Created on Mon Sep 06 2010, 16:00:29 CEST GENUS: 3 NUMBER OF MAPS: 103 REFLEXIBLE MAPS: 63 CHIRAL MAPS: 40 #TYPE I: 78 #TYPE II: 25 CAYLEY MAPS: 100 NON-CAYLEY MAPS: 3 NON-CAYLEY REPRESENTATIVES: A3.191, A3.382, A3.1382 MAP : A3.1 NOTES : type I, reflexible, isomorphic to Trun({3,7}), QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.2 * x.1)^7, (x.1 * x.2 * x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 14, 14) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 420)(170, 435)(171, 437)(172, 434)(173, 456)(174, 443)(175, 436)(176, 453)(177, 418)(178, 417)(179, 433)(180, 401)(181, 441)(182, 394)(183, 393)(184, 442)(185, 423)(186, 422)(187, 351)(188, 440)(189, 348)(190, 352)(191, 349)(192, 363)(193, 419)(194, 404)(195, 402)(196, 407)(197, 403)(198, 479)(199, 478)(200, 396)(201, 502)(202, 503)(203, 500)(204, 350)(205, 498)(206, 365)(207, 368)(208, 497)(209, 421)(210, 424)(211, 406)(212, 389)(213, 391)(214, 380)(215, 387)(216, 390)(217, 488)(218, 485)(219, 392)(220, 483)(221, 382)(222, 481)(223, 482)(224, 383)(225, 355)(226, 372)(227, 370)(228, 375)(229, 371)(230, 439)(231, 438)(232, 388)(233, 357)(234, 360)(235, 374)(236, 469)(237, 471)(238, 484)(239, 467)(240, 470)(241, 354)(242, 353)(243, 337)(244, 369)(245, 345)(246, 386)(247, 385)(248, 346)(249, 416)(250, 413)(251, 472)(252, 411)(253, 486)(254, 409)(255, 410)(256, 487)(257, 356)(258, 339)(259, 341)(260, 338)(261, 408)(262, 347)(263, 340)(264, 405)(265, 430)(266, 431)(267, 428)(268, 494)(269, 426)(270, 501)(271, 504)(272, 425)(273, 359)(274, 358)(275, 495)(276, 344)(277, 492)(278, 496)(279, 493)(280, 499)(281, 463)(282, 462)(283, 447)(284, 480)(285, 444)(286, 448)(287, 445)(288, 427)(289, 460)(290, 475)(291, 477)(292, 474)(293, 376)(294, 491)(295, 476)(296, 373)(297, 366)(298, 367)(299, 364)(300, 446)(301, 362)(302, 429)(303, 432)(304, 361)(305, 458)(306, 457)(307, 473)(308, 449)(309, 489)(310, 466)(311, 465)(312, 490)(313, 384)(314, 381)(315, 400)(316, 379)(317, 414)(318, 377)(319, 378)(320, 415)(321, 459)(322, 452)(323, 450)(324, 455)(325, 451)(326, 343)(327, 342)(328, 468)(329, 461)(330, 464)(331, 454)(332, 397)(333, 399)(334, 412)(335, 395)(336, 398) MAP : A3.3 NOTES : type I, reflexible, isomorphic to Trun({3,8}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 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, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(193, 248)(194, 279)(195, 242)(196, 266)(197, 254)(198, 247)(199, 280)(200, 274)(201, 263)(202, 249)(203, 271)(204, 262)(205, 264)(206, 273)(207, 270)(208, 283)(209, 267)(210, 256)(211, 281)(212, 284)(213, 260)(214, 285)(215, 250)(216, 286)(217, 255)(218, 278)(219, 276)(220, 272)(221, 287)(222, 265)(223, 282)(224, 275)(225, 245)(226, 241)(227, 268)(228, 257)(229, 259)(230, 244)(231, 243)(232, 246)(233, 277)(234, 251)(235, 258)(236, 261)(237, 252)(238, 253)(239, 288)(240, 269) MAP : A3.13 NOTES : type II, reflexible, isomorphic to DBar({3,7}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 7, 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)^7 > CTG (small) : <168, 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 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^7, x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 843)(170, 860)(171, 858)(172, 863)(173, 859)(174, 935)(175, 934)(176, 876)(177, 845)(178, 848)(179, 862)(180, 997)(181, 999)(182, 980)(183, 995)(184, 998)(185, 842)(186, 841)(187, 849)(188, 857)(189, 865)(190, 874)(191, 873)(192, 866)(193, 912)(194, 909)(195, 1000)(196, 907)(197, 982)(198, 905)(199, 906)(200, 983)(201, 844)(202, 851)(203, 853)(204, 850)(205, 944)(206, 867)(207, 852)(208, 941)(209, 902)(210, 903)(211, 900)(212, 958)(213, 898)(214, 965)(215, 968)(216, 897)(217, 847)(218, 846)(219, 959)(220, 856)(221, 956)(222, 960)(223, 957)(224, 963)(225, 991)(226, 990)(227, 919)(228, 976)(229, 916)(230, 920)(231, 917)(232, 899)(233, 988)(234, 971)(235, 973)(236, 970)(237, 864)(238, 955)(239, 972)(240, 861)(241, 886)(242, 887)(243, 884)(244, 918)(245, 882)(246, 901)(247, 904)(248, 881)(249, 986)(250, 985)(251, 969)(252, 1001)(253, 953)(254, 994)(255, 993)(256, 954)(257, 896)(258, 893)(259, 928)(260, 891)(261, 910)(262, 889)(263, 890)(264, 911)(265, 987)(266, 1004)(267, 1002)(268, 1007)(269, 1003)(270, 855)(271, 854)(272, 996)(273, 989)(274, 992)(275, 1006)(276, 925)(277, 927)(278, 908)(279, 923)(280, 926)(281, 948)(282, 931)(283, 933)(284, 930)(285, 1008)(286, 915)(287, 932)(288, 1005)(289, 946)(290, 945)(291, 929)(292, 937)(293, 913)(294, 922)(295, 921)(296, 914)(297, 951)(298, 950)(299, 871)(300, 936)(301, 868)(302, 872)(303, 869)(304, 883)(305, 947)(306, 940)(307, 938)(308, 943)(309, 939)(310, 975)(311, 974)(312, 924)(313, 966)(314, 967)(315, 964)(316, 870)(317, 962)(318, 885)(319, 888)(320, 961)(321, 949)(322, 952)(323, 942)(324, 877)(325, 879)(326, 892)(327, 875)(328, 878)(329, 984)(330, 981)(331, 880)(332, 979)(333, 894)(334, 977)(335, 978)(336, 895)(337, 674)(338, 673)(339, 681)(340, 689)(341, 697)(342, 706)(343, 705)(344, 698)(345, 675)(346, 692)(347, 690)(348, 695)(349, 691)(350, 767)(351, 766)(352, 708)(353, 676)(354, 683)(355, 685)(356, 682)(357, 776)(358, 699)(359, 684)(360, 773)(361, 677)(362, 680)(363, 694)(364, 829)(365, 831)(366, 812)(367, 827)(368, 830)(369, 679)(370, 678)(371, 791)(372, 688)(373, 788)(374, 792)(375, 789)(376, 795)(377, 744)(378, 741)(379, 832)(380, 739)(381, 814)(382, 737)(383, 738)(384, 815)(385, 734)(386, 735)(387, 732)(388, 790)(389, 730)(390, 797)(391, 800)(392, 729)(393, 728)(394, 725)(395, 760)(396, 723)(397, 742)(398, 721)(399, 722)(400, 743)(401, 718)(402, 719)(403, 716)(404, 750)(405, 714)(406, 733)(407, 736)(408, 713)(409, 821)(410, 824)(411, 838)(412, 757)(413, 759)(414, 740)(415, 755)(416, 758)(417, 823)(418, 822)(419, 751)(420, 808)(421, 748)(422, 752)(423, 749)(424, 731)(425, 819)(426, 836)(427, 834)(428, 839)(429, 835)(430, 687)(431, 686)(432, 828)(433, 820)(434, 803)(435, 805)(436, 802)(437, 696)(438, 787)(439, 804)(440, 693)(441, 818)(442, 817)(443, 801)(444, 833)(445, 785)(446, 826)(447, 825)(448, 786)(449, 781)(450, 784)(451, 774)(452, 709)(453, 711)(454, 724)(455, 707)(456, 710)(457, 816)(458, 813)(459, 712)(460, 811)(461, 726)(462, 809)(463, 810)(464, 727)(465, 779)(466, 772)(467, 770)(468, 775)(469, 771)(470, 807)(471, 806)(472, 756)(473, 798)(474, 799)(475, 796)(476, 702)(477, 794)(478, 717)(479, 720)(480, 793)(481, 778)(482, 777)(483, 761)(484, 769)(485, 745)(486, 754)(487, 753)(488, 746)(489, 783)(490, 782)(491, 703)(492, 768)(493, 700)(494, 704)(495, 701)(496, 715)(497, 780)(498, 763)(499, 765)(500, 762)(501, 840)(502, 747)(503, 764)(504, 837) MAP : A3.19 NOTES : type II, reflexible, isomorphic to DBar({3,8}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3^-1 * x.2)^3, x.3^2 * x.2 * x.3^-1 * x.2 * x.3^2 * x.2 * x.3^3 * x.2, (x.3^2 * x.2 * x.3^-3 * x.2)^2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 484)(98, 488)(99, 485)(100, 481)(101, 483)(102, 514)(103, 517)(104, 482)(105, 498)(106, 561)(107, 562)(108, 513)(109, 497)(110, 501)(111, 565)(112, 533)(113, 493)(114, 489)(115, 510)(116, 509)(117, 494)(118, 543)(119, 538)(120, 505)(121, 504)(122, 528)(123, 544)(124, 539)(125, 500)(126, 499)(127, 512)(128, 511)(129, 492)(130, 486)(131, 519)(132, 524)(133, 487)(134, 520)(135, 515)(136, 518)(137, 523)(138, 525)(139, 521)(140, 516)(141, 522)(142, 527)(143, 526)(144, 506)(145, 560)(146, 576)(147, 555)(148, 559)(149, 496)(150, 556)(151, 550)(152, 554)(153, 574)(154, 503)(155, 508)(156, 551)(157, 569)(158, 573)(159, 502)(160, 507)(161, 571)(162, 575)(163, 572)(164, 566)(165, 570)(166, 535)(167, 540)(168, 567)(169, 563)(170, 536)(171, 531)(172, 534)(173, 568)(174, 564)(175, 532)(176, 529)(177, 490)(178, 491)(179, 553)(180, 558)(181, 495)(182, 548)(183, 552)(184, 557)(185, 541)(186, 549)(187, 545)(188, 547)(189, 542)(190, 537)(191, 546)(192, 530)(193, 394)(194, 395)(195, 457)(196, 462)(197, 399)(198, 452)(199, 456)(200, 461)(201, 445)(202, 453)(203, 449)(204, 451)(205, 446)(206, 441)(207, 450)(208, 434)(209, 396)(210, 390)(211, 423)(212, 428)(213, 391)(214, 424)(215, 419)(216, 422)(217, 427)(218, 429)(219, 425)(220, 420)(221, 426)(222, 431)(223, 430)(224, 410)(225, 464)(226, 480)(227, 459)(228, 463)(229, 400)(230, 460)(231, 454)(232, 458)(233, 478)(234, 407)(235, 412)(236, 455)(237, 473)(238, 477)(239, 406)(240, 411)(241, 397)(242, 393)(243, 414)(244, 413)(245, 398)(246, 447)(247, 442)(248, 409)(249, 408)(250, 432)(251, 448)(252, 443)(253, 404)(254, 403)(255, 416)(256, 415)(257, 388)(258, 392)(259, 389)(260, 385)(261, 387)(262, 418)(263, 421)(264, 386)(265, 402)(266, 465)(267, 466)(268, 417)(269, 401)(270, 405)(271, 469)(272, 437)(273, 475)(274, 479)(275, 476)(276, 470)(277, 474)(278, 439)(279, 444)(280, 471)(281, 467)(282, 440)(283, 435)(284, 438)(285, 472)(286, 468)(287, 436)(288, 433) MAP : A3.25 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: [ 2, 3, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 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, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 211)(98, 217)(99, 209)(100, 213)(101, 212)(102, 218)(103, 234)(104, 219)(105, 210)(106, 214)(107, 216)(108, 232)(109, 202)(110, 233)(111, 200)(112, 197)(113, 231)(114, 230)(115, 238)(116, 206)(117, 237)(118, 226)(119, 225)(120, 220)(121, 222)(122, 215)(123, 199)(124, 205)(125, 229)(126, 227)(127, 198)(128, 194)(129, 208)(130, 240)(131, 207)(132, 203)(133, 224)(134, 239)(135, 235)(136, 223)(137, 204)(138, 221)(139, 196)(140, 201)(141, 236)(142, 228)(143, 195)(144, 193) MAP : A3.37 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: [ 4, 6, 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)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^-2, x.2^-1 * x.3 * x.2^2 * x.3 * x.2^-1 * x.3^-1 * x.2^-2 * x.3^-1, x.3 * x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 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, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 262)(51, 247)(52, 258)(53, 241)(54, 288)(55, 245)(56, 286)(57, 271)(58, 252)(59, 269)(60, 272)(61, 267)(62, 250)(63, 265)(64, 268)(65, 253)(66, 248)(67, 249)(68, 278)(69, 255)(70, 276)(71, 251)(72, 242)(73, 275)(74, 270)(75, 