 448)(269, 329, 389, 449)(270, 330, 390, 450)(271, 331, 391, 451)(272, 332, 392, 452)(273, 333, 393, 453)(274, 334, 394, 454)(275, 335, 395, 455)(276, 336, 396, 456)(277, 337, 397, 457)(278, 338, 398, 458)(279, 339, 399, 459)(280, 340, 400, 460)(281, 341, 401, 461)(282, 342, 402, 462)(283, 343, 403, 463)(284, 344, 404, 464)(285, 345, 405, 465)(286, 346, 406, 466)(287, 347, 407, 467)(288, 348, 408, 468)(289, 349, 409, 469)(290, 350, 410, 470)(291, 351, 411, 471)(292, 352, 412, 472)(293, 353, 413, 473)(294, 354, 414, 474)(295, 355, 415, 475)(296, 356, 416, 476)(297, 357, 417, 477)(298, 358, 418, 478)(299, 359, 419, 479)(300, 360, 420, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)(181, 307)(182, 308)(183, 309)(184, 310)(185, 311)(186, 312)(187, 301)(188, 302)(189, 303)(190, 304)(191, 305)(192, 306)(193, 331)(194, 332)(195, 333)(196, 334)(197, 335)(198, 336)(199, 337)(200, 338)(201, 339)(202, 340)(203, 341)(204, 342)(205, 343)(206, 344)(207, 345)(208, 346)(209, 347)(210, 348)(211, 313)(212, 314)(213, 315)(214, 316)(215, 317)(216, 318)(217, 319)(218, 320)(219, 321)(220, 322)(221, 323)(222, 324)(223, 325)(224, 326)(225, 327)(226, 328)(227, 329)(228, 330)(229, 355)(230, 356)(231, 357)(232, 358)(233, 359)(234, 360)(235, 349)(236, 350)(237, 351)(238, 352)(239, 353)(240, 354)(361, 423)(362, 471)(363, 448)(364, 447)(365, 435)(366, 469)(367, 424)(368, 421)(369, 468)(370, 438)(371, 422)(372, 428)(373, 450)(374, 436)(375, 446)(376, 437)(377, 433)(378, 459)(379, 456)(380, 430)(381, 452)(382, 431)(383, 427)(384, 477)(385, 442)(386, 439)(387, 474)(388, 432)(389, 440)(390, 434)(391, 458)(392, 461)(393, 451)(394, 457)(395, 426)(396, 425)(397, 473)(398, 462)(399, 449)(400, 470)(401, 472)(402, 478)(403, 467)(404, 480)(405, 455)(406, 464)(407, 466)(408, 460)(409, 476)(410, 479)(411, 445)(412, 475)(413, 444)(414, 443)(415, 441)(416, 465)(417, 454)(418, 453)(419, 429)(420, 463) MAP : A4.209 NOTES : type I, reflexible, isomorphic to Med2({4,6}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.2 * x.4 * x.3, (x.2^-1 * x.4)^2, (x.3 * x.1^-1)^2, x.4^6, x.2^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 288 R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 76)(38, 75)(39, 101)(40, 105)(41, 96)(42, 95)(43, 77)(44, 73)(45, 88)(46, 84)(47, 93)(48, 74)(49, 83)(50, 79)(51, 94)(52, 78)(53, 87)(54, 80)(55, 98)(56, 102)(57, 92)(58, 91)(59, 97)(60, 106)(61, 104)(62, 108)(63, 86)(64, 85)(65, 103)(66, 100)(67, 82)(68, 81)(69, 107)(70, 99)(71, 90)(72, 89)(109, 183)(110, 203)(111, 181)(112, 185)(113, 184)(114, 199)(115, 210)(116, 214)(117, 216)(118, 212)(119, 206)(120, 213)(121, 207)(122, 215)(123, 205)(124, 209)(125, 208)(126, 211)(127, 186)(128, 202)(129, 204)(130, 200)(131, 182)(132, 201)(133, 195)(134, 191)(135, 193)(136, 197)(137, 196)(138, 187)(139, 198)(140, 190)(141, 192)(142, 188)(143, 194)(144, 189)(217, 254)(218, 258)(219, 260)(220, 259)(221, 253)(222, 274)(223, 272)(224, 276)(225, 278)(226, 277)(227, 271)(228, 256)(229, 286)(230, 285)(231, 275)(232, 255)(233, 282)(234, 281)(235, 268)(236, 267)(237, 257)(238, 273)(239, 264)(240, 263)(241, 269)(242, 265)(243, 280)(244, 288)(245, 261)(246, 266)(247, 287)(248, 283)(249, 262)(250, 270)(251, 279)(252, 284) MAP : A4.211 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.5 * x.4)^2, (x.3 * x.4)^2, (x.2 * x.1)^2, x.4 * x.1 * x.5^-1 * x.2, (x.5 * x.3^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 288 R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 74)(75, 79)(76, 85)(77, 80)(78, 86)(81, 83)(82, 84)(87, 108)(88, 107)(89, 106)(90, 105)(91, 92)(93, 97)(94, 103)(95, 98)(96, 104)(99, 101)(100, 102)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)(217, 226)(218, 228)(219, 222)(220, 221)(223, 230)(224, 229)(225, 235)(227, 236)(231, 247)(232, 241)(233, 248)(234, 242)(237, 251)(238, 252)(239, 249)(240, 250)(243, 246)(244, 245) MAP : A4.213 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^6, (x.2 * x.3^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 288 R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 207)(110, 209)(111, 197)(112, 198)(113, 195)(114, 196)(115, 214)(116, 216)(117, 192)(118, 191)(119, 190)(120, 189)(121, 213)(122, 215)(123, 185)(124, 186)(125, 183)(126, 184)(127, 208)(128, 210)(129, 204)(130, 203)(131, 202)(132, 201)(133, 212)(134, 211)(135, 181)(136, 199)(137, 182)(138, 200)(139, 206)(140, 205)(141, 193)(142, 187)(143, 194)(144, 188) MAP : A4.247 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^2, x.3^3, (x.1 * x.2)^2, (x.2 * x.4)^2, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, x.2 * x.3 * x.4 * x.3^-1 * x.4 * x.3 * x.4, (x.3 * x.4)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 158)(50, 160)(51, 157)(52, 159)(53, 163)(54, 161)(55, 164)(56, 162)(57, 148)(58, 147)(59, 146)(60, 145)(61, 154)(62, 156)(63, 153)(64, 155)(65, 167)(66, 165)(67, 168)(68, 166)(69, 152)(70, 151)(71, 150)(72, 149)(73, 133)(74, 134)(75, 135)(76, 136)(77, 137)(78, 138)(79, 139)(80, 140)(81, 141)(82, 142)(83, 143)(84, 144)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132) MAP : A4.253 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.4^2, x.1^2, x.2^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.4, x.5^-1 * x.1 * x.5 * x.4, x.4 * x.1 * x.5^-1 * x.2, (x.2 * x.1)^2, (x.2 * x.5)^3, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(73, 123)(74, 121)(75, 124)(76, 122)(77, 126)(78, 128)(79, 125)(80, 127)(81, 138)(82, 140)(83, 137)(84, 139)(85, 132)(86, 131)(87, 130)(88, 129)(89, 144)(90, 143)(91, 142)(92, 141)(93, 135)(94, 133)(95, 136)(96, 134)(145, 155)(146, 153)(147, 156)(148, 154)(149, 166)(150, 168)(151, 165)(152, 167)(157, 164)(158, 163)(159, 162)(160, 161) MAP : A4.254 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.1 * x.4 * x.2, x.5 * x.4^-1 * x.5^-1 * x.4^-1, (x.5 * x.3^-1)^2, x.4 * x.1 * x.5^-1 * x.2, x.5 * x.1 * x.2 * x.5^-1 * x.4^-1 * x.1, (x.2 * x.1)^3, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 172)(27, 169)(28, 171)(29, 175)(30, 173)(31, 176)(32, 174)(33, 184)(34, 183)(35, 182)(36, 181)(37, 190)(38, 192)(39, 189)(40, 191)(41, 179)(42, 177)(43, 180)(44, 178)(45, 188)(46, 187)(47, 186)(48, 185)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(73, 125)(74, 126)(75, 127)(76, 128)(77, 121)(78, 122)(79, 123)(80, 124)(81, 133)(82, 134)(83, 135)(84, 136)(85, 129)(86, 130)(87, 131)(88, 132)(89, 141)(90, 142)(91, 143)(92, 144)(93, 137)(94, 138)(95, 139)(96, 140)(145, 165)(146, 166)(147, 167)(148, 168)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164) MAP : A4.259 NOTES : type I, reflexible, isomorphic to Med2({4,10}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {10, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 10, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^10 > CTG (small) : <40, 8> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^10 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 10) #DARTS : 160 R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160) L = (1, 43)(2, 48)(3, 67)(4, 47)(5, 52)(6, 71)(7, 66)(8, 63)(9, 46)(10, 56)(11, 75)(12, 68)(13, 51)(14, 60)(15, 79)(16, 72)(17, 55)(18, 59)(19, 80)(20, 76)(21, 44)(22, 41)(23, 65)(24, 49)(25, 42)(26, 61)(27, 62)(28, 70)(29, 53)(30, 45)(31, 64)(32, 74)(33, 57)(34, 50)(35, 69)(36, 78)(37, 58)(38, 54)(39, 73)(40, 77)(81, 122)(82, 125)(83, 141)(84, 121)(85, 130)(86, 149)(87, 144)(88, 142)(89, 124)(90, 134)(91, 153)(92, 145)(93, 129)(94, 138)(95, 157)(96, 150)(97, 133)(98, 137)(99, 158)(100, 154)(101, 126)(102, 127)(103, 148)(104, 131)(105, 123)(106, 147)(107, 143)(108, 152)(109, 135)(110, 128)(111, 146)(112, 156)(113, 139)(114, 132)(115, 151)(116, 160)(117, 140)(118, 136)(119, 155)(120, 159) MAP : A4.279 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {5, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^5 > CTG (small) : <20, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2^-1 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^5 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 10) #DARTS : 160 R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117) MAP : A4.286 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {5, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^5 > CTG (small) : <20, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.3 * x.2^-1 * x.3, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.2^4, x.4^4, x.2^-1 * x.4^-1 * x.3^-2, (x.4 * x.2^-1)^2, (x.3 * x.1^-1)^5 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 10) #DARTS : 160 R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 54)(23, 52)(24, 45)(25, 57)(26, 42)(27, 48)(28, 60)(29, 47)(30, 41)(31, 44)(32, 50)(33, 59)(34, 58)(35, 53)(36, 55)(37, 51)(38, 46)(39, 56)(40, 49)(61, 102)(62, 108)(63, 120)(64, 107)(65, 101)(66, 104)(67, 110)(68, 119)(69, 118)(70, 113)(71, 115)(72, 111)(73, 106)(74, 116)(75, 109)(76, 103)(77, 114)(78, 112)(79, 105)(80, 117)(121, 144)(122, 150)(123, 159)(124, 158)(125, 153)(126, 155)(127, 151)(128, 146)(129, 156)(130, 149)(131, 143)(132, 154)(133, 152)(134, 145)(135, 157)(136, 142)(137, 148)(138, 160)(139, 147)(140, 141) MAP : A4.329 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {5, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^5 > CTG (small) : <20, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.5^-1 * x.1, x.5 * x.2 * x.5^-1 * x.2, x.4^-1 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^2, x.4 * x.5^-1 * x.1 * x.2, (x.3 * x.4^-1)^5 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 10) #DARTS : 160 R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55)(46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)(121, 128)(122, 139)(123, 124)(125, 140)(126, 135)(127, 132)(129, 136)(130, 131)(133, 138)(134, 137) MAP : A4.353 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 126)(38, 112)(39, 121)(40, 120)(41, 116)(42, 113)(43, 117)(44, 114)(45, 118)(46, 115)(47, 111)(48, 110)(49, 119)(50, 123)(51, 125)(52, 109)(53, 122)(54, 124)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101) MAP : A4.356 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.3^-1 * x.4 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95) MAP : A4.357 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.4 * x.3^-1)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.4 * x.3^-1 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 125)(38, 120)(39, 110)(40, 121)(41, 124)(42, 123)(43, 113)(44, 126)(45, 116)(46, 109)(47, 112)(48, 111)(49, 119)(50, 114)(51, 122)(52, 115)(53, 118)(54, 117)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95) MAP : A4.419 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.5 * x.2 * x.1, x.4^-1 * x.2 * x.1 * x.5, x.5^-1 * x.1 * x.5 * x.1, x.4^-1 * x.1 * x.4 * x.2, (x.5 * x.3^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 95)(56, 108)(57, 98)(58, 91)(59, 94)(60, 93)(61, 101)(62, 96)(63, 104)(64, 97)(65, 100)(66, 99)(67, 107)(68, 102)(69, 92)(70, 103)(71, 106)(72, 105)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122) MAP : A4.515 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.2 * x.3)^2, x.2 * x.1 * x.2 * x.3 * x.1 * x.3^-1, (x.1 * x.2)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 8, 8) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 64)(3, 61)(4, 63)(5, 67)(6, 65)(7, 68)(8, 66)(9, 52)(10, 51)(11, 50)(12, 49)(13, 58)(14, 60)(15, 57)(16, 59)(17, 71)(18, 69)(19, 72)(20, 70)(21, 56)(22, 55)(23, 54)(24, 53)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93) MAP : A4.517 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3 * x.1)^2, (x.1 * x.2)^2, x.2 * x.3 * x.2 * x.3^-1 * x.1 * x.2 * x.3^-1, (x.3^-1 * x.2)^4 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 8, 8) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 69)(6, 70)(7, 71)(8, 72)(9, 65)(10, 66)(11, 67)(12, 68)(13, 53)(14, 54)(15, 55)(16, 56)(17, 49)(18, 50)(19, 51)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93) MAP : A4.521 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({4,5}), QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {5, 4, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 5, 4 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^4, (u.1 * u.2)^5 > CTG (small) : <120, 34> CTG (fp) : < x.1, x.2 | x.2^2, x.1^4, (x.2 * x.1)^5, (x.2 * x.1^-1 * x.2 * x.1)^3, x.2 * x.1^-2 * x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1 * x.2 * x.1^-1 * x.2 * x.1^-2 * x.2 * x.1^-1 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (4, 5, 4, 5) #DARTS : 240 R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 134, 14, 124)(5, 133, 13, 125)(6, 128, 8, 126)(9, 136, 16, 129)(10, 222, 102, 130)(11, 219, 99, 131)(12, 137, 17, 132)(15, 239, 119, 135)(18, 238, 118, 138)(19, 174, 54, 139)(20, 171, 51, 140)(21, 210, 90, 141)(22, 169, 49, 142)(23, 170, 50, 143)(24, 207, 87, 144)(25, 160, 40, 145)(26, 161, 41, 146)(27, 158, 38, 147)(28, 197, 77, 148)(29, 196, 76, 149)(30, 157, 37, 150)(31, 231, 111, 151)(32, 234, 114, 152)(33, 220, 100, 153)(34, 186, 66, 154)(35, 183, 63, 155)(36, 221, 101, 156)(39, 162, 42, 159)(43, 230, 110, 163)(44, 229, 109, 164)(45, 235, 115, 165)(46, 218, 98, 166)(47, 217, 97, 167)(48, 236, 116, 168)(52, 173, 53, 172)(55, 233, 113, 175)(56, 232, 112, 176)(57, 203, 83, 177)(58, 237, 117, 178)(59, 240, 120, 179)(60, 202, 82, 180)(61, 191, 71, 181)(62, 190, 70, 182)(64, 201, 81, 184)(65, 204, 84, 185)(67, 188, 68, 187)(69, 199, 79, 189)(72, 200, 80, 192)(73, 226, 106, 193)(74, 227, 107, 194)(75, 224, 104, 195)(78, 223, 103, 198)(85, 216, 96, 205)(86, 213, 93, 206)(88, 211, 91, 208)(89, 212, 92, 209)(94, 215, 95, 214)(105, 228, 108, 225) L = (1, 123)(2, 126)(3, 136)(4, 222)(5, 219)(6, 137)(7, 174)(8, 171)(9, 210)(10, 169)(11, 170)(12, 207)(13, 122)(14, 121)(15, 127)(16, 134)(17, 133)(18, 128)(19, 160)(20, 161)(21, 158)(22, 197)(23, 196)(24, 157)(25, 125)(26, 124)(27, 239)(28, 129)(29, 132)(30, 238)(31, 233)(32, 232)(33, 203)(34, 237)(35, 240)(36, 202)(37, 230)(38, 229)(39, 235)(40, 218)(41, 217)(42, 236)(43, 142)(44, 143)(45, 140)(46, 173)(47, 172)(48, 139)(49, 231)(50, 234)(51, 220)(52, 186)(53, 183)(54, 221)(55, 150)(56, 147)(57, 162)(58, 145)(59, 146)(60, 159)(61, 226)(62, 227)(63, 224)(64, 149)(65, 148)(66, 223)(67, 191)(68, 190)(69, 155)(70, 201)(71, 204)(72, 154)(73, 216)(74, 213)(75, 144)(76, 211)(77, 212)(78, 141)(79, 188)(80, 187)(81, 199)(82, 182)(83, 181)(84, 200)(85, 189)(86, 192)(87, 184)(88, 180)(89, 177)(90, 185)(91, 164)(92, 163)(93, 151)(94, 176)(95, 175)(96, 152)(97, 165)(98, 168)(99, 178)(100, 138)(101, 135)(102, 179)(103, 167)(104, 166)(105, 131)(106, 153)(107, 156)(108, 130)(109, 198)(110, 195)(111, 228)(112, 193)(113, 194)(114, 225)(115, 208)(116, 209)(117, 206)(118, 215)(119, 214)(120, 205) MAP : A4.525 NOTES : type I, reflexible, isomorphic to Med2({6,6}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 6, 4, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 130)(20, 141)(21, 132)(22, 131)(23, 127)(24, 134)(25, 136)(26, 129)(27, 138)(28, 137)(29, 133)(30, 140)(31, 142)(32, 135)(33, 144)(34, 143)(35, 139)(36, 128)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95) MAP : A4.526 NOTES : type I, reflexible, isomorphic to Med({4,6}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 6, 4, 6) #DARTS : 144 R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97) MAP : A4.655 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^4, (u.3^-1 * u.1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^-1 * x.2 * x.3 * x.1, x.3^4, (x.2 * x.3)^3, x.3^-2 * x.2 * x.1 * x.3^-1 * x.1, (x.3^-1 * x.1 * x.2)^2, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2) LOCAL TYPE : (4, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(73, 83)(74, 81)(75, 84)(76, 82)(77, 94)(78, 96)(79, 93)(80, 95)(85, 92)(86, 91)(87, 90)(88, 89) MAP : A4.656 NOTES : type I, non-Cayley, reflexible, isomorphic to {4,5}, QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 5, 5 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^5, (u.1 * u.2)^5 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2 | x.2^2, x.1^5, (x.1^2 * x.2)^3, (x.2 * x.1 * x.2 * x.1^-2)^2, (x.1 * x.2)^5 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (5, 5, 5, 5) #DARTS : 120 R = (1, 103, 43, 61)(2, 104, 44, 62)(3, 105, 45, 63)(4, 106, 46, 64)(5, 107, 47, 65)(6, 108, 48, 66)(7, 109, 49, 67)(8, 110, 50, 68)(9, 111, 51, 69)(10, 112, 52, 70)(11, 113, 53, 71)(12, 114, 54, 72)(13, 115, 55, 73)(14, 116, 56, 74)(15, 117, 57, 75)(16, 118, 58, 76)(17, 119, 59, 77)(18, 120, 60, 78)(19, 85, 25, 79)(20, 86, 26, 80)(21, 87, 27, 81)(22, 88, 28, 82)(23, 89, 29, 83)(24, 90, 30, 84)(31, 97, 37, 91)(32, 98, 38, 92)(33, 99, 39, 93)(34, 100, 40, 94)(35, 101, 41, 95)(36, 102, 42, 96) L = (1, 65)(2, 78)(3, 101)(4, 62)(5, 64)(6, 94)(7, 74)(8, 77)(9, 79)(10, 73)(11, 90)(12, 89)(13, 87)(14, 63)(15, 100)(16, 99)(17, 111)(18, 61)(19, 88)(20, 85)(21, 72)(22, 114)(23, 86)(24, 116)(25, 102)(26, 112)(27, 98)(28, 113)(29, 109)(30, 75)(31, 71)(32, 96)(33, 83)(34, 68)(35, 70)(36, 76)(37, 92)(38, 95)(39, 97)(40, 91)(41, 108)(42, 107)(43, 105)(44, 69)(45, 82)(46, 81)(47, 117)(48, 67)(49, 106)(50, 103)(51, 66)(52, 120)(53, 104)(54, 110)(55, 84)(56, 118)(57, 80)(58, 119)(59, 115)(60, 93) MAP : A4.659 NOTES : type I, chiral, isomorphic to Snub({3,12}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^12 > CTG (small) : <72, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^2 * x.1 * x.3^-4 * x.2^-1 * x.3, x.2 * x.3^-1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.1 * x.3^-1, x.3^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 360 R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360) L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 147)(74, 152)(75, 150)(76, 149)(77, 153)(78, 145)(79, 202)(80, 155)(81, 148)(82, 156)(83, 146)(84, 187)(85, 159)(86, 164)(87, 162)(88, 161)(89, 165)(90, 157)(91, 190)(92, 167)(93, 160)(94, 168)(95, 158)(96, 175)(97, 183)(98, 188)(99, 186)(100, 185)(101, 189)(102, 181)(103, 166)(104, 191)(105, 184)(106, 192)(107, 182)(108, 151)(109, 195)(110, 200)(111, 198)(112, 197)(113, 201)(114, 193)(115, 154)(116, 203)(117, 196)(118, 204)(119, 194)(120, 211)(121, 171)(122, 176)(123, 174)(124, 173)(125, 177)(126, 169)(127, 214)(128, 179)(129, 172)(130, 180)(131, 170)(132, 163)(133, 207)(134, 212)(135, 210)(136, 209)(137, 213)(138, 205)(139, 178)(140, 215)(141, 208)(142, 216)(143, 206)(144, 199)(217, 290)(218, 295)(219, 292)(220, 326)(221, 289)(222, 331)(223, 304)(224, 294)(225, 355)(226, 291)(227, 340)(228, 338)(229, 309)(230, 303)(231, 312)(232, 306)(233, 324)(234, 311)(235, 308)(236, 321)(237, 347)(238, 323)(239, 348)(240, 345)(241, 346)(242, 305)(243, 344)(244, 310)(245, 296)(246, 341)(247, 301)(248, 298)(249, 339)(250, 293)(251, 337)(252, 342)(253, 314)(254, 319)(255, 316)(256, 302)(257, 313)(258, 307)(259, 328)(260, 318)(261, 343)(262, 315)(263, 352)(264, 350)(265, 333)(266, 327)(267, 336)(268, 330)(269, 300)(270, 335)(271, 332)(272, 297)(273, 359)(274, 299)(275, 360)(276, 357)(277, 358)(278, 329)(279, 356)(280, 334)(281, 320)(282, 353)(283, 325)(284, 322)(285, 351)(286, 317)(287, 349)(288, 