279)(76, 266)(77, 273)(78, 256)(79, 277)(80, 254)(81, 263)(82, 284)(83, 261)(84, 264)(85, 259)(86, 282)(87, 257)(88, 260)(89, 285)(90, 280)(91, 281)(92, 246)(93, 287)(94, 244)(95, 283)(96, 274)(97, 196)(98, 197)(99, 232)(100, 193)(101, 194)(102, 199)(103, 198)(104, 237)(105, 216)(106, 211)(107, 238)(108, 215)(109, 236)(110, 209)(111, 234)(112, 219)(113, 206)(114, 231)(115, 202)(116, 229)(117, 224)(118, 227)(119, 204)(120, 201)(121, 220)(122, 221)(123, 208)(124, 217)(125, 218)(126, 223)(127, 222)(128, 213)(129, 240)(130, 235)(131, 214)(132, 239)(133, 212)(134, 233)(135, 210)(136, 195)(137, 230)(138, 207)(139, 226)(140, 205)(141, 200)(142, 203)(143, 228)(144, 225) MAP : A3.43 NOTES : type II, reflexible, isomorphic to DBar({4,8}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 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, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 132)(66, 148)(67, 130)(68, 138)(69, 154)(70, 146)(71, 145)(72, 134)(73, 135)(74, 143)(75, 156)(76, 159)(77, 149)(78, 153)(79, 160)(80, 155)(81, 133)(82, 139)(83, 129)(84, 140)(85, 136)(86, 144)(87, 141)(88, 131)(89, 147)(90, 150)(91, 137)(92, 151)(93, 158)(94, 152)(95, 157)(96, 142) MAP : A3.48 NOTES : type II, reflexible, isomorphic to DBar({4,8}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 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)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 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, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 187)(34, 180)(35, 182)(36, 186)(37, 189)(38, 165)(39, 177)(40, 178)(41, 188)(42, 184)(43, 169)(44, 161)(45, 163)(46, 179)(47, 181)(48, 164)(49, 176)(50, 175)(51, 191)(52, 172)(53, 190)(54, 167)(55, 174)(56, 192)(57, 183)(58, 173)(59, 166)(60, 168)(61, 162)(62, 171)(63, 170)(64, 185)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.145 NOTES : type I, reflexible, isomorphic to TDual({3,7}), QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2)^3, x.2^7, x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^-3 * x.1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 7) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 472)(170, 469)(171, 360)(172, 467)(173, 374)(174, 465)(175, 466)(176, 375)(177, 486)(178, 487)(179, 484)(180, 382)(181, 482)(182, 389)(183, 392)(184, 481)(185, 413)(186, 416)(187, 430)(188, 357)(189, 359)(190, 372)(191, 355)(192, 358)(193, 415)(194, 414)(195, 383)(196, 400)(197, 380)(198, 384)(199, 381)(200, 387)(201, 411)(202, 428)(203, 426)(204, 431)(205, 427)(206, 495)(207, 494)(208, 444)(209, 412)(210, 395)(211, 397)(212, 394)(213, 464)(214, 403)(215, 396)(216, 461)(217, 410)(218, 409)(219, 393)(220, 425)(221, 401)(222, 442)(223, 441)(224, 402)(225, 349)(226, 352)(227, 342)(228, 453)(229, 455)(230, 468)(231, 451)(232, 454)(233, 440)(234, 437)(235, 456)(236, 435)(237, 470)(238, 433)(239, 434)(240, 471)(241, 347)(242, 340)(243, 338)(244, 343)(245, 339)(246, 399)(247, 398)(248, 356)(249, 422)(250, 423)(251, 420)(252, 502)(253, 418)(254, 485)(255, 488)(256, 417)(257, 346)(258, 345)(259, 361)(260, 337)(261, 377)(262, 354)(263, 353)(264, 378)(265, 351)(266, 350)(267, 503)(268, 368)(269, 500)(270, 504)(271, 501)(272, 483)(273, 348)(274, 363)(275, 365)(276, 362)(277, 432)(278, 379)(279, 364)(280, 429)(281, 474)(282, 473)(283, 489)(284, 457)(285, 497)(286, 450)(287, 449)(288, 498)(289, 475)(290, 460)(291, 458)(292, 463)(293, 459)(294, 367)(295, 366)(296, 452)(297, 476)(298, 491)(299, 493)(300, 490)(301, 344)(302, 499)(303, 492)(304, 341)(305, 477)(306, 480)(307, 462)(308, 445)(309, 447)(310, 436)(311, 443)(312, 446)(313, 479)(314, 478)(315, 407)(316, 496)(317, 404)(318, 408)(319, 405)(320, 419)(321, 376)(322, 373)(323, 448)(324, 371)(325, 438)(326, 369)(327, 370)(328, 439)(329, 390)(330, 391)(331, 388)(332, 406)(333, 386)(334, 421)(335, 424)(336, 385) MAP : A3.147 NOTES : type I, reflexible, isomorphic to TDual({3,8}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 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, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 284)(50, 276)(51, 260)(52, 254)(53, 272)(54, 261)(55, 277)(56, 252)(57, 273)(58, 257)(59, 248)(60, 281)(61, 275)(62, 288)(63, 258)(64, 262)(65, 253)(66, 246)(67, 283)(68, 271)(69, 255)(70, 249)(71, 241)(72, 243)(73, 242)(74, 270)(75, 269)(76, 266)(77, 247)(78, 274)(79, 264)(80, 282)(81, 256)(82, 268)(83, 250)(84, 285)(85, 267)(86, 286)(87, 244)(88, 245)(89, 251)(90, 280)(91, 278)(92, 287)(93, 265)(94, 259)(95, 263)(96, 279)(97, 198)(98, 202)(99, 193)(100, 201)(101, 205)(102, 195)(103, 238)(104, 208)(105, 232)(106, 229)(107, 222)(108, 199)(109, 226)(110, 219)(111, 225)(112, 228)(113, 223)(114, 221)(115, 207)(116, 224)(117, 218)(118, 239)(119, 203)(120, 217)(121, 240)(122, 237)(123, 236)(124, 235)(125, 234)(126, 215)(127, 230)(128, 233)(129, 211)(130, 197)(131, 214)(132, 200)(133, 194)(134, 209)(135, 220)(136, 196)(137, 212)(138, 210)(139, 231)(140, 206)(141, 213)(142, 204)(143, 227)(144, 216) MAP : A3.173 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: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2 * x.3 * x.2^-2 * x.3, x.2^6, (x.3 * x.1^-1)^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #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, 131)(26, 134)(27, 121)(28, 135)(29, 136)(30, 122)(31, 124)(32, 125)(33, 139)(34, 142)(35, 129)(36, 143)(37, 144)(38, 130)(39, 132)(40, 133)(41, 123)(42, 126)(43, 137)(44, 127)(45, 128)(46, 138)(47, 140)(48, 141)(49, 98)(50, 101)(51, 103)(52, 107)(53, 97)(54, 111)(55, 114)(56, 119)(57, 108)(58, 116)(59, 109)(60, 110)(61, 100)(62, 105)(63, 117)(64, 106)(65, 104)(66, 99)(67, 118)(68, 112)(69, 102)(70, 120)(71, 113)(72, 115) MAP : A3.183 NOTES : type I, reflexible, isomorphic to TDual({4,6}), QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^6, u.3^6, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 > CTG (small) : <24, 13> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, x.3^-3 * x.2^-3, x.3^-3 * x.2^3, x.2^-3 * x.3^3, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 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, 66)(26, 49)(27, 68)(28, 51)(29, 70)(30, 53)(31, 72)(32, 55)(33, 50)(34, 57)(35, 52)(36, 59)(37, 54)(38, 61)(39, 56)(40, 63)(41, 58)(42, 65)(43, 60)(44, 67)(45, 62)(46, 69)(47, 64)(48, 71)(97, 136)(98, 132)(99, 135)(100, 125)(101, 143)(102, 130)(103, 141)(104, 124)(105, 133)(106, 127)(107, 129)(108, 144)(109, 140)(110, 128)(111, 122)(112, 126)(113, 123)(114, 142)(115, 134)(116, 138)(117, 121)(118, 131)(119, 139)(120, 137) MAP : A3.191 NOTES : type I, non-Cayley, reflexible, isomorphic to {3,7}, QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 3 ], faces: [ 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2)^7, (x.1 * x.2^-1 * x.1 * x.2)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (7, 7, 7) #DARTS : 168 R = (1, 18, 3)(2, 17, 20)(4, 33, 23)(5, 9, 19)(6, 50, 95)(7, 49, 94)(8, 10, 36)(11, 34, 22)(12, 39, 157)(13, 35, 159)(14, 103, 140)(15, 102, 155)(16, 52, 158)(21, 72, 25)(24, 69, 26)(27, 38, 160)(28, 133, 67)(29, 135, 142)(30, 148, 65)(31, 131, 66)(32, 134, 143)(37, 156, 104)(40, 163, 101)(41, 80, 62)(42, 77, 63)(43, 136, 60)(44, 75, 118)(45, 150, 58)(46, 73, 125)(47, 74, 128)(48, 151, 57)(51, 92, 119)(53, 90, 116)(54, 165, 120)(55, 168, 117)(56, 89, 123)(59, 64, 79)(61, 78, 76)(68, 110, 130)(70, 93, 115)(71, 96, 132)(81, 127, 146)(82, 126, 145)(83, 111, 129)(84, 144, 161)(85, 108, 113)(86, 112, 154)(87, 109, 153)(88, 91, 114)(97, 124, 147)(98, 139, 164)(99, 141, 162)(100, 138, 167)(105, 122, 149)(106, 121, 152)(107, 137, 166) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168) MAP : A3.193 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 6, 3)(2, 10, 37)(4, 9, 40)(5, 13, 34)(7, 46, 12)(8, 16, 36)(11, 30, 23)(14, 27, 44)(15, 33, 19)(17, 31, 38)(18, 29, 42)(20, 32, 41)(21, 26, 45)(22, 47, 35)(24, 25, 48)(28, 43, 39)(49, 68, 59)(50, 75, 96)(51, 69, 73)(52, 53, 76)(54, 92, 77)(55, 89, 90)(56, 93, 78)(57, 62, 95)(58, 84, 70)(60, 67, 64)(61, 80, 79)(63, 91, 74)(65, 94, 85)(66, 88, 81)(71, 82, 83)(72, 87, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.319 NOTES : type I, reflexible, isomorphic to Med2({3,7}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^7, (x.1^-2 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 7, 4) #DARTS : 672 R = (1, 169, 337, 505)(2, 170, 338, 506)(3, 171, 339, 507)(4, 172, 340, 508)(5, 173, 341, 509)(6, 174, 342, 510)(7, 175, 343, 511)(8, 176, 344, 512)(9, 177, 345, 513)(10, 178, 346, 514)(11, 179, 347, 515)(12, 180, 348, 516)(13, 181, 349, 517)(14, 182, 350, 518)(15, 183, 351, 519)(16, 184, 352, 520)(17, 185, 353, 521)(18, 186, 354, 522)(19, 187, 355, 523)(20, 188, 356, 524)(21, 189, 357, 525)(22, 190, 358, 526)(23, 191, 359, 527)(24, 192, 360, 528)(25, 193, 361, 529)(26, 194, 362, 530)(27, 195, 363, 531)(28, 196, 364, 532)(29, 197, 365, 533)(30, 198, 366, 534)(31, 199, 367, 535)(32, 200, 368, 536)(33, 201, 369, 537)(34, 202, 370, 538)(35, 203, 371, 539)(36, 204, 372, 540)(37, 205, 373, 541)(38, 206, 374, 542)(39, 207, 375, 543)(40, 208, 376, 544)(41, 209, 377, 545)(42, 210, 378, 546)(43, 211, 379, 547)(44, 212, 380, 548)(45, 213, 381, 549)(46, 214, 382, 550)(47, 215, 383, 551)(48, 216, 384, 552)(49, 217, 385, 553)(50, 218, 386, 554)(51, 219, 387, 555)(52, 220, 388, 556)(53, 221, 389, 557)(54, 222, 390, 558)(55, 223, 391, 559)(56, 224, 392, 560)(57, 225, 393, 561)(58, 226, 394, 562)(59, 227, 395, 563)(60, 228, 396, 564)(61, 229, 397, 565)(62, 230, 398, 566)(63, 231, 399, 567)(64, 232, 400, 568)(65, 233, 401, 569)(66, 234, 402, 570)(67, 235, 403, 571)(68, 236, 404, 572)(69, 237, 405, 573)(70, 238, 406, 574)(71, 239, 407, 575)(72, 240, 408, 576)(73, 241, 409, 577)(74, 242, 410, 578)(75, 243, 411, 579)(76, 244, 412, 580)(77, 245, 413, 581)(78, 246, 414, 582)(79, 247, 415, 583)(80, 248, 416, 584)(81, 249, 417, 585)(82, 250, 418, 586)(83, 251, 419, 587)(84, 252, 420, 588)(85, 253, 421, 589)(86, 254, 422, 590)(87, 255, 423, 591)(88, 256, 424, 592)(89, 257, 425, 593)(90, 258, 426, 594)(91, 259, 427, 595)(92, 260, 428, 596)(93, 261, 429, 597)(94, 262, 430, 598)(95, 263, 431, 599)(96, 264, 432, 600)(97, 265, 433, 601)(98, 266, 