354) MAP : A4.663 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, (x.3 * x.2)^2, (x.4 * x.3)^3, x.4^6, x.3 * x.1 * x.4^-1 * x.3 * x.4 * x.1 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 180 R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180) L = (1, 12)(2, 10)(3, 14)(4, 8)(5, 13)(6, 7)(9, 20)(11, 19)(15, 22)(16, 21)(17, 24)(18, 23)(25, 35)(26, 33)(27, 28)(29, 30)(31, 36)(32, 34)(37, 69)(38, 71)(39, 41)(40, 42)(43, 64)(44, 66)(45, 60)(46, 59)(47, 58)(48, 57)(49, 63)(50, 65)(51, 53)(52, 54)(55, 70)(56, 72)(61, 62)(67, 68)(73, 170)(74, 169)(75, 157)(76, 151)(77, 158)(78, 152)(79, 171)(80, 173)(81, 161)(82, 162)(83, 159)(84, 160)(85, 172)(86, 174)(87, 168)(88, 167)(89, 166)(90, 165)(91, 176)(92, 175)(93, 145)(94, 163)(95, 146)(96, 164)(97, 177)(98, 179)(99, 149)(100, 150)(101, 147)(102, 148)(103, 178)(104, 180)(105, 156)(106, 155)(107, 154)(108, 153)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139) MAP : A4.667 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, x.4 * x.1 * x.4^-1 * x.2, (x.4 * x.3 * x.2)^2, (x.3 * x.2)^3, (x.3 * x.1)^3, (x.2 * x.1 * x.3 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 8, 8) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 9)(6, 10)(7, 11)(8, 12)(13, 17)(14, 18)(15, 19)(16, 20)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 105)(50, 106)(51, 107)(52, 108)(53, 117)(54, 118)(55, 119)(56, 120)(57, 113)(58, 114)(59, 115)(60, 116)(61, 101)(62, 102)(63, 103)(64, 104)(65, 97)(66, 98)(67, 99)(68, 100)(69, 109)(70, 110)(71, 111)(72, 112)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93) MAP : A4.668 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, (x.3 * x.1)^2, (x.3 * x.2)^3, (x.4 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 8, 8) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 45)(26, 46)(27, 47)(28, 48)(29, 33)(30, 34)(31, 35)(32, 36)(37, 41)(38, 42)(39, 43)(40, 44)(49, 105)(50, 106)(51, 107)(52, 108)(53, 117)(54, 118)(55, 119)(56, 120)(57, 113)(58, 114)(59, 115)(60, 116)(61, 101)(62, 102)(63, 103)(64, 104)(65, 97)(66, 98)(67, 99)(68, 100)(69, 109)(70, 110)(71, 111)(72, 112)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93) MAP : A4.670 NOTES : type I, chiral, isomorphic to Snub({4,5}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {5, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 5, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^5 > CTG (small) : <120, 34> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.3 * x.2, x.2^4, x.3^5, x.1 * x.2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1, x.3^2 * x.2^-1 * x.3 * x.1 * x.3^-2 * x.2^-1 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 5) #DARTS : 600 R = (1, 121, 241, 361, 481)(2, 122, 242, 362, 482)(3, 123, 243, 363, 483)(4, 124, 244, 364, 484)(5, 125, 245, 365, 485)(6, 126, 246, 366, 486)(7, 127, 247, 367, 487)(8, 128, 248, 368, 488)(9, 129, 249, 369, 489)(10, 130, 250, 370, 490)(11, 131, 251, 371, 491)(12, 132, 252, 372, 492)(13, 133, 253, 373, 493)(14, 134, 254, 374, 494)(15, 135, 255, 375, 495)(16, 136, 256, 376, 496)(17, 137, 257, 377, 497)(18, 138, 258, 378, 498)(19, 139, 259, 379, 499)(20, 140, 260, 380, 500)(21, 141, 261, 381, 501)(22, 142, 262, 382, 502)(23, 143, 263, 383, 503)(24, 144, 264, 384, 504)(25, 145, 265, 385, 505)(26, 146, 266, 386, 506)(27, 147, 267, 387, 507)(28, 148, 268, 388, 508)(29, 149, 269, 389, 509)(30, 150, 270, 390, 510)(31, 151, 271, 391, 511)(32, 152, 272, 392, 512)(33, 153, 273, 393, 513)(34, 154, 274, 394, 514)(35, 155, 275, 395, 515)(36, 156, 276, 396, 516)(37, 157, 277, 397, 517)(38, 158, 278, 398, 518)(39, 159, 279, 399, 519)(40, 160, 280, 400, 520)(41, 161, 281, 401, 521)(42, 162, 282, 402, 522)(43, 163, 283, 403, 523)(44, 164, 284, 404, 524)(45, 165, 285, 405, 525)(46, 166, 286, 406, 526)(47, 167, 287, 407, 527)(48, 168, 288, 408, 528)(49, 169, 289, 409, 529)(50, 170, 290, 410, 530)(51, 171, 291, 411, 531)(52, 172, 292, 412, 532)(53, 173, 293, 413, 533)(54, 174, 294, 414, 534)(55, 175, 295, 415, 535)(56, 176, 296, 416, 536)(57, 177, 297, 417, 537)(58, 178, 298, 418, 538)(59, 179, 299, 419, 539)(60, 180, 300, 420, 540)(61, 181, 301, 421, 541)(62, 182, 302, 422, 542)(63, 183, 303, 423, 543)(64, 184, 304, 424, 544)(65, 185, 305, 425, 545)(66, 186, 306, 426, 546)(67, 187, 307, 427, 547)(68, 188, 308, 428, 548)(69, 189, 309, 429, 549)(70, 190, 310, 430, 550)(71, 191, 311, 431, 551)(72, 192, 312, 432, 552)(73, 193, 313, 433, 553)(74, 194, 314, 434, 554)(75, 195, 315, 435, 555)(76, 196, 316, 436, 556)(77, 197, 317, 437, 557)(78, 198, 318, 438, 558)(79, 199, 319, 439, 559)(80, 200, 320, 440, 560)(81, 201, 321, 441, 561)(82, 202, 322, 442, 562)(83, 203, 323, 443, 563)(84, 204, 324, 444, 564)(85, 205, 325, 445, 565)(86, 206, 326, 446, 566)(87, 207, 327, 447, 567)(88, 208, 328, 448, 568)(89, 209, 329, 449, 569)(90, 210, 330, 450, 570)(91, 211, 331, 451, 571)(92, 212, 332, 452, 572)(93, 213, 333, 453, 573)(94, 214, 334, 454, 574)(95, 215, 335, 455, 575)(96, 216, 336, 456, 576)(97, 217, 337, 457, 577)(98, 218, 338, 458, 578)(99, 219, 339, 459, 579)(100, 220, 340, 460, 580)(101, 221, 341, 461, 581)(102, 222, 342, 462, 582)(103, 223, 343, 463, 583)(104, 224, 344, 464, 584)(105, 225, 345, 465, 585)(106, 226, 346, 466, 586)(107, 227, 347, 467, 587)(108, 228, 348, 468, 588)(109, 229, 349, 469, 589)(110, 230, 350, 470, 590)(111, 231, 351, 471, 591)(112, 232, 352, 472, 592)(113, 233, 353, 473, 593)(114, 234, 354, 474, 594)(115, 235, 355, 475, 595)(116, 236, 356, 476, 596)(117, 237, 357, 477, 597)(118, 238, 358, 478, 598)(119, 239, 359, 479, 599)(120, 240, 360, 480, 600) L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)(121, 243)(122, 246)(123, 256)(124, 342)(125, 339)(126, 257)(127, 294)(128, 291)(129, 330)(130, 289)(131, 290)(132, 327)(133, 242)(134, 241)(135, 247)(136, 254)(137, 253)(138, 248)(139, 280)(140, 281)(141, 278)(142, 317)(143, 316)(144, 277)(145, 245)(146, 244)(147, 359)(148, 249)(149, 252)(150, 358)(151, 353)(152, 352)(153, 323)(154, 357)(155, 360)(156, 322)(157, 350)(158, 349)(159, 355)(160, 338)(161, 337)(162, 356)(163, 262)(164, 263)(165, 260)(166, 293)(167, 292)(168, 259)(169, 351)(170, 354)(171, 340)(172, 306)(173, 303)(174, 341)(175, 270)(176, 267)(177, 282)(178, 265)(179, 266)(180, 279)(181, 346)(182, 347)(183, 344)(184, 269)(185, 268)(186, 343)(187, 311)(188, 310)(189, 275)(190, 321)(191, 324)(192, 274)(193, 336)(194, 333)(195, 264)(196, 331)(197, 332)(198, 261)(199, 308)(200, 307)(201, 319)(202, 302)(203, 301)(204, 320)(205, 309)(206, 312)(207, 304)(208, 300)(209, 297)(210, 305)(211, 284)(212, 283)(213, 271)(214, 296)(215, 295)(216, 272)(217, 285)(218, 288)(219, 298)(220, 258)(221, 255)(222, 299)(223, 287)(224, 286)(225, 251)(226, 273)(227, 276)(228, 250)(229, 318)(230, 315)(231, 348)(232, 313)(233, 314)(234, 345)(235, 328)(236, 329)(237, 326)(238, 335)(239, 334)(240, 325)(361, 484)(362, 485)(363, 482)(364, 521)(365, 520)(366, 481)(367, 599)(368, 598)(369, 557)(370, 585)(371, 588)(372, 556)(373, 492)(374, 489)(375, 516)(376, 487)(377, 488)(378, 513)(379, 596)(380, 595)(381, 583)(382, 590)(383, 589)(384, 584)(385, 597)(386, 600)(387, 592)(388, 564)(389, 561)(390, 593)(391, 566)(392, 565)(393, 553)(394, 560)(395, 559)(396, 554)(397, 567)(398, 570)(399, 562)(400, 534)(401, 531)(402, 563)(403, 569)(404, 568)(405, 527)(406, 555)(407, 558)(408, 526)(409, 582)(410, 579)(411, 486)(412, 577)(413, 578)(414, 483)(415, 574)(416, 575)(417, 572)(418, 491)(419, 490)(420, 571)(421, 537)(422, 540)(423, 532)(424, 504)(425, 501)(426, 533)(427, 552)(428, 549)(429, 576)(430, 547)(431, 548)(432, 573)(433, 536)(434, 535)(435, 523)(436, 530)(437, 529)(438, 524)(439, 544)(440, 545)(441, 542)(442, 581)(443, 580)(444, 541)(445, 539)(446, 538)(447, 497)(448, 525)(449, 528)(450, 496)(451, 509)(452, 508)(453, 587)(454, 495)(455, 498)(456, 586)(457, 506)(458, 505)(459, 493)(460, 500)(461, 499)(462, 494)(463, 514)(464, 515)(465, 512)(466, 551)(467, 550)(468, 511)(469, 507)(470, 510)(471, 502)(472, 594)(473, 591)(474, 503)(475, 522)(476, 519)(477, 546)(478, 517)(479, 518)(480, 543) MAP : A4.671 NOTES : type I, chiral, isomorphic to Snub({4,6}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^6 > CTG (small) : <72, 40> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^6, x.