434, 602)(99, 267, 435, 603)(100, 268, 436, 604)(101, 269, 437, 605)(102, 270, 438, 606)(103, 271, 439, 607)(104, 272, 440, 608)(105, 273, 441, 609)(106, 274, 442, 610)(107, 275, 443, 611)(108, 276, 444, 612)(109, 277, 445, 613)(110, 278, 446, 614)(111, 279, 447, 615)(112, 280, 448, 616)(113, 281, 449, 617)(114, 282, 450, 618)(115, 283, 451, 619)(116, 284, 452, 620)(117, 285, 453, 621)(118, 286, 454, 622)(119, 287, 455, 623)(120, 288, 456, 624)(121, 289, 457, 625)(122, 290, 458, 626)(123, 291, 459, 627)(124, 292, 460, 628)(125, 293, 461, 629)(126, 294, 462, 630)(127, 295, 463, 631)(128, 296, 464, 632)(129, 297, 465, 633)(130, 298, 466, 634)(131, 299, 467, 635)(132, 300, 468, 636)(133, 301, 469, 637)(134, 302, 470, 638)(135, 303, 471, 639)(136, 304, 472, 640)(137, 305, 473, 641)(138, 306, 474, 642)(139, 307, 475, 643)(140, 308, 476, 644)(141, 309, 477, 645)(142, 310, 478, 646)(143, 311, 479, 647)(144, 312, 480, 648)(145, 313, 481, 649)(146, 314, 482, 650)(147, 315, 483, 651)(148, 316, 484, 652)(149, 317, 485, 653)(150, 318, 486, 654)(151, 319, 487, 655)(152, 320, 488, 656)(153, 321, 489, 657)(154, 322, 490, 658)(155, 323, 491, 659)(156, 324, 492, 660)(157, 325, 493, 661)(158, 326, 494, 662)(159, 327, 495, 663)(160, 328, 496, 664)(161, 329, 497, 665)(162, 330, 498, 666)(163, 331, 499, 667)(164, 332, 500, 668)(165, 333, 501, 669)(166, 334, 502, 670)(167, 335, 503, 671)(168, 336, 504, 672) L = (1, 173)(2, 176)(3, 190)(4, 325)(5, 327)(6, 308)(7, 323)(8, 326)(9, 240)(10, 237)(11, 328)(12, 235)(13, 310)(14, 233)(15, 234)(16, 311)(17, 171)(18, 188)(19, 186)(20, 191)(21, 187)(22, 263)(23, 262)(24, 204)(25, 230)(26, 231)(27, 228)(28, 286)(29, 226)(30, 293)(31, 296)(32, 225)(33, 170)(34, 169)(35, 177)(36, 185)(37, 193)(38, 202)(39, 201)(40, 194)(41, 175)(42, 174)(43, 287)(44, 184)(45, 284)(46, 288)(47, 285)(48, 291)(49, 172)(50, 179)(51, 181)(52, 178)(53, 272)(54, 195)(55, 180)(56, 269)(57, 314)(58, 313)(59, 297)(60, 329)(61, 281)(62, 322)(63, 321)(64, 282)(65, 315)(66, 332)(67, 330)(68, 335)(69, 331)(70, 183)(71, 182)(72, 324)(73, 316)(74, 299)(75, 301)(76, 298)(77, 192)(78, 283)(79, 300)(80, 189)(81, 317)(82, 320)(83, 334)(84, 253)(85, 255)(86, 236)(87, 251)(88, 254)(89, 319)(90, 318)(91, 247)(92, 304)(93, 244)(94, 248)(95, 245)(96, 227)(97, 224)(98, 221)(99, 256)(100, 219)(101, 238)(102, 217)(103, 218)(104, 239)(105, 214)(106, 215)(107, 212)(108, 246)(109, 210)(110, 229)(111, 232)(112, 209)(113, 312)(114, 309)(115, 208)(116, 307)(117, 222)(118, 305)(119, 306)(120, 223)(121, 294)(122, 295)(123, 292)(124, 198)(125, 290)(126, 213)(127, 216)(128, 289)(129, 277)(130, 280)(131, 270)(132, 205)(133, 207)(134, 220)(135, 203)(136, 206)(137, 279)(138, 278)(139, 199)(140, 264)(141, 196)(142, 200)(143, 197)(144, 211)(145, 275)(146, 268)(147, 266)(148, 271)(149, 267)(150, 303)(151, 302)(152, 252)(153, 276)(154, 259)(155, 261)(156, 258)(157, 336)(158, 243)(159, 260)(160, 333)(161, 274)(162, 273)(163, 257)(164, 265)(165, 241)(166, 250)(167, 249)(168, 242)(337, 507)(338, 524)(339, 522)(340, 527)(341, 523)(342, 599)(343, 598)(344, 540)(345, 509)(346, 512)(347, 526)(348, 661)(349, 663)(350, 644)(351, 659)(352, 662)(353, 506)(354, 505)(355, 513)(356, 521)(357, 529)(358, 538)(359, 537)(360, 530)(361, 576)(362, 573)(363, 664)(364, 571)(365, 646)(366, 569)(367, 570)(368, 647)(369, 508)(370, 515)(371, 517)(372, 514)(373, 608)(374, 531)(375, 516)(376, 605)(377, 566)(378, 567)(379, 564)(380, 622)(381, 562)(382, 629)(383, 632)(384, 561)(385, 511)(386, 510)(387, 623)(388, 520)(389, 620)(390, 624)(391, 621)(392, 627)(393, 655)(394, 654)(395, 583)(396, 640)(397, 580)(398, 584)(399, 581)(400, 563)(401, 652)(402, 635)(403, 637)(404, 634)(405, 528)(406, 619)(407, 636)(408, 525)(409, 550)(410, 551)(411, 548)(412, 582)(413, 546)(414, 565)(415, 568)(416, 545)(417, 650)(418, 649)(419, 633)(420, 665)(421, 617)(422, 658)(423, 657)(424, 618)(425, 560)(426, 557)(427, 592)(428, 555)(429, 574)(430, 553)(431, 554)(432, 575)(433, 651)(434, 668)(435, 666)(436, 671)(437, 667)(438, 519)(439, 518)(440, 660)(441, 653)(442, 656)(443, 670)(444, 589)(445, 591)(446, 572)(447, 587)(448, 590)(449, 612)(450, 595)(451, 597)(452, 594)(453, 672)(454, 579)(455, 596)(456, 669)(457, 610)(458, 609)(459, 593)(460, 601)(461, 577)(462, 586)(463, 585)(464, 578)(465, 615)(466, 614)(467, 535)(468, 600)(469, 532)(470, 536)(471, 533)(472, 547)(473, 611)(474, 604)(475, 602)(476, 607)(477, 603)(478, 639)(479, 638)(480, 588)(481, 630)(482, 631)(483, 628)(484, 534)(485, 626)(486, 549)(487, 552)(488, 625)(489, 613)(490, 616)(491, 606)(492, 541)(493, 543)(494, 556)(495, 539)(496, 542)(497, 648)(498, 645)(499, 544)(500, 643)(501, 558)(502, 641)(503, 642)(504, 559) MAP : A3.323 NOTES : type I, reflexible, isomorphic to Med2({3,8}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 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)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(145, 284)(146, 276)(147, 260)(148, 254)(149, 272)(150, 261)(151, 277)(152, 252)(153, 273)(154, 257)(155, 248)(156, 281)(157, 275)(158, 288)(159, 258)(160, 262)(161, 253)(162, 246)(163, 283)(164, 271)(165, 255)(166, 249)(167, 241)(168, 243)(169, 242)(170, 270)(171, 269)(172, 266)(173, 247)(174, 274)(175, 264)(176, 282)(177, 256)(178, 268)(179, 250)(180, 285)(181, 267)(182, 286)(183, 244)(184, 245)(185, 251)(186, 280)(187, 278)(188, 287)(189, 265)(190, 259)(191, 263)(192, 279)(289, 366)(290, 360)(291, 384)(292, 379)(293, 345)(294, 378)(295, 354)(296, 359)(297, 371)(298, 383)(299, 368)(300, 372)(301, 374)(302, 376)(303, 381)(304, 351)(305, 338)(306, 355)(307, 343)(308, 342)(309, 337)(310, 344)(311, 358)(312, 353)(313, 362)(314, 375)(315, 346)(316, 349)(317, 350)(318, 357)(319, 377)(320, 370)(321, 340)(322, 347)(323, 341)(324, 373)(325, 348)(326, 364)(327, 361)(328, 365)(329, 382)(330, 356)(331, 369)(332, 339)(333, 352)(334, 367)(335, 363)(336, 380) MAP : A3.335 NOTES : type I, reflexible, isomorphic to Med2({3,12}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^-2 * x.1 * x.2^3 * x.1^-1 * x.2^-1, (x.1^-1 * x.2^5)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 53)(3, 54)(4, 55)(5, 49)(6, 56)(7, 72)(8, 51)(9, 61)(10, 92)(11, 62)(12, 78)(13, 88)(14, 69)(15, 94)(16, 87)(17, 63)(18, 60)(19, 64)(20, 80)(21, 59)(22, 77)(23, 70)(24, 52)(25, 96)(26, 95)(27, 79)(28, 75)(29, 71)(30, 66)(31, 76)(32, 93)(33, 90)(34, 74)(35, 89)(36, 83)(37, 58)(38, 73)(39, 67)(40, 57)(41, 84)(42, 91)(43, 81)(44, 85)(45, 68)(46, 65)(47, 82)(48, 86)(97, 182)(98, 189)(99, 178)(100, 177)(101, 183)(102, 172)(103, 175)(104, 190)(105, 181)(106, 184)(107, 179)(108, 180)(109, 171)(110, 176)(111, 185)(112, 186)(113, 150)(114, 157)(115, 146)(116, 145)(117, 151)(118, 188)(119, 191)(120, 158)(121, 149)(122, 152)(123, 147)(124, 148)(125, 187)(126, 192)(127, 153)(128, 154)(129, 166)(130, 173)(131, 162)(132, 161)(133, 167)(134, 156)(135, 159)(136, 174)(137, 165)(138, 168)(139, 163)(140, 164)(141, 155)(142, 160)(143, 169)(144, 170) MAP : A3.345 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, {7, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 7, 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)^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 14, 4) #DARTS : 168 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84)(85, 106, 127, 148)(86, 107, 128, 149)(87, 108, 129, 150)(88, 109, 130, 151)(89, 110, 131, 152)(90, 111, 132, 153)(91, 112, 133, 154)(92, 113, 134, 155)(93, 114, 135, 156)(94, 115, 136, 157)(95, 116, 137, 158)(96, 117, 138, 159)(97, 118, 139, 160)(98, 119, 140, 161)(99, 120, 141, 162)(100, 121, 142, 163)(101, 122, 143, 164)(102, 123, 144, 165)(103, 124, 145, 166)(104, 125, 146, 167)(105, 126, 147, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 47)(23, 43)(24, 53)(25, 57)(26, 44)(27, 58)(28, 46)(29, 52)(30, 59)(31, 55)(32, 54)(33, 45)(34, 50)(35, 61)(36, 49)(37, 60)(38, 63)(39, 48)(40, 62)(41, 56)(42, 51)(64, 126)(65, 116)(66, 119)(67, 125)(68, 118)(69, 112)(70, 107)(71, 124)(72, 120)(73, 109)(74, 113)(75, 121)(76, 114)(77, 123)(78, 108)(79, 115)(80, 111)(81, 110)(82, 122)(83, 106)(84, 117)(127, 166)(128, 162)(129, 151)(130, 155)(131, 163)(132, 156)(133, 165)(134, 150)(135, 157)(136, 153)(137, 152)(138, 164)(139, 148)(140, 159)(141, 168)(142, 158)(143, 161)(144, 167)(145, 160)(146, 154)(147, 149) MAP : A3.349 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169) MAP : A3.365 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^3, (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.3^3, x.2 * x.3 * x.1 * x.2 * x.3, x.1 * x.3^-1 * x.2 * x.3^-1 * x.2, (x.3^-1 * x.1 * x.2)^2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 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, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 66)(50, 67)(51, 65)(52, 58)(53, 63)(54, 61)(55, 62)(56, 69)(57, 68)(59, 60)(64, 70)(71, 72)(73, 88)(74, 96)(75, 80)(76, 79)(77, 84)(78, 92)(81, 95)(82, 93)(83, 94)(85, 91)(86, 89)(87, 90) MAP : A3.366 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) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1 * x.2 * x.1^-1 * x.2 * x.1, x.1^6, (x.1^-1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 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, 35)(2, 38)(3, 25)(4, 39)(5, 40)(6, 26)(7, 28)(8, 29)(9, 43)(10, 46)(11, 33)(12, 47)(13, 48)(14, 34)(15, 36)(16, 37)(17, 27)(18, 30)(19, 41)(20, 31)(21, 32)(22, 42)(23, 44)(24, 45)(49, 77)(50, 73)(51, 90)(52, 85)(53, 74)(54, 93)(55, 75)(56, 89)(57, 86)(58, 88)(59, 76)(60, 81)(61, 83)(62, 84)(63, 78)(64, 92)(65, 95)(66, 79)(67, 96)(68, 82)(69, 87)(70, 91)(71, 80)(72, 94) MAP : A3.370 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^3, (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.3^3, x.3 * x.1 * x.3^-1 * x.2, (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 : (3, 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, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 64)(50, 72)(51, 56)(52, 55)(53, 60)(54, 68)(57, 71)(58, 69)(59, 70)(61, 67)(62, 65)(63, 66)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96) MAP : A3.374 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^3, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.2^3, x.1^-2 * x.2^-1 * x.1 * x.2, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 42)(2, 32)(3, 35)(4, 41)(5, 34)(6, 28)(7, 23)(8, 40)(9, 36)(10, 25)(11, 29)(12, 37)(13, 30)(14, 39)(15, 24)(16, 31)(17, 27)(18, 26)(19, 38)(20, 22)(21, 33)(43, 65)(44, 68)(45, 75)(46, 70)(47, 64)(48, 81)(49, 78)(50, 76)(51, 84)(52, 71)(53, 66)(54, 74)(55, 73)(56, 83)(57, 67)(58, 69)(59, 72)(60, 79)(61, 77)(62, 82)(63, 80) MAP : A3.382 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,7}), QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.2^2, (u.1 * u.2)^3, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^2, (x.1 * x.2)^3, x.1^7, (x.2 * x.1^-3)^4 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 7, 3, 7) #DARTS : 336 R = (1, 187, 19, 169)(2, 204, 36, 170)(3, 202, 34, 171)(4, 207, 39, 172)(5, 203, 35, 173)(6, 271, 103, 174)(7, 270, 102, 175)(8, 220, 52, 176)(9, 189, 21, 177)(10, 192, 24, 178)(11, 206, 38, 179)(12, 301, 133, 180)(13, 303, 135, 181)(14, 316, 148, 182)(15, 299, 131, 183)(16, 302, 134, 184)(17, 186, 18, 185)(20, 201, 33, 188)(22, 218, 50, 190)(23, 217, 49, 191)(25, 248, 80, 193)(26, 245, 77, 194)(27, 304, 136, 195)(28, 243, 75, 196)(29, 318, 150, 197)(30, 241, 73, 198)(31, 242, 74, 199)(32, 319, 151, 200)(37, 240, 72, 205)(40, 237, 69, 208)(41, 262, 94, 209)(42, 263, 95, 210)(43, 260, 92, 211)(44, 326, 158, 212)(45, 258, 90, 213)(46, 333, 165, 214)(47, 336, 168, 215)(48, 257, 89, 216)(51, 327, 159, 219)(53, 324, 156, 221)(54, 328, 160, 222)(55, 325, 157, 223)(56, 331, 163, 224)(57, 295, 127, 225)(58, 294, 126, 226)(59, 279, 111, 227)(60, 312, 144, 228)(61, 276, 108, 229)(62, 280, 112, 230)(63, 277, 109, 231)(64, 259, 91, 232)(65, 292, 124, 233)(66, 307, 139, 234)(67, 309, 141, 235)(68, 306, 138, 236)(70, 323, 155, 238)(71, 308, 140, 239)(76, 278, 110, 244)(78, 261, 93, 246)(79, 264, 96, 247)(81, 290, 122, 249)(82, 289, 121, 250)(83, 305, 137, 251)(84, 281, 113, 252)(85, 321, 153, 253)(86, 298, 130, 254)(87, 297, 129, 255)(88, 322, 154, 256)(97, 291, 123, 265)(98, 284, 116, 266)(99, 282, 114, 267)(100, 287, 119, 268)(101, 283, 115, 269)(104, 300, 132, 272)(105, 293, 125, 273)(106, 296, 128, 274)(107, 286, 118, 275)(117, 288, 120, 285)(142, 311, 143, 310)(145, 334, 166, 313)(146, 335, 167, 314)(147, 332, 164, 315)(149, 330, 162, 317)(152, 329, 161, 320) L = (1, 173)(2, 176)(3, 190)(4, 325)(5, 327)(6, 308)(7, 323)(8, 326)(9, 240)(10, 237)(11, 328)(12, 235)(13, 310)(14, 233)(15, 234)(16, 311)(17, 171)(18, 188)(19, 186)(20, 191)(21, 187)(22, 263)(23, 262)(24, 204)(25, 230)(26, 231)(27, 228)(28, 286)(29, 226)(30, 293)(31, 296)(32, 225)(33, 170)(34, 169)(35, 177)(36, 185)(37, 193)(38, 202)(39, 201)(40, 194)(41, 175)(42, 174)(43, 287)(44, 184)(45, 284)(46, 288)(47, 285)(48, 291)(49, 172)(50, 179)(51, 181)(52, 178)(53, 272)(54, 195)(55, 180)(56, 269)(57, 314)(58, 313)(59, 297)(60, 329)(61, 281)(62, 322)(63, 321)(64, 282)(65, 315)(66, 332)(67, 330)(68, 335)(69, 331)(70, 183)(71, 182)(72, 324)(73, 316)(74, 299)(75, 301)(76, 298)(77, 192)(78, 283)(79, 300)(80, 189)(81, 317)(82, 320)(83, 334)(84, 253)(85, 255)(86, 236)(87, 251)(88, 254)(89, 319)(90, 318)(91, 247)(92, 304)(93, 244)(94, 248)(95, 245)(96, 227)(97, 224)(98, 221)(99, 256)(100, 219)(101, 238)(102, 217)(103, 218)(104, 239)(105, 214)(106, 215)(107, 212)(108, 246)(109, 210)(110, 229)(111, 232)(112, 209)(113, 312)(114, 309)(115, 208)(116, 307)(117, 222)(118, 305)(119, 306)(120, 223)(121, 294)(122, 295)(123, 292)(124, 198)(125, 290)(126, 213)(127, 216)(128, 289)(129, 277)(130, 280)(131, 270)(132, 205)(133, 207)(134, 220)(135, 203)(136, 206)(137, 279)(138, 278)(139, 199)(140, 264)(141, 196)(142, 200)(143, 197)(144, 211)(145, 275)(146, 268)(147, 266)(148, 271)(149, 267)(150, 303)(151, 302)(152, 252)(153, 276)(154, 259)(155, 261)(156, 258)(157, 336)(158, 243)(159, 260)(160, 333)(161, 274)(162, 273)(163, 257)(164, 265)(165, 241)(166, 250)(167, 249)(168, 242) MAP : A3.386 NOTES : type I, reflexible, isomorphic to Med({3,8}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 151)(98, 153)(99, 152)(100, 167)(101, 168)(102, 146)(103, 157)(104, 187)(105, 150)(106, 163)(107, 169)(108, 184)(109, 145)(110, 180)(111, 149)(112, 161)(113, 186)(114, 191)(115, 174)(116, 179)(117, 182)(118, 192)(119, 175)(120, 159)(121, 173)(122, 156)(123, 165)(124, 162)(125, 155)(126, 154)(127, 148)(128, 181)(129, 185)(130, 158)(131, 189)(132, 178)(133, 183)(134, 171)(135, 176)(136, 170)(137, 188)(138, 160)(139, 147)(140, 177)(141, 164)(142, 166)(143, 172)(144, 190) MAP : A3.398 NOTES : type I, reflexible, isomorphic to Med2({4,6}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1 * x.2)^2, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 95)(3, 50)(4, 93)(5, 88)(6, 91)(7, 52)(8, 49)(9, 68)(10, 69)(11, 96)(12, 65)(13, 66)(14, 71)(15, 70)(16, 77)(17, 64)(18, 59)(19, 78)(20, 63)(21, 76)(22, 57)(23, 74)(24, 83)(25, 80)(26, 75)(27, 62)(28, 79)(29, 60)(30, 73)(31, 58)(32, 67)(33, 94)(34, 55)(35, 90)(36, 53)(37, 72)(38, 51)(39, 92)(40, 89)(41, 84)(42, 85)(43, 56)(44, 81)(45, 82)(46, 87)(47, 86)(48, 61)(97, 146)(98, 153)(99, 148)(100, 155)(101, 150)(102, 157)(103, 184)(104, 183)(105, 154)(106, 161)(107, 156)(108, 163)(109, 158)(110, 165)(111, 176)(112, 175)(113, 162)(114, 145)(115, 164)(116, 147)(117, 166)(118, 149)(119, 192)(120, 191)(121, 186)(122, 169)(123, 188)(124, 171)(125, 190)(126, 173)(127, 168)(128, 167)(129, 170)(130, 177)(131, 172)(132, 179)(133, 174)(134, 181)(135, 160)(136, 159)(137, 178)(138, 185)(139, 180)(140, 187)(141, 182)(142, 189)(143, 152)(144, 151) MAP : A3.400 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, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4 * x.1^-1)^3, x.2 * x.3 * x.4^-1 * x.2 * x.4 * x.2^-1 * x.4^-1, x.4 * x.2 * x.4 * x.2 * x.4 * x.2^-1 * x.4 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #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, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 129)(74, 130)(75, 131)(76, 132)(77, 141)(78, 142)(79, 143)(80, 144)(81, 137)(82, 138)(83, 139)(84, 140)(85, 125)(86, 126)(87, 127)(88, 128)(89, 121)(90, 122)(91, 123)(92, 124)(93, 133)(94, 134)(95, 135)(96, 136) MAP : A3.404 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^3, (x.3 * x.4)^2, x.4 * x.2 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.2^2 * x.3 * x.2^2 * x.3^-1, (x.2^-1 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #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, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 126)(74, 127)(75, 125)(76, 142)(77, 123)(78, 121)(79, 122)(80, 129)(81, 128)(82, 136)(83, 144)(84, 143)(85, 138)(86, 139)(87, 137)(88, 130)(89, 135)(90, 133)(91, 134)(92, 141)(93, 140)(94, 124)(95, 132)(96, 131) MAP : A3.415 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.4 * x.1 * x.5^-1 * x.2, x.5^-1 * x.1 * x.5 * x.2, x.4 * x.2 * x.1 * x.4 * x.5^-1, (x.5 * x.3^-1)^3, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #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, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 140)(74, 124)(75, 132)(76, 131)(77, 128)(78, 136)(79, 144)(80, 143)(81, 123)(82, 121)(83, 122)(84, 129)(85, 135)(86, 133)(87, 134)(88, 141)(89, 138)(90, 139)(91, 137)(92, 130)(93, 126)(94, 127)(95, 125)(96, 142)(145, 151)(146, 149)(147, 150)(148, 157)(152, 162)(153, 166)(154, 167)(155, 165)(156, 158)(159, 164)(160, 163)(161, 168) MAP : A3.427 NOTES : type I, reflexible, isomorphic to Med2({4,8}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 44)(2, 61)(3, 45)(4, 48)(5, 38)(6, 59)(7, 54)(8, 60)(9, 43)(10, 63)(11, 62)(12, 52)(13, 58)(14, 55)(15, 50)(16, 49)(17, 39)(18, 40)(19, 46)(20, 34)(21, 47)(22, 35)(23, 57)(24, 42)(25, 64)(26, 36)(27, 33)(28, 41)(29, 37)(30, 53)(31, 51)(32, 56)(65, 99)(66, 105)(67, 121)(68, 101)(69, 104)(70, 122)(71, 120)(72, 115)(73, 106)(74, 113)(75, 116)(76, 126)(77, 123)(78, 114)(79, 119)(80, 127)(81, 98)(82, 102)(83, 100)(84, 103)(85, 97)(86, 108)(87, 109)(88, 107)(89, 117)(90, 110)(91, 111)(92, 125)(93, 112)(94, 128)(95, 124)(96, 118) MAP : A3.429 NOTES : type I, reflexible, isomorphic to Med2({4,8}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | (x.1 * x.2)^2, x.2^4, x.1^-1 * x.2^-1 * x.1 * x.2^-1 * x.1^-2, x.2^-2 * x.1 * x.2^-2 * x.1^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 36)(2, 52)(3, 34)(4, 42)(5, 58)(6, 50)(7, 49)(8, 38)(9, 39)(10, 47)(11, 60)(12, 63)(13, 53)(14, 57)(15, 64)(16, 59)(17, 37)(18, 43)(19, 33)(20, 44)(21, 40)(22, 48)(23, 45)(24, 35)(25, 51)(26, 54)(27, 41)(28, 55)(29, 62)(30, 56)(31, 61)(32, 46)(65, 99)(66, 115)(67, 104)(68, 113)(69, 97)(70, 120)(71, 121)(72, 101)(73, 107)(74, 116)(75, 98)(76, 100)(77, 103)(78, 112)(79, 122)(80, 102)(81, 119)(82, 118)(83, 105)(84, 114)(85, 125)(86, 106)(87, 108)(88, 110)(89, 126)(90, 117)(91, 128)(92, 123)(93, 111)(94, 109)(95, 124)(96, 127) MAP : A3.475 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) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 106)(98, 110)(99, 102)(100, 111)(101, 103)(104, 109)(105, 107)(108, 112) MAP : A3.495 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) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.519 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: [ 4, 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)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.871 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, (x.3 * x.1)^3, x.3 * x.2 * x.1 * x.3^-2 * x.1 * x.3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 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, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.872 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3 * x.2)^2, x.3 * x.1 * x.3^-1 * x.2 * x.1 * x.2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 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, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 35)(26, 33)(27, 34)(28, 41)(29, 46)(30, 47)(31, 45)(32, 38)(36, 42)(37, 48)(39, 40)(43, 44)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.873 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3^-1 * x.2)^2, x.3^4, x.1 * x.2 * x.1 * x.3^-2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 