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 360 R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360) L = (1, 66)(2, 27)(3, 30)(4, 59)(5, 34)(6, 23)(7, 64)(8, 25)(9, 28)(10, 67)(11, 26)(12, 31)(13, 70)(14, 37)(15, 40)(16, 61)(17, 38)(18, 55)(19, 62)(20, 65)(21, 56)(22, 63)(24, 57)(29, 60)(32, 45)(33, 48)(35, 52)(36, 41)(39, 50)(42, 51)(43, 68)(44, 71)(46, 69)(47, 54)(49, 72)(53, 58)(73, 148)(74, 175)(75, 178)(76, 163)(77, 176)(78, 169)(79, 150)(80, 177)(81, 180)(82, 155)(83, 172)(84, 215)(85, 146)(86, 149)(87, 152)(88, 147)(89, 210)(90, 153)(91, 166)(92, 157)(93, 160)(94, 145)(95, 158)(96, 151)(97, 168)(98, 159)(99, 162)(100, 173)(101, 154)(102, 197)(103, 164)(104, 167)(105, 170)(106, 165)(107, 192)(108, 171)(109, 202)(110, 193)(111, 196)(112, 181)(113, 194)(114, 187)(115, 204)(116, 195)(117, 198)(118, 209)(119, 190)(120, 161)(121, 200)(122, 203)(123, 206)(124, 201)(125, 156)(126, 207)(127, 184)(128, 211)(129, 214)(130, 199)(131, 212)(132, 205)(133, 186)(134, 213)(135, 216)(136, 191)(137, 208)(138, 179)(139, 182)(140, 185)(141, 188)(142, 183)(143, 174)(144, 189)(217, 351)(218, 358)(219, 349)(220, 354)(221, 325)(222, 352)(223, 345)(224, 328)(225, 343)(226, 348)(227, 355)(228, 346)(229, 353)(230, 294)(231, 299)(232, 344)(233, 321)(234, 290)(235, 347)(236, 300)(237, 293)(238, 350)(239, 333)(240, 296)(241, 311)(242, 336)(243, 329)(244, 314)(245, 297)(246, 332)(247, 315)(248, 322)(249, 313)(250, 318)(251, 289)(252, 316)(253, 303)(254, 298)(255, 301)(256, 306)(257, 331)(258, 304)(259, 339)(260, 334)(261, 337)(262, 342)(263, 295)(264, 340)(265, 305)(266, 324)(267, 359)(268, 338)(269, 291)(270, 320)(271, 341)(272, 360)(273, 323)(274, 302)(275, 327)(276, 356)(277, 317)(278, 330)(279, 335)(280, 308)(281, 357)(282, 326)(283, 309)(284, 292)(285, 307)(286, 312)(287, 319)(288, 310) MAP : A4.673 NOTES : type I, chiral, isomorphic to Snub({4,10}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {10, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 10, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^10 > CTG (small) : <40, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^10 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 10) #DARTS : 200 R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200) L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 83)(42, 88)(43, 107)(44, 87)(45, 92)(46, 111)(47, 106)(48, 103)(49, 86)(50, 96)(51, 115)(52, 108)(53, 91)(54, 100)(55, 119)(56, 112)(57, 95)(58, 99)(59, 120)(60, 116)(61, 84)(62, 81)(63, 105)(64, 89)(65, 82)(66, 101)(67, 102)(68, 110)(69, 93)(70, 85)(71, 104)(72, 114)(73, 97)(74, 90)(75, 109)(76, 118)(77, 98)(78, 94)(79, 113)(80, 117)(121, 183)(122, 188)(123, 167)(124, 187)(125, 192)(126, 171)(127, 166)(128, 163)(129, 186)(130, 196)(131, 175)(132, 168)(133, 191)(134, 200)(135, 179)(136, 172)(137, 195)(138, 199)(139, 180)(140, 176)(141, 184)(142, 181)(143, 165)(144, 189)(145, 182)(146, 161)(147, 162)(148, 170)(149, 193)(150, 185)(151, 164)(152, 174)(153, 197)(154, 190)(155, 169)(156, 178)(157, 198)(158, 194)(159, 173)(160, 177) MAP : A4.678 NOTES : type I, reflexible, isomorphic to Snub({5,5}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 5, 5, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^5, u.3^5 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^5, x.3^5, (x.3 * x.2^-1)^3, x.2^-1 * x.1 * x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 * x.2^-1, x.2 * x.3^2 * x.1 * x.3^-1 * x.2^-1 * x.3 * x.1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 5, 3, 5) #DARTS : 300 R = (1, 61, 121, 181, 241)(2, 62, 122, 182, 242)(3, 63, 123, 183, 243)(4, 64, 124, 184, 244)(5, 65, 125, 185, 245)(6, 66, 126, 186, 246)(7, 67, 127, 187, 247)(8, 68, 128, 188, 248)(9, 69, 129, 189, 249)(10, 70, 130, 190, 250)(11, 71, 131, 191, 251)(12, 72, 132, 192, 252)(13, 73, 133, 193, 253)(14, 74, 134, 194, 254)(15, 75, 135, 195, 255)(16, 76, 136, 196, 256)(17, 77, 137, 197, 257)(18, 78, 138, 198, 258)(19, 79, 139, 199, 259)(20, 80, 140, 200, 260)(21, 81, 141, 201, 261)(22, 82, 142, 202, 262)(23, 83, 143, 203, 263)(24, 84, 144, 204, 264)(25, 85, 145, 205, 265)(26, 86, 146, 206, 266)(27, 87, 147, 207, 267)(28, 88, 148, 208, 268)(29, 89, 149, 209, 269)(30, 90, 150, 210, 270)(31, 91, 151, 211, 271)(32, 92, 152, 212, 272)(33, 93, 153, 213, 273)(34, 94, 154, 214, 274)(35, 95, 155, 215, 275)(36, 96, 156, 216, 276)(37, 97, 157, 217, 277)(38, 98, 158, 218, 278)(39, 99, 159, 219, 279)(40, 100, 160, 220, 280)(41, 101, 161, 221, 281)(42, 102, 162, 222, 282)(43, 103, 163, 223, 283)(44, 104, 164, 224, 284)(45, 105, 165, 225, 285)(46, 106, 166, 226, 286)(47, 107, 167, 227, 287)(48, 108, 168, 228, 288)(49, 109, 169, 229, 289)(50, 110, 170, 230, 290)(51, 111, 171, 231, 291)(52, 112, 172, 232, 292)(53, 113, 173, 233, 293)(54, 114, 174, 234, 294)(55, 115, 175, 235, 295)(56, 116, 176, 236, 296)(57, 117, 177, 237, 297)(58, 118, 178, 238, 298)(59, 119, 179, 239, 299)(60, 120, 180, 240, 300) L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)(181, 250)(182, 247)(183, 270)(184, 276)(185, 248)(186, 242)(187, 249)(188, 297)(189, 286)(190, 285)(191, 273)(192, 295)(193, 260)(194, 263)(195, 253)(196, 259)(197, 252)(198, 251)(199, 299)(200, 264)(201, 287)(202, 296)(203, 298)(204, 292)(205, 269)(206, 294)(207, 257)(208, 266)(209, 268)(210, 262)(211, 288)(212, 274)(213, 284)(214, 275)(215, 271)(216, 261)(217, 258)(218, 244)(219, 254)(220, 245)(221, 241)(222, 291)(223, 280)(224, 277)(225, 300)(226, 246)(227, 278)(228, 272)(229, 279)(230, 267)(231, 256)(232, 255)(233, 243)(234, 265)(235, 290)(236, 293)(237, 283)(238, 289)(239, 282)(240, 281) MAP : A4.682 NOTES : type I, chiral, isomorphic to Snub({6,6}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 > CTG (small) : <36, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3^2 * x.1, (x.2^-1 * x.3 * x.2^-1)^2, x.2^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 6, 3, 6) #DARTS : 180 R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180) L = (1, 2)(3, 5)(4, 6)(7, 27)(8, 12)(9, 10)(11, 16)(13, 34)(14, 33)(15, 28)(17, 30)(18, 19)(20, 25)(21, 32)(22, 36)(23, 31)(24, 26)(29, 35)(37, 75)(38, 88)(39, 85)(40, 74)(41, 80)(42, 93)(43, 94)(44, 89)(45, 78)(46, 79)(47, 84)(48, 95)(49, 87)(50, 100)(51, 97)(52, 86)(53, 92)(54, 105)(55, 106)(56, 101)(57, 90)(58, 91)(59, 96)(60, 107)(61, 99)(62, 76)(63, 73)(64, 98)(65, 104)(66, 81)(67, 82)(68, 77)(69, 102)(70, 103)(71, 108)(72, 83)(109, 151)(110, 150)(111, 146)(112, 168)(113, 165)(114, 154)(115, 153)(116, 147)(117, 161)(118, 167)(119, 166)(120, 160)(121, 149)(122, 155)(123, 178)(124, 145)(125, 156)(126, 176)(127, 180)(128, 174)(129, 148)(130, 171)(131, 152)(132, 175)(133, 172)(134, 159)(135, 164)(136, 177)(137, 169)(138, 158)(139, 157)(140, 179)(141, 163)(142, 162)(143, 170)(144, 173) MAP : A4.683 NOTES : type I, reflexible, isomorphic to Snub({6,6}), QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6) LOCAL TYPE : (3, 3, 6, 3, 6) #DARTS : 180 R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180) L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 148)(74, 152)(75, 153)(76, 150)(77, 162)(78, 145)(79, 161)(80, 160)(81, 158)(82, 159)(83, 151)(84, 149)(85, 154)(86, 147)(87, 157)(88, 146)(89, 155)(90, 156)(163, 173)(164, 176)(165, 178)(166, 179)(167, 172)(168, 169)(170, 171)(174, 177)(175, 180) MAP : A4.720 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 180 R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174) MAP : A4.721 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4^3, u.6^3, u.1 * u.3^-1 * u.6^-1 * u.5, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 180 R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180) L = (1, 9)(2, 13)(3, 4)(5, 17)(6, 14)(7, 18)(8, 15)(10, 16)(11, 12)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 160)(128, 156)(129, 155)(130, 146)(131, 150)(132, 152)(133, 154)(134, 149)(135, 151)(136, 153)(137, 157)(138, 148)(139, 147)(140, 161)(141, 158)(142, 162)(143, 159)(144, 145) MAP : A4.725 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 180 R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170) MAP : A4.806 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1, (u.4 * u.1^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2 * x.4 * x.5, x.3^3, x.2^3, x.5^3, x.3 * x.5 * x.4, x.2 * x.3 * x.4, x.2 * x.5^-1 * x.4 * x.3^-1, (x.5 * x.2^-1)^2, x.2 * x.5^-1 * x.3 * x.4^-1, x.3 * x.5^-1 * x.4 * x.2^-1, x.1 * x.2^-1 * x.3^-1 * x.5^-1, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 6, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 30)(14, 36)(15, 32)(16, 34)(17, 27)(18, 31)(19, 25)(20, 29)(21, 28)(22, 33)(23, 26)(24, 35)(37, 92)(38, 85)(39, 90)(40, 87)(41, 94)(42, 88)(43, 96)(44, 86)(45, 91)(46, 95)(47, 89)(48, 93)(49, 81)(50, 82)(51, 83)(52, 84)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)(97, 119)(98, 111)(99, 117)(100, 109)(101, 120)(102, 113)(103, 118)(104, 115)(105, 110)(106, 116)(107, 112)(108, 114) MAP : A4.810 NOTES : type I, non-biCayley, reflexible, isomorphic to Dual({4,5}), QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {5, 5, 2}) EMBEDDING : vertices: [ 5, 5 ], faces: [ 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2 * u.1^-1 * u.3)^2 > CTG (small) : <60, 5> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^2, (x.3^2 * x.2^-2)^2 > SCHREIER VEC. : (x.1)^5 LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 18, 2, 4, 5)(3, 14, 7, 48, 41)(6, 51, 17, 8, 34)(9, 44, 53, 28, 19)(10, 35, 38, 27, 13)(11, 31, 40, 15, 30)(12, 21, 46, 49, 29)(16, 36, 32, 37, 39)(20, 57, 47, 42, 25)(22, 45, 43, 50, 54)(23, 33, 60, 52, 26)(24, 55, 59, 58, 56)(61, 83, 92, 90, 69)(62, 72, 95, 76, 117)(63, 119, 97, 86, 106)(64, 80, 91, 77, 105)(65, 82, 108, 73, 93)(66, 88, 107, 99, 115)(67, 68, 71, 96, 70)(74, 81, 78, 79, 94)(75, 118, 101, 114, 104)(84, 98, 89, 103, 111)(85, 120, 87, 116, 100)(102, 113, 110, 109, 112) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) MAP : A4.812 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, (u.2 * u.3^-1)^2, u.3^4, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^3, (x.2^-1 * x.1)^2, (x.2 * x.3^-1)^2, x.3^4, x.1 * x.3 * x.1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3^-1 * x.1 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 58)(26, 60)(27, 57)(28, 59)(29, 71)(30, 69)(31, 72)(32, 70)(33, 56)(34, 55)(35, 54)(36, 53)(37, 62)(38, 64)(39, 61)(40, 63)(41, 67)(42, 65)(43, 68)(44, 66)(45, 52)(46, 51)(47, 50)(48, 49)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117) MAP : A4.813 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.1 * x.4 * x.5^-1, x.4 * x.2 * x.5^-1, x.5^2 * x.6, x.2 * x.4 * x.5, x.4 * x.1 * x.5, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, x.2 * x.6^-2 * x.1, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 