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, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(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, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.874 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, x.3^4, x.3 * x.2 * x.3^-2 * x.2 * x.1, x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.1, x.3^-1 * x.1 * x.2 * x.3^-2 * x.2, x.2 * x.3^2 * x.2 * x.3^-1 * x.1 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 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, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.876 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 4)(6, 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.3 * u.4^-1 * u.3^-1 * u.5^-1, (u.4 * u.1)^3, (u.5 * u.2)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5, x.2 * x.1, x.4^2 * x.5^-1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, x.1 * x.4 * x.1 * x.4 * x.1 * x.5^-1, (x.5 * x.2)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 39)(14, 37)(15, 38)(16, 45)(17, 44)(18, 40)(19, 48)(20, 47)(21, 42)(22, 43)(23, 41)(24, 46)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(61, 86)(62, 87)(63, 85)(64, 90)(65, 95)(66, 93)(67, 94)(68, 89)(69, 88)(70, 96)(71, 92)(72, 91)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84) MAP : A3.891 NOTES : type I, chiral, isomorphic to Snub({3,7}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^7, x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * 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, 3, 3, 7) #DARTS : 840 R = (1, 169, 337, 505, 673)(2, 170, 338, 506, 674)(3, 171, 339, 507, 675)(4, 172, 340, 508, 676)(5, 173, 341, 509, 677)(6, 174, 342, 510, 678)(7, 175, 343, 511, 679)(8, 176, 344, 512, 680)(9, 177, 345, 513, 681)(10, 178, 346, 514, 682)(11, 179, 347, 515, 683)(12, 180, 348, 516, 684)(13, 181, 349, 517, 685)(14, 182, 350, 518, 686)(15, 183, 351, 519, 687)(16, 184, 352, 520, 688)(17, 185, 353, 521, 689)(18, 186, 354, 522, 690)(19, 187, 355, 523, 691)(20, 188, 356, 524, 692)(21, 189, 357, 525, 693)(22, 190, 358, 526, 694)(23, 191, 359, 527, 695)(24, 192, 360, 528, 696)(25, 193, 361, 529, 697)(26, 194, 362, 530, 698)(27, 195, 363, 531, 699)(28, 196, 364, 532, 700)(29, 197, 365, 533, 701)(30, 198, 366, 534, 702)(31, 199, 367, 535, 703)(32, 200, 368, 536, 704)(33, 201, 369, 537, 705)(34, 202, 370, 538, 706)(35, 203, 371, 539, 707)(36, 204, 372, 540, 708)(37, 205, 373, 541, 709)(38, 206, 374, 542, 710)(39, 207, 375, 543, 711)(40, 208, 376, 544, 712)(41, 209, 377, 545, 713)(42, 210, 378, 546, 714)(43, 211, 379, 547, 715)(44, 212, 380, 548, 716)(45, 213, 381, 549, 717)(46, 214, 382, 550, 718)(47, 215, 383, 551, 719)(48, 216, 384, 552, 720)(49, 217, 385, 553, 721)(50, 218, 386, 554, 722)(51, 219, 387, 555, 723)(52, 220, 388, 556, 724)(53, 221, 389, 557, 725)(54, 222, 390, 558, 726)(55, 223, 391, 559, 727)(56, 224, 392, 560, 728)(57, 225, 393, 561, 729)(58, 226, 394, 562, 730)(59, 227, 395, 563, 731)(60, 228, 396, 564, 732)(61, 229, 397, 565, 733)(62, 230, 398, 566, 734)(63, 231, 399, 567, 735)(64, 232, 400, 568, 736)(65, 233, 401, 569, 737)(66, 234, 402, 570, 738)(67, 235, 403, 571, 739)(68, 236, 404, 572, 740)(69, 237, 405, 573, 741)(70, 238, 406, 574, 742)(71, 239, 407, 575, 743)(72, 240, 408, 576, 744)(73, 241, 409, 577, 745)(74, 242, 410, 578, 746)(75, 243, 411, 579, 747)(76, 244, 412, 580, 748)(77, 245, 413, 581, 749)(78, 246, 414, 582, 750)(79, 247, 415, 583, 751)(80, 248, 416, 584, 752)(81, 249, 417, 585, 753)(82, 250, 418, 586, 754)(83, 251, 419, 587, 755)(84, 252, 420, 588, 756)(85, 253, 421, 589, 757)(86, 254, 422, 590, 758)(87, 255, 423, 591, 759)(88, 256, 424, 592, 760)(89, 257, 425, 593, 761)(90, 258, 426, 594, 762)(91, 259, 427, 595, 763)(92, 260, 428, 596, 764)(93, 261, 429, 597, 765)(94, 262, 430, 598, 766)(95, 263, 431, 599, 767)(96, 264, 432, 600, 768)(97, 265, 433, 601, 769)(98, 266, 434, 602, 770)(99, 267, 435, 603, 771)(100, 268, 436, 604, 772)(101, 269, 437, 605, 773)(102, 270, 438, 606, 774)(103, 271, 439, 607, 775)(104, 272, 440, 608, 776)(105, 273, 441, 609, 777)(106, 274, 442, 610, 778)(107, 275, 443, 611, 779)(108, 276, 444, 612, 780)(109, 277, 445, 613, 781)(110, 278, 446, 614, 782)(111, 279, 447, 615, 783)(112, 280, 448, 616, 784)(113, 281, 449, 617, 785)(114, 282, 450, 618, 786)(115, 283, 451, 619, 787)(116, 284, 452, 620, 788)(117, 285, 453, 621, 789)(118, 286, 454, 622, 790)(119, 287, 455, 623, 791)(120, 288, 456, 624, 792)(121, 289, 457, 625, 793)(122, 290, 458, 626, 794)(123, 291, 459, 627, 795)(124, 292, 460, 628, 796)(125, 293, 461, 629, 797)(126, 294, 462, 630, 798)(127, 295, 463, 631, 799)(128, 296, 464, 632, 800)(129, 297, 465, 633, 801)(130, 298, 466, 634, 802)(131, 299, 467, 635, 803)(132, 300, 468, 636, 804)(133, 301, 469, 637, 805)(134, 302, 470, 638, 806)(135, 303, 471, 639, 807)(136, 304, 472, 640, 808)(137, 305, 473, 641, 809)(138, 306, 474, 642, 810)(139, 307, 475, 643, 811)(140, 308, 476, 644, 812)(141, 309, 477, 645, 813)(142, 310, 478, 646, 814)(143, 311, 479, 647, 815)(144, 312, 480, 648, 816)(145, 313, 481, 649, 817)(146, 314, 482, 650, 818)(147, 315, 483, 651, 819)(148, 316, 484, 652, 820)(149, 317, 485, 653, 821)(150, 318, 486, 654, 822)(151, 319, 487, 655, 823)(152, 320, 488, 656, 824)(153, 321, 489, 657, 825)(154, 322, 490, 658, 826)(155, 323, 491, 659, 827)(156, 324, 492, 660, 828)(157, 325, 493, 661, 829)(158, 326, 494, 662, 830)(159, 327, 495, 663, 831)(160, 328, 496, 664, 832)(161, 329, 497, 665, 833)(162, 330, 498, 666, 834)(163, 331, 499, 667, 835)(164, 332, 500, 668, 836)(165, 333, 501, 669, 837)(166, 334, 502, 670, 838)(167, 335, 503, 671, 839)(168, 336, 504, 672, 840) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 339)(170, 356)(171, 354)(172, 359)(173, 355)(174, 431)(175, 430)(176, 372)(177, 341)(178, 344)(179, 358)(180, 493)(181, 495)(182, 476)(183, 491)(184, 494)(185, 338)(186, 337)(187, 345)(188, 353)(189, 361)(190, 370)(191, 369)(192, 362)(193, 408)(194, 405)(195, 496)(196, 403)(197, 478)(198, 401)(199, 402)(200, 479)(201, 340)(202, 347)(203, 349)(204, 346)(205, 440)(206, 363)(207, 348)(208, 437)(209, 398)(210, 399)(211, 396)(212, 454)(213, 394)(214, 461)(215, 464)(216, 393)(217, 343)(218, 342)(219, 455)(220, 352)(221, 452)(222, 456)(223, 453)(224, 459)(225, 487)(226, 486)(227, 415)(228, 472)(229, 412)(230, 416)(231, 413)(232, 395)(233, 484)(234, 467)(235, 469)(236, 466)(237, 360)(238, 451)(239, 468)(240, 357)(241, 382)(242, 383)(243, 380)(244, 414)(245, 378)(246, 397)(247, 400)(248, 377)(249, 482)(250, 481)(251, 465)(252, 497)(253, 449)(254, 490)(255, 489)(256, 450)(257, 392)(258, 389)(259, 424)(260, 387)(261, 406)(262, 385)(263, 386)(264, 407)(265, 483)(266, 500)(267, 498)(268, 503)(269, 499)(270, 351)(271, 350)(272, 492)(273, 485)(274, 488)(275, 502)(276, 421)(277, 423)(278, 404)(279, 419)(280, 422)(281, 444)(282, 427)(283, 429)(284, 426)(285, 504)(286, 411)(287, 428)(288, 501)(289, 442)(290, 441)(291, 425)(292, 433)(293, 409)(294, 418)(295, 417)(296, 410)(297, 447)(298, 446)(299, 367)(300, 432)(301, 364)(302, 368)(303, 365)(304, 379)(305, 443)(306, 436)(307, 434)(308, 439)(309, 435)(310, 471)(311, 470)(312, 420)(313, 462)(314, 463)(315, 460)(316, 366)(317, 458)(318, 381)(319, 384)(320, 457)(321, 445)(322, 448)(323, 438)(324, 373)(325, 375)(326, 388)(327, 371)(328, 374)(329, 480)(330, 477)(331, 376)(332, 475)(333, 390)(334, 473)(335, 474)(336, 391)(505, 683)(506, 676)(507, 674)(508, 679)(509, 675)(510, 735)(511, 734)(512, 692)(513, 685)(514, 688)(515, 678)(516, 789)(517, 791)(518, 804)(519, 787)(520, 790)(521, 682)(522, 681)(523, 697)(524, 673)(525, 713)(526, 690)(527, 689)(528, 714)(529, 776)(530, 773)(531, 792)(532, 771)(533, 806)(534, 769)(535, 770)(536, 807)(537, 684)(538, 699)(539, 701)(540, 698)(541, 768)(542, 715)(543, 700)(544, 765)(545, 758)(546, 759)(547, 756)(548, 838)(549, 754)(550, 821)(551, 824)(552, 753)(553, 687)(554, 686)(555, 839)(556, 704)(557, 836)(558, 840)(559, 837)(560, 819)(561, 815)(562, 814)(563, 743)(564, 832)(565, 740)(566, 744)(567, 741)(568, 755)(569, 812)(570, 827)(571, 829)(572, 826)(573, 680)(574, 835)(575, 828)(576, 677)(577, 726)(578, 727)(579, 724)(580, 742)(581, 722)(582, 757)(583, 760)(584, 721)(585, 810)(586, 809)(587, 825)(588, 793)(589, 833)(590, 786)(591, 785)(592, 834)(593, 712)(594, 709)(595, 784)(596, 707)(597, 774)(598, 705)(599, 706)(600, 775)(601, 811)(602, 796)(603, 794)(604, 799)(605, 795)(606, 703)(607, 702)(608, 788)(609, 813)(610, 816)(611, 798)(612, 781)(613, 783)(614, 772)(615, 779)(616, 782)(617, 748)(618, 731)(619, 733)(620, 730)(621, 800)(622, 739)(623, 732)(624, 797)(625, 746)(626, 745)(627, 729)(628, 761)(629, 737)(630, 778)(631, 777)(632, 738)(633, 751)(634, 750)(635, 719)(636, 736)(637, 716)(638, 720)(639, 717)(640, 723)(641, 747)(642, 764)(643, 762)(644, 767)(645, 763)(646, 831)(647, 830)(648, 780)(649, 822)(650, 823)(651, 820)(652, 718)(653, 818)(654, 725)(655, 728)(656, 817)(657, 749)(658, 752)(659, 766)(660, 693)(661, 695)(662, 708)(663, 691)(664, 694)(665, 808)(666, 805)(667, 696)(668, 803)(669, 710)(670, 801)(671, 802)(672, 711) MAP : A3.895 NOTES : type I, chiral, isomorphic to Snub({3,8}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^8, x.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-2 * x.3, x.2^2 * x.3 * x.2^-2 * x.1 * x.2 * x.3^-1 * x.2^-3 * x.1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 480 R = (1, 97, 193, 289, 385)(2, 98, 194, 290, 386)(3, 99, 195, 291, 387)(4, 100, 196, 292, 388)(5, 101, 197, 293, 389)(6, 102, 198, 294, 390)(7, 103, 199, 295, 391)(8, 104, 200, 296, 392)(9, 105, 201, 297, 393)(10, 106, 202, 298, 394)(11, 107, 203, 299, 395)(12, 108, 204, 300, 396)(13, 109, 205, 301, 397)(14, 110, 206, 302, 398)(15, 111, 207, 303, 399)(16, 112, 208, 304, 400)(17, 113, 209, 305, 401)(18, 114, 210, 306, 402)(19, 115, 211, 307, 403)(20, 116, 212, 308, 404)(21, 117, 213, 309, 405)(22, 118, 214, 310, 406)(23, 119, 215, 311, 407)(24, 120, 216, 312, 408)(25, 121, 217, 313, 409)(26, 122, 218, 314, 410)(27, 123, 219, 315, 411)(28, 124, 220, 316, 412)(29, 125, 221, 317, 413)(30, 126, 222, 318, 414)(31, 127, 223, 319, 415)(32, 128, 224, 320, 416)(33, 129, 225, 321, 417)(34, 130, 226, 322, 418)(35, 131, 227, 323, 419)(36, 132, 228, 324, 420)(37, 133, 229, 325, 421)(38, 134, 230, 326, 422)(39, 135, 231, 327, 423)(40, 136, 232, 328, 424)(41, 137, 233, 329, 425)(42, 138, 234, 330, 426)(43, 139, 235, 331, 427)(44, 140, 236, 332, 428)(45, 141, 237, 333, 429)(46, 142, 238, 334, 430)(47, 143, 239, 335, 431)(48, 144, 240, 336, 432)(49, 145, 241, 337, 433)(50, 146, 242, 338, 434)(51, 147, 243, 339, 435)(52, 148, 244, 340, 436)(53, 149, 245, 341, 437)(54, 150, 246, 342, 438)(55, 151, 247, 343, 439)(56, 152, 248, 344, 440)(57, 153, 249, 345, 441)(58, 154, 250, 346, 442)(59, 155, 251, 347, 443)(60, 156, 252, 348, 444)(61, 157, 253, 349, 445)(62, 158, 254, 350, 446)(63, 159, 255, 351, 447)(64, 160, 256, 352, 448)(65, 161, 257, 353, 449)(66, 162, 258, 354, 450)(67, 163, 259, 355, 451)(68, 164, 260, 356, 452)(69, 165, 261, 357, 453)(70, 166, 262, 358, 454)(71, 167, 263, 359, 455)(72, 168, 264, 360, 456)(73, 169, 265, 361, 457)(74, 170, 266, 362, 458)(75, 171, 267, 363, 459)(76, 172, 268, 364, 460)(77, 173, 269, 365, 461)(78, 174, 270, 366, 462)(79, 175, 271, 367, 463)(80, 176, 272, 368, 464)(81, 177, 273, 369, 465)(82, 178, 274, 370, 466)(83, 179, 275, 371, 467)(84, 180, 276, 372, 468)(85, 181, 277, 373, 469)(86, 182, 278, 374, 470)(87, 183, 279, 375, 471)(88, 184, 280, 376, 472)(89, 185, 281, 377, 473)(90, 186, 282, 378, 474)(91, 187, 283, 379, 475)(92, 188, 284, 380, 476)(93, 189, 285, 381, 477)(94, 190, 286, 382, 478)(95, 191, 287, 383, 479)(96, 192, 288, 384, 480) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 195)(98, 196)(99, 198)(100, 199)(101, 200)(102, 202)(103, 203)(104, 204)(105, 236)(106, 265)(107, 270)(108, 207)(109, 231)(110, 230)(111, 269)(112, 253)(113, 197)(114, 193)(115, 226)(116, 229)(117, 194)(118, 273)(119, 274)(120, 225)(121, 228)(122, 275)(123, 276)(124, 277)(125, 227)(126, 232)(127, 280)(128, 281)(129, 206)(130, 205)(131, 287)(132, 282)(133, 201)(134, 272)(135, 288)(136, 283)(137, 278)(138, 267)(139, 271)(140, 208)(141, 284)(142, 279)(143, 266)(144, 286)(145, 211)(146, 212)(147, 214)(148, 215)(149, 216)(150, 218)(151, 219)(152, 220)(153, 268)(154, 233)(155, 238)(156, 223)(157, 263)(158, 262)(159, 237)(160, 285)(161, 213)(162, 209)(163, 258)(164, 261)(165, 210)(166, 241)(167, 242)(168, 257)(169, 260)(170, 243)(171, 244)(172, 245)(173, 259)(174, 264)(175, 248)(176, 249)(177, 222)(178, 221)(179, 255)(180, 250)(181, 217)(182, 240)(183, 256)(184, 251)(185, 246)(186, 235)(187, 239)(188, 224)(189, 252)(190, 247)(191, 234)(192, 254)(289, 393)(290, 398)(291, 388)(292, 392)(293, 397)(294, 389)(295, 385)(296, 387)(297, 391)(298, 418)(299, 421)(300, 386)(301, 390)(302, 396)(303, 417)(304, 420)(305, 479)(306, 474)(307, 464)(308, 480)(309, 475)(310, 459)(311, 463)(312, 400)(313, 399)(314, 460)(315, 454)(316, 458)(317, 395)(318, 394)(319, 455)(320, 451)(321, 409)(322, 414)(323, 404)(324, 408)(325, 413)(326, 405)(327, 401)(328, 403)(329, 407)(330, 450)(331, 453)(332, 402)(333, 406)(334, 412)(335, 449)(336, 452)(337, 439)(338, 444)(339, 440)(340, 435)(341, 438)(342, 445)(343, 441)(344, 436)(345, 433)(346, 462)(347, 461)(348, 446)(349, 437)(350, 434)(351, 457)(352, 456)(353, 471)(354, 476)(355, 472)(356, 467)(357, 470)(358, 477)(359, 473)(360, 468)(361, 465)(362, 430)(363, 429)(364, 478)(365, 469)(366, 466)(367, 425)(368, 424)(369, 447)(370, 442)(371, 432)(372, 448)(373, 443)(374, 427)(375, 431)(376, 416)(377, 415)(378, 428)(379, 422)(380, 426)(381, 411)(382, 410)(383, 423)(384, 419) MAP : A3.899 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) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.1 * x.3^-2 * x.2 * x.3^3, 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 : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 126)(50, 110)(51, 119)(52, 125)(53, 142)(54, 103)(55, 109)(56, 135)(57, 118)(58, 114)(59, 108)(60, 111)(61, 102)(62, 140)(63, 107)(64, 100)(65, 123)(66, 127)(67, 116)(68, 121)(69, 124)(70, 128)(71, 144)(72, 141)(73, 115)(74, 113)(75, 122)(76, 138)(77, 112)(78, 143)(79, 106)(80, 105)(81, 133)(82, 129)(83, 136)(84, 104)(85, 130)(86, 131)(87, 132)(88, 134)(89, 120)(90, 117)(91, 101)(92, 98)(93, 137)(94, 139)(95, 97)(96, 99)(145, 227)(146, 233)(147, 225)(148, 229)(149, 228)(150, 234)(151, 202)(152, 235)(153, 226)(154, 230)(155, 232)(156, 200)(157, 218)(158, 201)(159, 216)(160, 213)(161, 199)(162, 198)(163, 206)(164, 222)(165, 205)(166, 194)(167, 193)(168, 236)(169, 238)(170, 231)(171, 215)(172, 221)(173, 197)(174, 195)(175, 214)(176, 210)(177, 224)(178, 208)(179, 223)(180, 219)(181, 240)(182, 207)(183, 203)(184, 239)(185, 220)(186, 237)(187, 212)(188, 217)(189, 204)(190, 196)(191, 211)(192, 209) MAP : A3.907 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) : <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.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #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, 6)(2, 7)(3, 5)(4, 22)(8, 9)(10, 16)(11, 24)(12, 23)(13, 18)(14, 19)(15, 17)(20, 21)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.908 NOTES : type I, reflexible, 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) : <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.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #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, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(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, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.909 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) : <24, 12> 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.1)^2, x.4^4, x.4 * x.3 * x.4^-2 * x.3 * x.2, (x.4 * x.3)^3, (x.3 * x.2)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #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, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.910 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) : <24, 12> 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.4^4, x.1 * x.3 * x.4^-2 * x.3, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #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, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(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, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.916 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) : <48, 48> 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.3^-1 * x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 4)(2, 5)(3, 40)(6, 7)(8, 45)(9, 24)(10, 19)(11, 46)(12, 23)(13, 44)(14, 17)(15, 42)(16, 27)(18, 39)(20, 37)(21, 32)(22, 35)(25, 28)(26, 29)(30, 31)(33, 48)(34, 43)(36, 47)(38, 41)(49, 99)(50, 118)(51, 103)(52, 114)(53, 97)(54, 144)(55, 101)(56, 142)(57, 127)(58, 108)(59, 125)(60, 128)(61, 123)(62, 106)(63, 121)(64, 124)(65, 109)(66, 104)(67, 105)(68, 134)(69, 111)(70, 132)(71, 107)(72, 98)(73, 131)(74, 126)(75, 135)(76, 122)(77, 129)(78, 112)(79, 133)(80, 110)(81, 119)(82, 140)(83, 117)(84, 120)(85, 115)(86, 138)(87, 113)(88, 116)(89, 141)(90, 136)(91, 137)(92, 102)(93, 143)(94, 100)(95, 139)(96, 130)(145, 194)(146, 201)(147, 196)(148, 203)(149, 198)(150, 205)(151, 232)(152, 231)(153, 202)(154, 209)(155, 204)(156, 211)(157, 206)(158, 213)(159, 224)(160, 223)(161, 210)(162, 193)(163, 212)(164, 195)(165, 214)(166, 197)(167, 240)(168, 239)(169, 234)(170, 217)(171, 236)(172, 219)(173, 238)(174, 221)(175, 216)(176, 215)(177, 218)(178, 225)(179, 220)(180, 227)(181, 222)(182, 229)(183, 208)(184, 207)(185, 226)(186, 233)(187, 228)(188, 235)(189, 230)(190, 237)(191, 200)(192, 199) MAP : A3.918 NOTES : type I, chiral, isomorphic to Snub({4,8}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> 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.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 82)(34, 86)(35, 84)(36, 87)(37, 81)(38, 92)(39, 93)(40, 91)(41, 69)(42, 94)(43, 95)(44, 77)(45, 96)(46, 80)(47, 76)(48, 70)(49, 83)(50, 89)(51, 73)(52, 85)(53, 88)(54, 74)(55, 72)(56, 67)(57, 90)(58, 65)(59, 68)(60, 78)(61, 75)(62, 66)(63, 71)(64, 79)(97, 140)(98, 157)(99, 141)(100, 144)(101, 134)(102, 155)(103, 150)(104, 156)(105, 139)(106, 159)(107, 158)(108, 148)(109, 154)(110, 151)(111, 146)(112, 145)(113, 135)(114, 136)(115, 142)(116, 130)(117, 143)(118, 131)(119, 153)(120, 138)(121, 160)(122, 132)(123, 129)(124, 137)(125, 133)(126, 149)(127, 147)(128, 152) MAP : A3.921 NOTES : type I, chiral, isomorphic to Snub({4,8}), QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^2 * x.1 * x.3^-1 * x.2, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 94)(34, 78)(35, 77)(36, 73)(37, 89)(38, 93)(39, 96)(40, 71)(41, 70)(42, 67)(43, 88)(44, 83)(45, 91)(46, 90)(47, 81)(48, 85)(49, 75)(50, 69)(51, 80)(52, 72)(53, 76)(54, 65)(55, 66)(56, 79)(57, 95)(58, 87)(59, 74)(60, 86)(61, 68)(62, 92)(63, 82)(64, 84)(97, 143)(98, 159)(99, 140)(100, 160)(101, 144)(102, 156)(103, 154)(104, 139)(105, 133)(106, 142)(107, 141)(108, 158)(109, 134)(110, 129)(111, 153)(112, 135)(113, 150)(114, 151)(115, 138)(116, 157)(117, 146)(118, 137)(119, 136)(120, 148)(121, 132)(122, 155)(123, 145)(124, 149)(125, 131)(126, 130)(127, 152)(128, 147) MAP : A3.944 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.3^-1)^2, x.3^-1 * x.1 * x.3^-1 * x.2^-1, (x.2^-1 * x.1)^2, x.2^4 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 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, 96)(2, 80)(3, 88)(4, 87)(5, 76)(6, 84)(7, 92)(8, 91)(9, 79)(10, 77)(11, 78)(12, 85)(13, 83)(14, 81)(15, 82)(16, 89)(17, 94)(18, 95)(19, 93)(20, 86)(21, 74)(22, 75)(23, 73)(24, 90)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.945 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) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^2, x.2^3, x.5^3, x.4 * x.5 * x.4^-1 * x.2, x.5 * x.4 * x.5 * x.2^-1, x.1 * x.2^-1 * x.3 * x.5^-1, x.5 * x.2 * x.3 * x.4, (x.4 * x.1^-1)^2, x.3 * x.5 * x.2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 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, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 26)(14, 27)(15, 25)(16, 30)(17, 35)(18, 33)(19, 34)(20, 29)(21, 28)(22, 36)(23, 32)(24, 31)(37, 90)(38, 91)(39, 89)(40, 94)(41, 87)(42, 85)(43, 86)(44, 93)(45, 92)(46, 88)(47, 96)(48, 95)(49, 83)(50, 81)(51, 82)(52, 77)(53, 76)(54, 