12)(2, 6)(3, 11)(4, 5)(7, 10)(8, 9)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 98)(26, 97)(27, 100)(28, 99)(29, 103)(30, 105)(31, 101)(32, 107)(33, 102)(34, 108)(35, 104)(36, 106)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71) MAP : A4.814 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.6 * x.4^-1, x.2 * x.4 * x.6, x.5 * x.1 * x.5 * x.2, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 12)(2, 6)(3, 11)(4, 5)(7, 10)(8, 9)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 86)(38, 85)(39, 88)(40, 87)(41, 91)(42, 93)(43, 89)(44, 95)(45, 90)(46, 96)(47, 92)(48, 94)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71) MAP : A4.816 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.2 * x.6 * x.1, x.5^-2 * x.6^-1, x.2 * x.4 * x.6, x.1 * x.6 * x.4^-1, (x.3 * x.4^-1)^2, (x.4 * x.5^-1)^2, (x.5 * x.6^-1)^2, (x.5 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 12)(2, 6)(3, 11)(4, 5)(7, 10)(8, 9)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71) MAP : A4.820 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, (u.2 * u.3^-1)^2, u.3^4, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^3, (x.2 * x.3^-1)^2, x.3^4, (x.2^-1 * x.1)^2, (x.3^-1 * x.1)^2, x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.1 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 67)(26, 65)(27, 68)(28, 66)(29, 62)(30, 64)(31, 61)(32, 63)(33, 58)(34, 60)(35, 57)(36, 59)(37, 52)(38, 51)(39, 50)(40, 49)(41, 56)(42, 55)(43, 54)(44, 53)(45, 71)(46, 69)(47, 72)(48, 70)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117) MAP : A4.828 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.4 * x.3, x.4 * x.1 * x.2 * x.3, (x.4 * x.2)^2, x.4^4, (x.2 * x.1)^3, (x.4^-1 * x.1)^3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 106)(2, 108)(3, 105)(4, 107)(5, 119)(6, 117)(7, 120)(8, 118)(9, 104)(10, 103)(11, 102)(12, 101)(13, 110)(14, 112)(15, 109)(16, 111)(17, 115)(18, 113)(19, 116)(20, 114)(21, 100)(22, 99)(23, 98)(24, 97)(25, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96) MAP : A4.830 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.3 * u.4^-1 * u.5^-1 * u.2, u.4^5, u.6^5 > CTG (small) : <10, 1> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.5^2, x.2^2, x.1^2, x.6 * x.4^-2, x.6^-2 * x.4^-1, x.1 * x.5 * x.6, x.2 * x.1 * x.4^-1, x.1 * x.2 * x.4, x.3 * x.4^-1 * x.5 * x.2, x.4 * x.5 * x.6^-1 * x.1 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 5) #DARTS : 100 R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100) L = (1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 35)(22, 38)(23, 37)(24, 32)(25, 34)(26, 33)(27, 39)(28, 31)(29, 40)(30, 36)(41, 97)(42, 100)(43, 95)(44, 96)(45, 93)(46, 94)(47, 91)(48, 99)(49, 98)(50, 92)(51, 53)(52, 59)(54, 60)(55, 56)(57, 58)(71, 84)(72, 81)(73, 89)(74, 88)(75, 82)(76, 87)(77, 90)(78, 85)(79, 86)(80, 83) MAP : A4.831 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1, u.5^5, u.6^5 > CTG (small) : <10, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^-1 * x.6^-1, x.2 * x.1, x.4^-1 * x.1 * x.6^-1, x.4 * x.2 * x.5^-1, x.1 * x.6 * x.4, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1, x.6^5, x.5^5 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 5) #DARTS : 100 R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 60)(12, 58)(13, 59)(14, 57)(15, 54)(16, 53)(17, 56)(18, 55)(19, 51)(20, 52)(21, 37)(22, 33)(23, 35)(24, 40)(25, 31)(26, 38)(27, 32)(28, 39)(29, 34)(30, 36)(41, 44)(42, 46)(43, 48)(45, 49)(47, 50)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 85)(72, 87)(73, 82)(74, 89)(75, 83)(76, 90)(77, 81)(78, 86)(79, 88)(80, 84) MAP : A4.838 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^6 > CTG (small) : <36, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 216 R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216) L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)(145, 183)(146, 188)(147, 189)(148, 201)(149, 215)(150, 192)(151, 198)(152, 207)(153, 216)(154, 213)(155, 195)(156, 214)(157, 184)(158, 181)(159, 186)(160, 182)(161, 193)(162, 205)(163, 194)(164, 202)(165, 212)(166, 185)(167, 187)(168, 196)(169, 190)(170, 191)(171, 209)(172, 210)(173, 204)(174, 200)(175, 197)(176, 211)(177, 203)(178, 206)(179, 208)(180, 199) MAP : A4.874 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, (x.2 * x.3^-1)^2, (x.4 * x.2)^2, x.1 * x.4^-1 * x.3 * x.4^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 216 R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216) L = (1, 2)(3, 7)(4, 13)(5, 8)(6, 14)(9, 11)(10, 12)(15, 36)(16, 35)(17, 34)(18, 33)(19, 20)(21, 25)(22, 31)(23, 26)(24, 32)(27, 29)(28, 30)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 73)(44, 74)(45, 75)(46, 76)(47, 77)(48, 78)(49, 91)(50, 92)(51, 93)(52, 94)(53, 95)(54, 96)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(109, 183)(110, 185)(111, 191)(112, 192)(113, 189)(114, 190)(115, 202)(116, 204)(117, 198)(118, 197)(119, 196)(120, 195)(121, 201)(122, 203)(123, 209)(124, 210)(125, 207)(126, 208)(127, 184)(128, 186)(129, 216)(130, 215)(131, 214)(132, 213)(133, 200)(134, 199)(135, 205)(136, 211)(137, 206)(138, 212)(139, 182)(140, 181)(141, 187)(142, 193)(143, 188)(144, 194)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168) MAP : A4.875 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, (x.2 * x.1)^2, (x.2 * x.4^-1)^2, x.1 * x.4^-1 * x.3 * x.4^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 216 R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216) L = (1, 10)(2, 12)(3, 6)(4, 5)(7, 14)(8, 13)(9, 19)(11, 20)(15, 31)(16, 25)(17, 32)(18, 26)(21, 35)(22, 36)(23, 33)(24, 34)(27, 30)(28, 29)(37, 96)(38, 94)(39, 74)(40, 92)(41, 73)(42, 91)(43, 90)(44, 88)(45, 80)(46, 86)(47, 79)(48, 85)(49, 89)(50, 87)(51, 82)(52, 81)(53, 84)(54, 83)(55, 95)(56, 93)(57, 76)(58, 75)(59, 78)(60, 77)(61, 101)(62, 99)(63, 106)(64, 105)(65, 108)(66, 107)(67, 102)(68, 100)(69, 104)(70, 98)(71, 103)(72, 97)(109, 184)(110, 186)(111, 216)(112, 215)(113, 214)(114, 213)(115, 200)(116, 199)(117, 205)(118, 211)(119, 206)(120, 212)(121, 182)(122, 181)(123, 187)(124, 193)(125, 188)(126, 194)(127, 183)(128, 185)(129, 191)(130, 192)(131, 189)(132, 190)(133, 202)(134, 204)(135, 198)(136, 197)(137, 196)(138, 195)(139, 201)(140, 203)(141, 209)(142, 210)(143, 207)(144, 208)(145, 146)(147, 151)(148, 157)(149, 152)(150, 158)(153, 155)(154, 156)(159, 180)(160, 179)(161, 178)(162, 177)(163, 164)(165, 169)(166, 175)(167, 170)(168, 176)(171, 173)(172, 174) MAP : A4.879 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.3^-1 * x.4^-1 * x.1, x.3^3, x.2 * x.3 * x.7^-1, x.6^3, x.1 * x.6 * x.7^-1, x.6 * x.2 * x.7^-1, (x.6^-1, x.3^-1), x.4 * x.5^-1 * x.7 * x.5, x.3 * x.7 * x.6 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 216 R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(37, 78)(38, 83)(39, 76)(40, 80)(41, 75)(42, 77)(43, 74)(44, 73)(45, 89)(46, 87)(47, 90)(48, 85)(49, 81)(50, 88)(51, 79)(52, 84)(53, 86)(54, 82)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 214)(110, 207)(111, 216)(112, 215)(113, 211)(114, 200)(115, 202)(116, 213)(117, 204)(118, 203)(119, 199)(120, 206)(121, 208)(122, 201)(123, 210)(124, 209)(125, 205)(126, 212)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)(145, 188)(146, 187)(147, 185)(148, 183)(149, 186)(150, 181)(151, 195)(152, 184)(153, 193)(154, 198)(155, 182)(156, 196)(157, 192)(158, 197)(159, 190)(160, 194)(161, 189)(162, 191) MAP : A4.880 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6 * x.3^-1, x.2 * x.1, x.6^3, x.3^3, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.4 * x.5^-1 * x.7 * x.5, x.4^2 * x.1 * x.4^-1 * x.3, x.1 * x.7 * x.3 * x.7^-2, x.3 * x.7^2 * x.4^-1 * x.3^-1 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 216 R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(13, 25)(14, 26)(15, 27)(16, 28)(17, 29)(18, 30)(37, 81)(38, 88)(39, 79)(40, 84)(41, 86)(42, 82)(43, 78)(44, 83)(45, 76)(46, 80)(47, 75)(48, 77)(49, 74)(50, 73)(51, 89)(52, 87)(53, 90)(54, 85)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 211)(110, 212)(111, 213)(112, 214)(113, 215)(114, 216)(115, 199)(116, 200)(117, 201)(118, 202)(119, 203)(120, 204)(121, 205)(122, 206)(123, 207)(124, 208)(125, 209)(126, 210)(127, 128)(129, 143)(130, 141)(131, 144)(132, 139)(133, 135)(134, 142)(136, 138)(137, 140)(145, 194)(146, 193)(147, 191)(148, 189)(149, 192)(150, 187)(151, 183)(152, 190)(153, 181)(154, 186)(155, 188)(156, 184)(157, 198)(158, 185)(159, 196)(160, 182)(161, 195)(162, 197) MAP : A4.886 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^3 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.1 * x.4^-1 * x.3, x.4^3, x.4 * x.2 * x.4^-1 * x.2, (x.3^-1 * x.2)^3, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 6, 6) #DARTS : 108 R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108) L = (1, 80)(2, 79)(3, 77)(4, 75)(5, 78)(6, 73)(7, 87)(8, 76)(9, 85)(10, 90)(11, 74)(12, 88)(13, 84)(14, 89)(15, 82)(16, 86)(17, 81)(18, 83)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104) MAP : A4.890 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4, u.3^4 > CTG (small) : <36, 9> CTG (fp) : < x.1, x.2, x.3 | x.1 * x.3 * x.2, x.1^3, x.3^4, x.2^4, (x.3^-1 * x.2)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 216 R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 55)(32, 56)(33, 57)(34, 58)(35, 59)(36, 60)(73, 117)(74, 124)(75, 109)(76, 131)(77, 138)(78, 140)(79, 111)(80, 130)(81, 115)(82, 125)(83, 144)(84, 134)(85, 126)(86, 129)(87, 122)(88, 116)(89, 112)(90, 127)(91, 132)(92, 123)(93, 128)(94, 110)(95, 118)(96, 121)(97, 136)(98, 114)(99, 137)(100, 139)(101, 141)(102, 119)(103, 142)(104, 120)(105, 143)(106, 133)(107, 135)(108, 113)(145, 207)(146, 214)(147, 199)(148, 185)(149, 192)(150, 194)(151, 201)(152, 184)(153, 205)(154, 215)(155, 198)(156, 188)(157, 216)(158, 183)(159, 212)(160, 206)(161, 202)(162, 181)(163, 186)(164, 213)(165, 182)(166, 200)(167, 208)(168, 211)(169, 190)(170, 204)(171, 191)(172, 193)(173, 195)(174, 209)(175, 196)(176, 210)(177, 197)(178, 187)(179, 189)(180, 203) MAP : A4.918 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.2 * x.1 * x.3, x.4^3, (x.3^-1 * x.4)^2, (x.4^-1 * x.1)^2, x.4 * x.3^-1 * x.2 * x.3 * x.4^-1 * x.2, x.4 * x.3 * x.4 * x.3^-3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 216 R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216) L = (1, 112)(2, 114)(3, 144)(4, 143)(5, 142)(6, 141)(7, 128)(8, 127)(9, 133)(10, 139)(11, 134)(12, 140)(13, 110)(14, 109)(15, 115)(16, 121)(17, 116)(18, 122)(19, 111)(20, 113)(21, 119)(22, 120)(23, 117)(24, 118)(25, 130)(26, 132)(27, 126)(28, 125)(29, 124)(30, 123)(31, 129)(32, 131)(33, 137)(34, 138)(35, 135)(36, 136)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210) MAP : A4.930 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.2 * x.1, x.3^3, (x.3 * x.4^-1)^2, x.4^4, (x.4^-1 * x.1)^2, x.2 * x.4^-2 * x.3^-1 * x.4^-1, x.2 * x.4^-1 * x.2 * x.3 * x.4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(97, 104)(98, 103)(99, 102)(100, 101)(105, 115)(106, 113)(107, 116)(108, 114)(109, 119)(110, 117)(111, 120)(112, 118)(121, 141)(122, 142)(123, 143)(124, 144)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140) MAP : A4.931 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.3^-1 * x.1 * x.2, (x.3 * x.4^-1)^2, x.4 * x.1 * x.4^-1 * x.2, x.4^4, x.4^-2 * x.1 * x.4 * x.3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(97, 117)(98, 118)(99, 119)(100, 120)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141) MAP : A4.933 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^-1 * x.4^-1 * x.1, x.4^3, (x.2 * x.4^-1)^2, x.3^4, (x.2 * x.1)^2, x.2 * x.4 * x.3 * x.2 * x.1, x.2 * x.3^2 * x.4 * x.3^-1, x.4 * x.2 * x.3^-1 * x.1 * x.3 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 51)(26, 49)(27, 52)(28, 50)(29, 54)(30, 56)(31, 53)(32, 55)(33, 66)(34, 68)(35, 65)(36, 67)(37, 60)(38, 59)(39, 58)(40, 57)(41, 72)(42, 71)(43, 70)(44, 69)(45, 63)(46, 61)(47, 64)(48, 62)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117) MAP : A4.934 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.4^3, (x.4 * x.2)^2, (x.3 * x.2)^2, x.3^4, x.1 * x.2 * x.3^-1 * x.4 * x.3^-1 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 11)(2, 9)(3, 12)(4, 10)(5, 22)(6, 24)(7, 21)(8, 23)(13, 20)(14, 19)(15, 18)(16, 17)(25, 64)(26, 63)(27, 62)(28, 61)(29, 68)(30, 67)(31, 66)(32, 65)(33, 59)(34, 57)(35, 60)(36, 58)(37, 55)(38, 53)(39, 56)(40, 54)(41, 50)(42, 52)(43, 49)(44, 51)(45, 70)(46, 72)(47, 69)(48, 71)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117) MAP : A4.935 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.4^3, x.3^4, x.3^-1 * x.1 * x.3 * x.2, (x.4 * x.2)^2, x.2 * x.3 * x.2 * x.4 * x.3^-1, (x.2 * x.1)^3 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 72)(26, 71)(27, 70)(28, 69)(29, 60)(30, 59)(31, 58)(32, 57)(33, 51)(34, 49)(35, 52)(36, 50)(37, 63)(38, 61)(39, 64)(40, 62)(41, 66)(42, 68)(43, 65)(44, 67)(45, 54)(46, 56)(47, 53)(48, 55)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117) MAP : A4.939 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {5, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 5, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, (u.3^-1 * u.2)^2, u.4^5 > CTG (small) : <20, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.3^-1 * x.2)^2, (x.4 * x.2)^2, (x.2 * x.1)^2, x.4^5 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 5) #DARTS : 120 R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120) L = (1, 86)(2, 83)(3, 90)(4, 99)(5, 82)(6, 87)(7, 98)(8, 97)(9, 94)(10, 89)(11, 84)(12, 95)(13, 92)(14, 81)(15, 88)(16, 91)(17, 96)(18, 85)(19, 100)(20, 93)(21, 43)(22, 46)(23, 47)(24, 48)(25, 41)(26, 50)(27, 49)(28, 60)(29, 45)(30, 58)(31, 55)(32, 44)(33, 51)(34, 42)(35, 59)(36, 52)(37, 53)(38, 54)(39, 57)(40, 56)(61, 62)(63, 66)(64, 75)(65, 74)(67, 70)(68, 79)(69, 78)(71, 72)(73, 76)(77, 80)(101, 111)(102, 112)(103, 113)(104, 114)(105, 115)(106, 116)(107, 117)(108, 118)(109, 119)(110, 120) MAP : A4.947 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^5, u.6^5 > CTG (small) : <10, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.7 * x.1 * x.3^-1, x.6 * x.2 * x.7^-1, x.1 * x.3 * x.7^-1, x.4 * x.2 * x.3, x.4 * x.5^-1 * x.7 * x.5, x.3^5, x.3^2 * x.7 * x.3 * x.4^-1, x.6^5 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 5, 3, 4, 4) #DARTS : 120 R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120) L = (1, 12)(2, 15)(3, 11)(4, 16)(5, 17)(6, 19)(7, 13)(8, 14)(9, 20)(10, 18)(21, 48)(22, 44)(23, 50)(24, 43)(25, 46)(26, 41)(27, 49)(28, 47)(29, 42)(30, 45)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(51, 54)(52, 56)(53, 58)(55, 59)(57, 60)(61, 112)(62, 115)(63, 111)(64, 116)(65, 117)(66, 119)(67, 113)(68, 114)(69, 120)(70, 118)(71, 74)(72, 76)(73, 78)(75, 79)(77, 80)(81, 106)(82, 109)(83, 104)(84, 102)(85, 110)(86, 105)(87, 108)(88, 101)(89, 107)(90, 103) MAP : A4.951 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {5, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 5, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.3^4, u.2^5 > CTG (small) : <20, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.3^4, x.1^-1 * x.3^-1 * x.2^-2, (x.3^-1 * x.1)^2, x.3 * x.2^-1 * x.1 * x.2^-1, x.2^5 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 5) #DARTS : 120 R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120) L = (1, 23)(2, 34)(3, 32)(4, 25)(5, 37)(6, 22)(7, 28)(8, 40)(9, 27)(10, 21)(11, 24)(12, 30)(13, 39)(14, 38)(15, 33)(16, 35)(17, 31)(18, 26)(19, 36)(20, 29)(41, 62)(42, 68)(43, 80)(44, 67)(45, 61)(46, 64)(47, 70)(48, 79)(49, 78)(50, 73)(51, 75)(52, 71)(53, 66)(54, 76)(55, 69)(56, 63)(57, 74)(58, 72)(59, 65)(60, 77)(81, 104)(82, 110)(83, 119)(84, 118)(85, 113)(86, 115)(87, 111)(88, 106)(89, 116)(90, 109)(91, 103)(92, 114)(93, 112)(94, 105)(95, 117)(96, 102)(97, 108)(98, 120)(99, 107)(100, 101) MAP : A4.953 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.2^5, u.6^5 > CTG (small) : <10, 1> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.4^2, x.2 * x.3, x.3^2 * x.6, x.2 * x.6^2, x.2^2 * x.6^-1, x.4 * x.5^-1 * x.6^-1, x.3 * x.6^-1 * x.5^-1 * x.4, x.3 * x.5 * x.6 * x.4, (x.5 * x.1^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 5) #DARTS : 120 R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 24)(12, 21)(13, 29)(14, 28)(15, 22)(16, 27)(17, 30)(18, 25)(19, 26)(20, 23)(31, 72)(32, 75)(33, 80)(34, 71)(35, 78)(36, 79)(37, 76)(38, 74)(39, 73)(40, 77)(41, 63)(42, 69)(43, 61)(44, 70)(45, 66)(46, 65)(47, 68)(48, 67)(49, 62)(50, 64)(51, 97)(52, 100)(53, 95)(54, 96)(55, 93)(56, 94)(57, 91)(58, 99)(59, 98)(60, 92)(101, 118)(102, 114)(103, 116)(104, 115)(105, 111)(106, 120)(107, 113)(108, 112)(109, 117)(110, 119) MAP : A4.961 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.1 * x.4^-1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4^-1, x.4^-1 * x.1 * x.2 * x.3, x.3^-1 * x.1 * x.3 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 4, 4) #DARTS : 108 R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108) L = (1, 106)(2, 99)(3, 108)(4, 107)(5, 103)(6, 92)(7, 94)(8, 105)(9, 96)(10, 95)(11, 91)(12, 98)(13, 100)(14, 93)(15, 102)(16, 101)(17, 97)(18, 104)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90) MAP : A4.964 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.4 * x.1 * x.3^-1 * x.1, x.4 * x.2 * x.4^-1 * x.1, x.1 * x.4 * x.3^-1 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 4, 4) #DARTS : 108 R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90) MAP : A4.965 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1) LOCAL TYPE : (3, 4, 3, 4, 4, 4) #DARTS : 108 R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108) L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73) MAP : A4.1111 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4) LOCAL TYPE : (3, 4, 4, 3, 4, 4) #DARTS : 108 R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108) L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86) MAP : A4.1211 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.6^3, u.8^3, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 252 R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252) L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 92)(74, 95)(75, 97)(76, 98)(77, 91)(78, 106)(79, 105)(80, 108)(81, 107)(82, 104)(83, 100)(84, 96)(85, 99)(86, 101)(87, 93)(88, 102)(89, 103)(90, 94)(109, 244)(110, 245)(111, 246)(112, 247)(113, 248)(114, 249)(115, 250)(116, 251)(117, 252)(118, 235)(119, 236)(120, 237)(121, 238)(122, 239)(123, 240)(124, 241)(125, 242)(126, 243)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 226)(218, 227)(219, 228)(220, 229)(221, 230)(222, 231)(223, 232)(224, 233)(225, 234) MAP : A4.1212 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, (x.4 * x.1)^2, x.4^-1 * x.5 * x.3 * x.5^-2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 252 R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252) L = (1, 41)(2, 39)(3, 58)(4, 57)(5, 60)(6, 59)(7, 47)(8, 45)(9, 52)(10, 51)(11, 54)(12, 53)(13, 48)(14, 