84)(55, 80)(56, 79)(57, 74)(58, 75)(59, 73)(60, 78)(97, 112)(98, 120)(99, 116)(100, 115)(101, 110)(102, 111)(103, 109)(104, 114)(105, 119)(106, 117)(107, 118)(108, 113) MAP : A3.947 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, x.2^3, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, x.1 * x.3^-1 * x.1 * x.2 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 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, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 57)(26, 58)(27, 59)(28, 60)(29, 69)(30, 70)(31, 71)(32, 72)(33, 65)(34, 66)(35, 67)(36, 68)(37, 53)(38, 54)(39, 55)(40, 56)(41, 49)(42, 50)(43, 51)(44, 52)(45, 61)(46, 62)(47, 63)(48, 64)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.950 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, x.2^3, (x.2^-1 * x.3)^2, (x.2^-1 * x.1)^2, (x.3^-1 * x.1)^2 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 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, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.951 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.3^-1)^2, (x.2^-1 * x.1)^2, x.2^4, x.1 * x.2^-1 * x.3 * x.2 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 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, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.952 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 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.4^3, u.4 * u.1 * u.2 * u.3 > 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.4 * x.1 * x.2 * x.3, (x.4 * x.2)^2, x.4^-1 * x.3 * x.4^-1 * x.1 * x.3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 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, 105)(2, 106)(3, 107)(4, 108)(5, 117)(6, 118)(7, 119)(8, 120)(9, 113)(10, 114)(11, 115)(12, 116)(13, 101)(14, 102)(15, 103)(16, 104)(17, 97)(18, 98)(19, 99)(20, 100)(21, 109)(22, 110)(23, 111)(24, 112)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96) MAP : A3.953 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 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.4^3, u.4 * u.1 * u.2 * u.3 > 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.4 * x.1 * x.2 * x.3, x.4^-1 * x.1 * x.4 * x.3, x.2 * x.3 * x.1 * x.2 * x.4^-1, x.1 * x.2 * x.4^-1 * x.2 * x.3, (x.3 * x.1)^3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 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, 113)(2, 114)(3, 115)(4, 116)(5, 109)(6, 110)(7, 111)(8, 112)(9, 97)(10, 98)(11, 99)(12, 100)(13, 117)(14, 118)(15, 119)(16, 120)(17, 105)(18, 106)(19, 107)(20, 108)(21, 101)(22, 102)(23, 103)(24, 104)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 60)(50, 68)(51, 52)(53, 64)(54, 72)(55, 56)(57, 67)(58, 65)(59, 66)(61, 71)(62, 69)(63, 70)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96) MAP : A3.955 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 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.4^3, u.4 * u.1 * u.2 * u.3 > 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.4^-1 * x.3 * x.2, x.3 * x.4^-1 * x.2 * x.4, (x.3 * x.1)^2 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 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, 100)(2, 108)(3, 116)(4, 115)(5, 120)(6, 104)(7, 112)(8, 111)(9, 107)(10, 105)(11, 106)(12, 113)(13, 103)(14, 101)(15, 102)(16, 109)(17, 98)(18, 99)(19, 97)(20, 114)(21, 118)(22, 119)(23, 117)(24, 110)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.961 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, {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.5^3, u.6^3, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^3, x.6^3, x.4 * x.2 * x.5^-1, x.1 * x.5^-1 * x.6^-1, x.2 * x.6 * x.1 * x.6^-1, x.4 * x.5^-1 * x.1 * x.3^-1, (x.2 * x.1)^2, x.3 * x.4^-1 * x.2 * x.6^-1, x.4 * x.1 * x.2 * x.6 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (3, 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, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 63)(14, 61)(15, 62)(16, 69)(17, 68)(18, 64)(19, 72)(20, 71)(21, 66)(22, 67)(23, 65)(24, 70)(25, 40)(26, 48)(27, 44)(28, 43)(29, 38)(30, 39)(31, 37)(32, 42)(33, 47)(34, 45)(35, 46)(36, 41)(49, 60)(50, 56)(51, 52)(53, 58)(54, 59)(55, 57)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 105)(86, 106)(87, 107)(88, 108)(89, 97)(90, 98)(91, 99)(92, 100)(93, 101)(94, 102)(95, 103)(96, 104) MAP : A3.966 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 45)(10, 48)(11, 47)(12, 41)(13, 46)(14, 44)(15, 42)(16, 43)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 34)(35, 38)(36, 39)(37, 40)(49, 50)(51, 54)(52, 55)(53, 56)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.968 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 44)(10, 47)(11, 48)(12, 46)(13, 41)(14, 45)(15, 43)(16, 42)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 35)(34, 38)(36, 40)(37, 39)(49, 50)(51, 54)(52, 55)(53, 56)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.969 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) : <16, 13> 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.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 63)(50, 56)(51, 58)(52, 54)(53, 59)(55, 62)(57, 60)(61, 64) MAP : A3.1004 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 149)(98, 145)(99, 172)(100, 161)(101, 163)(102, 148)(103, 147)(104, 150)(105, 181)(106, 155)(107, 162)(108, 165)(109, 156)(110, 157)(111, 192)(112, 173)(113, 152)(114, 183)(115, 146)(116, 170)(117, 158)(118, 151)(119, 184)(120, 178)(121, 167)(122, 153)(123, 175)(124, 166)(125, 168)(126, 177)(127, 174)(128, 187)(129, 171)(130, 160)(131, 185)(132, 188)(133, 164)(134, 189)(135, 154)(136, 190)(137, 159)(138, 182)(139, 180)(140, 176)(141, 191)(142, 169)(143, 186)(144, 179)(193, 277)(194, 273)(195, 252)(196, 241)(197, 243)(198, 276)(199, 275)(200, 278)(201, 261)(202, 283)(203, 242)(204, 245)(205, 284)(206, 285)(207, 272)(208, 253)(209, 280)(210, 263)(211, 274)(212, 250)(213, 286)(214, 279)(215, 264)(216, 258)(217, 247)(218, 281)(219, 255)(220, 246)(221, 248)(222, 257)(223, 254)(224, 267)(225, 251)(226, 288)(227, 265)(228, 268)(229, 244)(230, 269)(231, 282)(232, 270)(233, 287)(234, 262)(235, 260)(236, 256)(237, 271)(238, 249)(239, 266)(240, 259) MAP : A3.1028 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) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.3 * x.1 * x.3^-1, x.3^6 > 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 : 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, 26)(2, 29)(3, 31)(4, 35)(5, 25)(6, 39)(7, 42)(8, 47)(9, 36)(10, 44)(11, 37)(12, 38)(13, 28)(14, 33)(15, 45)(16, 34)(17, 32)(18, 27)(19, 46)(20, 40)(21, 30)(22, 48)(23, 41)(24, 43)(49, 76)(50, 84)(51, 77)(52, 78)(53, 92)(54, 73)(55, 85)(56, 74)(57, 96)(58, 91)(59, 86)(60, 80)(61, 94)(62, 88)(63, 81)(64, 83)(65, 90)(66, 93)(67, 95)(68, 75)(69, 89)(70, 79)(71, 82)(72, 87)(97, 141)(98, 137)(99, 130)(100, 125)(101, 138)(102, 133)(103, 139)(104, 129)(105, 126)(106, 128)(107, 140)(108, 121)(109, 123)(110, 124)(111, 142)(112, 132)(113, 135)(114, 143)(115, 136)(116, 122)(117, 127)(118, 131)(119, 144)(120, 134) MAP : A3.1034 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^-2, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83)(85, 108)(86, 115)(87, 111)(88, 110)(89, 122)(90, 106)(91, 117)(92, 126)(93, 116)(94, 119)(95, 125)(96, 118)(97, 112)(98, 107)(99, 124)(100, 120)(101, 109)(102, 113)(103, 121)(104, 114)(105, 123) MAP : A3.1036 NOTES : type I, reflexible, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.1^-1 * x.2 * x.3^-1, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83)(85, 116)(86, 118)(87, 121)(88, 107)(89, 126)(90, 110)(91, 108)(92, 114)(93, 117)(94, 124)(95, 119)(96, 113)(97, 109)(98, 106)(99, 125)(100, 112)(101, 120)(102, 115)(103, 123)(104, 122)(105, 111) MAP : A3.1046 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(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.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * 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 * x.4^-1 * x.1, x.4^3, x.3 * x.4 * x.2 * x.4, (x.3^-1 * x.2)^2, x.4 * x.1 * x.3 * x.4, x.3^4, (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, 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, 120)(2, 104)(3, 112)(4, 111)(5, 100)(6, 108)(7, 116)(8, 115)(9, 103)(10, 101)(11, 102)(12, 109)(13, 107)(14, 105)(15, 106)(16, 113)(17, 118)(18, 119)(19, 117)(20, 110)(21, 98)(22, 99)(23, 97)(24, 114)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1047 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) : <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.3^3, (x.2 * x.4^-1)^2, (x.2 * x.1)^2, x.4^4, x.1 * x.3 * x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.4^2 * x.3^-1 > 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 : 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, 6)(2, 7)(3, 5)(4, 22)(8, 9)(10, 16)(11, 24)(12, 23)(13, 18)(14, 19)(15, 17)(20, 21)(25, 52)(26, 60)(27, 68)(28, 67)(29, 72)(30, 56)(31, 64)(32, 63)(33, 59)(34, 57)(35, 58)(36, 65)(37, 55)(38, 53)(39, 54)(40, 61)(41, 50)(42, 51)(43, 49)(44, 66)(45, 70)(46, 71)(47, 69)(48, 62)(73, 134)(74, 135)(75, 133)(76, 126)(77, 139)(78, 137)(79, 138)(80, 121)(81, 136)(82, 144)(83, 128)(84, 127)(85, 130)(86, 131)(87, 129)(88, 122)(89, 143)(90, 141)(91, 142)(92, 125)(93, 132)(94, 140)(95, 124)(96, 123)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.1048 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) : <12, 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.3^3, x.4^2 * x.7^-1, x.6^3, 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.3 * x.4 * x.1 * 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 : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 55)(26, 53)(27, 54)(28, 49)(29, 60)(30, 56)(31, 52)(32, 51)(33, 58)(34, 59)(35, 57)(36, 50)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 135)(74, 133)(75, 134)(76, 141)(77, 140)(78, 136)(79, 144)(80, 143)(81, 138)(82, 139)(83, 137)(84, 142)(85, 90)(86, 91)(87, 89)(88, 94)(92, 93)(95, 96)(97, 124)(98, 132)(99, 128)(100, 127)(101, 122)(102, 123)(103, 121)(104, 126)(105, 131)(106, 129)(107, 130)(108, 125) MAP : A3.1049 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) : <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.3^3, x.4^3, (x.4 * x.2)^2, x.2 * x.3 * x.4^-1 * x.2 * x.3^-1 > 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 : 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, 10)(4, 17)(5, 22)(6, 23)(7, 21)(8, 14)(12, 18)(13, 24)(15, 16)(19, 20)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1050 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) : <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.3^3, x.4^3, (x.3 * x.2)^2, (x.4 * x.2)^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 : 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, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1052 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(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.