46)(15, 50)(16, 44)(17, 49)(18, 43)(19, 42)(20, 40)(21, 56)(22, 38)(23, 55)(24, 37)(25, 72)(26, 70)(27, 62)(28, 68)(29, 61)(30, 67)(31, 71)(32, 69)(33, 64)(34, 63)(35, 66)(36, 65)(73, 201)(74, 203)(75, 209)(76, 210)(77, 207)(78, 208)(79, 184)(80, 186)(81, 216)(82, 215)(83, 214)(84, 213)(85, 183)(86, 185)(87, 191)(88, 192)(89, 189)(90, 190)(91, 202)(92, 204)(93, 198)(94, 197)(95, 196)(96, 195)(97, 182)(98, 181)(99, 187)(100, 193)(101, 188)(102, 194)(103, 200)(104, 199)(105, 205)(106, 211)(107, 206)(108, 212)(109, 120)(110, 118)(111, 122)(112, 116)(113, 121)(114, 115)(117, 128)(119, 127)(123, 130)(124, 129)(125, 132)(126, 131)(133, 143)(134, 141)(135, 136)(137, 138)(139, 144)(140, 142)(145, 177)(146, 179)(147, 149)(148, 150)(151, 172)(152, 174)(153, 168)(154, 167)(155, 166)(156, 165)(157, 171)(158, 173)(159, 161)(160, 162)(163, 178)(164, 180)(169, 170)(175, 176)(217, 243)(218, 245)(219, 233)(220, 234)(221, 231)(222, 232)(223, 250)(224, 252)(225, 228)(226, 227)(229, 249)(230, 251)(235, 244)(236, 246)(237, 240)(238, 239)(241, 248)(242, 247) MAP : A4.1221 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <36, 10> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.2 * x.1 * x.4, x.5^3, x.4 * x.5^-1 * x.3, (x.5 * x.1)^2, (x.3 * x.2)^2, x.3 * x.5 * x.1 * x.4 * x.1, x.4^2 * x.3 * x.4^-1 * x.5^-1 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 252 R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252) L = (1, 6)(2, 4)(3, 20)(5, 19)(7, 36)(8, 34)(9, 26)(10, 32)(11, 25)(12, 31)(13, 35)(14, 33)(15, 28)(16, 27)(17, 30)(18, 29)(21, 22)(23, 24)(37, 56)(38, 55)(39, 61)(40, 67)(41, 62)(42, 68)(43, 57)(44, 59)(45, 65)(46, 66)(47, 63)(48, 64)(49, 58)(50, 60)(51, 54)(52, 53)(69, 72)(70, 71)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 175)(116, 176)(117, 177)(118, 178)(119, 179)(120, 180)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 157)(128, 158)(129, 159)(130, 160)(131, 161)(132, 162)(133, 163)(134, 164)(135, 165)(136, 166)(137, 167)(138, 168)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210) MAP : A4.1242 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.2 * x.1 * x.5^-1, x.4^-1 * x.5^-1 * x.3, x.1 * x.3 * x.2 * x.4^-1, x.4^4, x.4 * x.3 * x.2 * x.1, x.3 * x.1 * x.4^-1 * x.5 * x.4^-1, x.4 * x.2 * x.4 * x.5 * x.3 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 109)(98, 110)(99, 111)(100, 112)(101, 113)(102, 114)(103, 115)(104, 116)(105, 117)(106, 118)(107, 119)(108, 120)(145, 162)(146, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165) MAP : A4.1244 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.4^4, x.4 * x.2 * x.4^-1 * x.3, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.1)^2, x.4^-1 * x.2 * x.4^-1 * x.5 * x.4^-1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96)(97, 117)(98, 118)(99, 119)(100, 120)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(145, 162)(146, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165) MAP : A4.1246 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.1 * x.5 * x.2 * x.5^-1, x.4^4, x.4 * x.1 * x.4^-1 * x.3, (x.4^-1 * x.2)^2, x.1 * x.3 * x.4 * x.5 * x.4^-1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 93)(74, 94)(75, 95)(76, 96)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)(145, 162)(146, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165) MAP : A4.1248 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^5, u.7^5 > CTG (small) : <10, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.2 * x.1, x.7 * x.3^-1, x.4 * x.6, x.6 * x.1 * x.3^-1, x.4 * x.2 * x.3, x.7 * x.2 * x.8^-1, x.1 * x.3 * x.6^-1, x.5 * x.6^-1 * x.8, x.3^2 * x.6 * x.3 * x.4^-1, x.3^5, x.7^5 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 5) #DARTS : 140 R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140) L = (1, 13)(2, 11)(3, 17)(4, 18)(5, 12)(6, 14)(7, 15)(8, 20)(9, 16)(10, 19)(21, 56)(22, 59)(23, 54)(24, 52)(25, 60)(26, 55)(27, 58)(28, 51)(29, 57)(30, 53)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 118)(42, 114)(43, 120)(44, 113)(45, 116)(46, 111)(47, 119)(48, 117)(49, 112)(50, 115)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 133)(72, 131)(73, 137)(74, 138)(75, 132)(76, 134)(77, 135)(78, 140)(79, 136)(80, 139)(81, 84)(82, 86)(83, 88)(85, 89)(87, 90)(91, 128)(92, 124)(93, 130)(94, 123)(95, 126)(96, 121)(97, 129)(98, 127)(99, 122)(100, 125) MAP : A4.1249 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^5, u.8^5 > CTG (small) : <10, 1> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.7^-1 * x.2, x.8^-1 * x.4^-1, x.2 * x.5 * x.6^-1, x.4 * x.1 * x.5, x.6^-2 * x.4, x.1 * x.2 * x.4^-1, x.1 * x.4 * x.2, x.4 * x.6 * x.4, x.8^5 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 5) #DARTS : 140 R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 85)(12, 88)(13, 87)(14, 82)(15, 84)(16, 83)(17, 89)(18, 81)(19, 90)(20, 86)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 77)(32, 80)(33, 75)(34, 76)(35, 73)(36, 74)(37, 71)(38, 79)(39, 78)(40, 72)(41, 52)(42, 55)(43, 60)(44, 51)(45, 58)(46, 59)(47, 56)(48, 54)(49, 53)(50, 57)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 131)(67, 132)(68, 133)(69, 134)(70, 135)(91, 108)(92, 104)(93, 106)(94, 105)(95, 101)(96, 110)(97, 103)(98, 102)(99, 107)(100, 109)(121, 126)(122, 127)(123, 128)(124, 129)(125, 130) MAP : A4.1250 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^5, u.8^5 > CTG (small) : <10, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6 * x.4^-1, x.6^-1 * x.8^-1, x.5 * x.6^-1 * x.7^-1, x.7 * x.3^-1 * x.2, x.3 * x.4^-1 * x.8^-1, x.8 * x.1 * x.5, x.4 * x.2 * x.5^-1, x.8^5, x.6^5 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 5) #DARTS : 140 R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 83)(12, 81)(13, 87)(14, 88)(15, 82)(16, 84)(17, 85)(18, 90)(19, 86)(20, 89)(21, 24)(22, 26)(23, 28)(25, 29)(27, 30)(31, 78)(32, 74)(33, 80)(34, 73)(35, 76)(36, 71)(37, 79)(38, 77)(39, 72)(40, 75)(41, 53)(42, 51)(43, 57)(44, 58)(45, 52)(46, 54)(47, 55)(48, 60)(49, 56)(50, 59)(61, 134)(62, 136)(63, 138)(64, 131)(65, 139)(66, 132)(67, 140)(68, 133)(69, 135)(70, 137)(91, 102)(92, 105)(93, 101)(94, 106)(95, 107)(96, 109)(97, 103)(98, 104)(99, 110)(100, 108)(121, 124)(122, 126)(123, 128)(125, 129)(127, 130) MAP : A4.1251 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {5, 5, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 5, 5, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^5, u.8^5 > CTG (small) : <10, 1> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.5^2, x.1^2, x.2^2, x.8 * x.4, x.4 * x.6^2, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.2 * x.1 * x.6, x.1 * x.2 * x.6^-1, x.4 * x.1 * x.5, x.4^2 * x.6^-1, x.8^5 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 5) #DARTS : 140 R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 82)(12, 85)(13, 90)(14, 81)(15, 88)(16, 89)(17, 86)(18, 84)(19, 83)(20, 87)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 80)(32, 73)(33, 72)(34, 77)(35, 79)(36, 78)(37, 74)(38, 76)(39, 75)(40, 71)(41, 55)(42, 58)(43, 57)(44, 52)(45, 54)(46, 53)(47, 59)(48, 51)(49, 60)(50, 56)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 131)(67, 132)(68, 133)(69, 134)(70, 135)(91, 104)(92, 101)(93, 109)(94, 108)(95, 102)(96, 107)(97, 110)(98, 105)(99, 106)(100, 103)(121, 126)(122, 127)(123, 128)(124, 129)(125, 130) MAP : A4.1254 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {5, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 5, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^5 > CTG (small) : <20, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, (x.5 * x.1)^2, (x.3 * x.1)^2, x.5^5 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 5) #DARTS : 140 R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140) L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21, 36)(22, 33)(23, 40)(24, 29)(25, 32)(26, 37)(27, 28)(30, 39)(31, 34)(35, 38)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 83)(62, 86)(63, 87)(64, 88)(65, 81)(66, 90)(67, 89)(68, 100)(69, 85)(70, 98)(71, 95)(72, 84)(73, 91)(74, 82)(75, 99)(76, 92)(77, 93)(78, 94)(79, 97)(80, 96)(101, 102)(103, 106)(104, 115)(105, 114)(107, 110)(108, 119)(109, 118)(111, 112)(113, 116)(117, 120) MAP : A4.1267 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 > CTG (small) : <18, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4, 4) #DARTS : 126 R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126) L = (1, 110)(2, 113)(3, 115)(4, 116)(5, 109)(6, 124)(7, 123)(8, 126)(9, 125)(10, 122)(11, 118)(12, 114)(13, 117)(14, 119)(15, 111)(16, 120)(17, 121)(18, 112)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88) MAP : A4.1277 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4, 4) #DARTS : 126 R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126) L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111) MAP : A4.1282 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4, 4) #DARTS : 126 R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126) L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113) MAP : A4.1292 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.3^3, x.2 * x.4^-1 * x.3^-1, x.4^3, x.2^3, (x.4 * x.1)^2, x.2 * x.1 * x.2^-1 * x.1, x.1 * x.2 * x.3 * x.1 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4, 4) #DARTS : 126 R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126) L = (1, 112)(2, 123)(3, 114)(4, 113)(5, 109)(6, 116)(7, 118)(8, 111)(9, 120)(10, 119)(11, 115)(12, 122)(13, 124)(14, 117)(15, 126)(16, 125)(17, 121)(18, 110)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86) MAP : A4.1489 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 5)(3, 4) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.1, u.4^3, u.2^3, (u.3 * u.4^-1)^2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.1 * x.2^-1 * x.3, x.4^3, x.2^3, (x.3 * x.4^-1)^2, x.4^-1 * x.1 * x.4^-1 * x.3^-1, (x.4, x.2) > SCHREIER VEC. : (x.2, x.3, x.4, x.4^-1, x.3^-1, x.1, x.2^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 3, 4) #DARTS : 126 R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126) L = (1, 112)(2, 123)(3, 114)(4, 113)(5, 109)(6, 116)(7, 118)(8, 111)(9, 120)(10, 119)(11, 115)(12, 122)(13, 124)(14, 117)(15, 126)(16, 125)(17, 121)(18, 110)(19, 78)(20, 83)(21, 76)(22, 80)(23, 75)(24, 77)(25, 74)(26, 73)(27, 89)(28, 87)(29, 90)(30, 85)(31, 81)(32, 88)(33, 79)(34, 84)(35, 86)(36, 82)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 55)(44, 56)(45, 57)(46, 58)(47, 59)(48, 60)(49, 61)(50, 62)(51, 63)(52, 64)(53, 65)(54, 66)(91, 93)(92, 100)(94, 96)(95, 98)(97, 108)(99, 106)(101, 105)(102, 107)(103, 104) MAP : A4.1493 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133) MAP : A4.1494 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144) L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133) MAP : A4.1495 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144) L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130) MAP : A4.1496 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, x.5^3, x.2 * x.3^-1 * x.4, x.1 * x.5 * x.3, x.3^-1 * x.2 * x.5^-1, x.4^-1 * x.5^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4^-1 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144) L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 66)(56, 71)(57, 64)(58, 68)(59, 63)(60, 65)(61, 62)(67, 69)(70, 72)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 133)(110, 134)(111, 135)(112, 136)(113, 137)(114, 138)(115, 139)(116, 140)(117, 141)(118, 142)(119, 143)(120, 144)(121, 127)(122, 128)(123, 129)(124, 130)(125, 131)(126, 132) MAP : A4.1497 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4 * x.3, x.3 * x.4^-1 * x.1, x.5^3, x.4^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.4^-1, x.5 * x.4 * x.2 * x.1, x.5^-1 * x.1 * x.4^-1 * x.2, x.5 * x.1 * x.5^-1 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144) L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 133)(110, 134)(111, 135)(112, 136)(113, 137)(114, 138)(115, 139)(116, 140)(117, 141)(118, 142)(119, 143)(120, 144)(121, 127)(122, 128)(123, 129)(124, 130)(125, 131)(126, 132) MAP : A4.1504 NOTES : type II, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15) ORBIFOLD : O(0, {3, 3, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 > CTG (small) : <9, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144) L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129) MAP : A4.1506 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 2)(4, 8)(5, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^3, u.5^3, u.3^-1 * u.1 * u.4^-1, u.4 * u.5^-1 * u.2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^3, x.5^3, x.1 * x.4 * x.3, x.3^-1 * x.1 * x.4^-1, x.4 * x.5^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.2 * x.3 * x.5 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.4, x.5, x.5^-1, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144) L = (1, 22)(2, 33)(3, 24)(4, 23)(5, 19)(6, 26)(7, 28)(8, 21)(9, 30)(10, 29)(11, 25)(12, 32)(13, 34)(14, 27)(15, 36)(16, 35)(17, 31)(18, 20)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 144)(56, 131)(57, 142)(58, 128)(59, 141)(60, 143)(61, 140)(62, 139)(63, 137)(64, 135)(65, 138)(66, 133)(67, 129)(68, 136)(69, 127)(70, 132)(71, 134)(72, 130)(73, 106)(74, 99)(75, 108)(76, 107)(77, 103)(78, 92)(79, 94)(80, 105)(81, 96)(82, 95)(83, 91)(84, 98)(85, 100)(86, 93)(87, 102)(88, 101)(89, 97)(90, 104)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126) MAP : A4.1510 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(4, 5) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 > CTG (small) : <18, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.5 * x.3^-1 * x.4, x.3^-1 * x.1 * x.2, x.5 * x.1 * x.5^-1 * x.2, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 144 R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144) L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 73)(68, 74)(69, 75)(70, 76)(71, 77)(72, 78)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144) MAP : A4.1868 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (2, 4)(5, 8) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1^2, u.2^2, u.3^2, u.4^2, u.1 * u.5^-1 * u.6^-1, u.6 * u.3 * u.4, (u.5 * u.2)^2 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4^2, x.1^2, x.2^2, x.3^2, x.1 * x.5^-1 * x.6^-1, x.3 * x.2 * x.6^-1, x.2 * x.4 * x.6^-1, x.6 * x.3 * x.4, x.1 * x.5 * x.6, x.2 * x.3 * x.6, x.3 * x.5 * x.4 * x.1, (x.5 * x.2)^2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.5, x.2, x.5^-1, x.6, x.3, x.4, x.6^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4, 4) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 3)(2, 4)(5, 6)(7, 9)(8, 10)(11, 12)(13, 42)(14, 48)(15, 41)(16, 47)(17, 46)(18, 44)(19, 40)(20, 39)(21, 38)(22, 37)(23, 45)(24, 43)(25, 26)(27, 28)(29, 31)(30, 33)(32, 35)(34, 36)(49, 92)(50, 91)(51, 94)(52, 93)(53, 85)(54, 87)(55, 95)(56, 89)(57, 96)(58, 90)(59, 86)(60, 88)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 83)(74, 77)(75, 84)(76, 78)(79, 80)(81, 82) MAP : A4.1872 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1 * u.2^-1 * u.4^-1, u.3^3, u.4^3, u.1^3, (u.2 * u.3^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.4 * x.2 * x.1^-1, x.1 * x.3^-1 * x.2^-1, x.4^3, x.1^3, x.1 * x.4^-1 * x.3^-1, x.2^3, x.3^3, x.2 * x.4 * x.3, (x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1, x.4, x.4^-1, x.1^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4, 3, 4) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 91)(2, 95)(3, 89)(4, 93)(5, 92)(6, 85)(7, 90)(8, 87)(9, 94)(10, 88)(11, 96)(12, 86)(13, 56)(14, 49)(15, 54)(16, 51)(17, 58)(18, 52)(19, 60)(20, 50)(21, 55)(22, 59)(23, 53)(24, 57)(25, 45)(26, 46)(27, 47)(28, 48)(29, 37)(30, 38)(31, 39)(32, 40)(33, 41)(34, 42)(35, 43)(36, 44)(61, 83)(62, 75)(63, 81)(64, 73)(65, 84)(66, 77)(67, 82)(68, 79)(69, 74)(70, 80)(71, 76)(72, 78) MAP : A4.1874 NOTES : type I, non-Cayley, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.4^2, u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.4^2, x.1^2, x.2^2, x.3^3, x.3^-1 * x.1 * x.2, x.3 * x.1 * x.3^-1 * x.2, (x.3 * x.4 * x.2)^2, (x.4 * x.2)^3, (x.4 * x.1)^3, (x.2 * x.1 * x.4 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2 LOCAL TYPE : (3, 3, 3, 4, 3, 3, 3, 4) #DARTS : 96 R = (1, 35, 59, 83, 11, 25, 49, 73)(2, 33, 57, 81, 9, 26, 50, 74)(3, 36, 60, 84, 12, 27, 51, 75)(4, 34, 58, 82, 10, 28, 52, 76)(5, 46, 70, 94, 22, 29, 53, 77)(6, 48, 72, 96, 24, 30, 54, 78)(7, 45, 69, 93, 21, 31, 55, 79)(8, 47, 71, 95, 23, 32, 56, 80)(13, 44, 68, 92, 20, 37, 61, 85)(14, 43, 67, 91, 19, 38, 62, 86)(15, 42, 66, 90, 18, 39, 63, 87)(16, 41, 65, 89, 17, 40, 64, 88) L = (1, 38)(2, 40)(3, 37)(4, 39)(5, 43)(6, 41)(7, 44)(8, 42)(9, 28)(10, 27)(11, 26)(12, 25)(13, 34)(14, 36)(15, 33)(16, 35)(17, 47)(18, 45)(19, 48)(20, 46)(21, 32)(22, 31)(23, 30)(24, 29)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(73, 80)(74, 79)(75, 78)(76, 77)(81, 91)(82, 89)(83, 92)(84, 90)(85, 95)(86, 93)(87, 96)(88, 94) MAP : A4.1875 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.7 * x.2 * x.3, x.1 * x.3 * x.5, x.3 * x.1 * x.5, x.2 * x.7 * x.4, x.1 * x.6 * x.7^-1, x.2 * x.4 * x.7^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 108 R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108) L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96)(97, 108)(98, 102)(99, 107)(100, 101)(103, 106)(104, 105) MAP : A4.1876 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 > CTG (small) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.1 * x.4 * x.2, x.3 * x.5 * x.7, x.2 * x.7 * x.5, x.1 * x.2 * x.4, x.7 * x.2 * x.3, x.1 * x.6 * x.7^-1, x.3 * x.7^-1 * x.5, (x.3 * x.1)^2 > SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 108 R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108) L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 88)(86, 87)(89, 93)(90, 91)(92, 96)(94, 95)(97, 103)(98, 104)(99, 105)(100, 106)(101, 107)(102, 108) MAP : A4.1883 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (2, 7)(3, 4)(5, 6)(8, 9) ORBIFOLD : O(0, {3, 3, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.1 * u.2^-1 * u.5^-1, u.3^3, u.4^3, u.5^3, u.2 * u.3^-1 * u.4^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2 * x.4^-1 * x.5^-1, x.1 * x.2^-1 * x.5^-1, x.2 * x.5^-1 * x.3^-1, x.3^3, x.4^3, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5 * x.3, x.1 * x.5^-1 * x.4, x.1 * x.3 * x.4^-1, x.1 * x.2 * x.3, x.2^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.4^-1, x.2^-1, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 108 R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108) L = (1, 12)(2, 5)(3, 10)(4, 7)(6, 8)(9, 11)(13, 74)(14, 80)(15, 76)(16, 78)(17, 83)(18, 75)(19, 81)(20, 73)(21, 84)(22, 77)(23, 82)(24, 79)(25, 45)(26, 46)(27, 47)(28, 48)(29, 37)(30, 38)(31, 39)(32, 40)(33, 41)(34, 42)(35, 43)(36, 44)(49, 71)(50, 63)(51, 69)(52, 61)(53, 72)(54, 65)(55, 70)(56, 67)(57, 62)(58, 68)(59, 64)(60, 66)(85, 102)(86, 108)(87, 104)(88, 106)(89, 99)(90, 103)(91, 97)(92, 101)(93, 100)(94, 105)(95, 98)(96, 107)