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * 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 * x.4^-1 * x.1, x.4^3, x.3^-1 * x.4^-1 * x.2 * x.1, (x.3^-1 * x.2)^2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 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, 110)(2, 111)(3, 109)(4, 102)(5, 115)(6, 113)(7, 114)(8, 97)(9, 112)(10, 120)(11, 104)(12, 103)(13, 106)(14, 107)(15, 105)(16, 98)(17, 119)(18, 117)(19, 118)(20, 101)(21, 108)(22, 116)(23, 100)(24, 99)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1053 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) : <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.3^3, x.4^3, (x.2 * x.4^-1)^2, (x.2 * x.1)^2, x.3 * x.4 * x.1 * x.4^-1 * x.3^-1 * x.1 > 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 : 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, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 52)(26, 60)(27, 68)(28, 67)(29, 72)(30, 56)(31, 64)(32, 63)(33, 59)(34, 57)(35, 58)(36, 65)(37, 55)(38, 53)(39, 54)(40, 61)(41, 50)(42, 51)(43, 49)(44, 66)(45, 70)(46, 71)(47, 69)(48, 62)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1059 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(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.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * 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 * x.4^-1 * x.1, x.4^3, (x.3^-1 * x.2)^2, x.3^4, (x.4 * x.2)^2, x.1 * x.3^-1 * x.4 * x.1 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 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, 120)(2, 104)(3, 112)(4, 111)(5, 100)(6, 108)(7, 116)(8, 115)(9, 103)(10, 101)(11, 102)(12, 109)(13, 107)(14, 105)(15, 106)(16, 113)(17, 118)(18, 119)(19, 117)(20, 110)(21, 98)(22, 99)(23, 97)(24, 114)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1062 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4^3, x.3^-1 * x.1 * x.2, (x.4^-1 * x.2)^2, (x.3 * x.4^-1)^2, x.3^4, x.1 * x.4 * x.3 * 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, 3, 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, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120)(121, 127)(122, 125)(123, 126)(124, 133)(128, 138)(129, 142)(130, 143)(131, 141)(132, 134)(135, 140)(136, 139)(137, 144) MAP : A3.1063 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4^3, x.3^-1 * x.1 * x.2, x.4 * x.3 * x.4 * x.2, (x.3 * x.4^-1)^2, x.3^4 > 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 : 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, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 108)(98, 116)(99, 100)(101, 112)(102, 120)(103, 104)(105, 115)(106, 113)(107, 114)(109, 119)(110, 117)(111, 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 : A3.1064 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: [ 4, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.3^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.1^-1 * x.2)^2, (x.3 * x.2^-1)^2, x.1^4, x.3^4 > 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 : 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, 26)(2, 39)(3, 32)(4, 25)(5, 31)(6, 36)(7, 42)(8, 34)(9, 44)(10, 41)(11, 33)(12, 47)(13, 30)(14, 35)(15, 28)(16, 29)(17, 27)(18, 40)(19, 46)(20, 38)(21, 48)(22, 45)(23, 37)(24, 43)(49, 86)(50, 75)(51, 92)(52, 85)(53, 91)(54, 96)(55, 78)(56, 94)(57, 80)(58, 77)(59, 93)(60, 83)(61, 90)(62, 95)(63, 88)(64, 89)(65, 87)(66, 76)(67, 82)(68, 74)(69, 84)(70, 81)(71, 73)(72, 79)(97, 132)(98, 129)(99, 121)(100, 127)(101, 128)(102, 125)(103, 141)(104, 131)(105, 139)(106, 144)(107, 126)(108, 142)(109, 135)(110, 124)(111, 130)(112, 122)(113, 138)(114, 143)(115, 136)(116, 137)(117, 134)(118, 123)(119, 140)(120, 133) MAP : A3.1066 NOTES : type I, reflexible, 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.2 * x.1 * x.3, x.4^3, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.4^-1)^2 > 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 : 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, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 103)(98, 101)(99, 102)(100, 109)(104, 114)(105, 118)(106, 119)(107, 117)(108, 110)(111, 116)(112, 115)(113, 120)(121, 125)(122, 126)(123, 127)(124, 128)(129, 133)(130, 134)(131, 135)(132, 136)(137, 141)(138, 142)(139, 143)(140, 144) MAP : A3.1074 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) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.2 * x.1 * x.3, x.4^3, (x.3 * x.4^-1)^2, (x.4 * x.1)^2, 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, 3, 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, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117)(121, 127)(122, 125)(123, 126)(124, 133)(128, 138)(129, 142)(130, 143)(131, 141)(132, 134)(135, 140)(136, 139)(137, 144) MAP : A3.1076 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) : <16, 11> 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.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > 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 : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80) MAP : A3.1077 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) : <16, 13> 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.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > 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 : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 90)(50, 94)(51, 95)(52, 83)(53, 89)(54, 93)(55, 88)(56, 92)(57, 82)(58, 86)(59, 87)(60, 91)(61, 81)(62, 85)(63, 96)(64, 84)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79) MAP : A3.1104 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.3^4, u.6^4 > CTG (small) : <8, 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.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 40)(18, 37)(19, 36)(20, 34)(21, 35)(22, 39)(23, 33)(24, 38)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 93)(50, 96)(51, 95)(52, 89)(53, 94)(54, 92)(55, 90)(56, 91)(57, 59)(58, 62)(60, 64)(61, 63)(65, 87)(66, 84)(67, 85)(68, 83)(69, 82)(70, 88)(71, 86)(72, 81) MAP : A3.1108 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.3^4, u.6^4 > CTG (small) : <8, 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.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 37)(18, 40)(19, 39)(20, 33)(21, 38)(22, 36)(23, 34)(24, 35)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 95)(50, 92)(51, 93)(52, 91)(53, 90)(54, 96)(55, 94)(56, 89)(57, 58)(59, 62)(60, 63)(61, 64)(65, 84)(66, 87)(67, 88)(68, 86)(69, 81)(70, 85)(71, 83)(72, 82) MAP : A3.1148 NOTES : type I, non-Cayley, reflexible, QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 54, 6, 51, 3, 49)(2, 58, 10, 85, 37, 50)(4, 57, 9, 88, 40, 52)(5, 61, 13, 82, 34, 53)(7, 94, 46, 60, 12, 55)(8, 64, 16, 84, 36, 56)(11, 78, 30, 71, 23, 59)(14, 75, 27, 92, 44, 62)(15, 81, 33, 67, 19, 63)(17, 79, 31, 86, 38, 65)(18, 77, 29, 90, 42, 66)(20, 80, 32, 89, 41, 68)(21, 74, 26, 93, 45, 69)(22, 95, 47, 83, 35, 70)(24, 73, 25, 96, 48, 72)(28, 91, 43, 87, 39, 76) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83) MAP : A3.1268 NOTES : type I, non-Cayley, reflexible, QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.3^2, u.1^2, u.2^3, (u.1 * u.3 * u.2^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.3^2, x.1^2, x.2^3, x.1 * x.3 * x.2 * x.3 * x.2, x.1 * x.2^-1 * x.3 * x.2^-1 * x.3, (x.1 * x.3 * x.2^-1)^2, (x.2 * x.1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1)^2 LOCAL TYPE : (3, 4, 4, 3, 4, 4) #DARTS : 72 R = (1, 40, 64, 16, 25, 49)(2, 48, 72, 24, 26, 50)(3, 32, 56, 8, 27, 51)(4, 31, 55, 7, 28, 52)(5, 36, 60, 12, 29, 53)(6, 44, 68, 20, 30, 54)(9, 47, 71, 23, 33, 57)(10, 45, 69, 21, 34, 58)(11, 46, 70, 22, 35, 59)(13, 43, 67, 19, 37, 61)(14, 41, 65, 17, 38, 62)(15, 42, 66, 18, 39, 63) L = (1, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63) MAP : A3.1271 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) : <24, 12> 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.5^3, x.4 * x.5^-1 * x.3, x.5^-1 * x.1 * x.3 * x.2, x.4^4, x.3 * x.4^-1 * x.5 * x.1 * x.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, 3) #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, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1272 NOTES : type I, reflexible, isomorphic to Dual({3,7}), 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) : <24, 12> 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.5^3, x.4 * x.5^-1 * x.3, x.5 * x.4 * x.3 * x.2, (x.5 * x.1)^2, x.4^4 > 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 : 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, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 36)(26, 44)(27, 28)(29, 40)(30, 48)(31, 32)(33, 43)(34, 41)(35, 42)(37, 47)(38, 45)(39, 46)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1274 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) : <24, 12> 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.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, (x.5 * x.1)^2, x.1 * x.3 * x.2 * x.3 * 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 : 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, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(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, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1276 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) : <12, 3> 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.7 * x.3^-1 * x.2, x.6^3, x.8^3, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.6^-1, x.3 * x.4^-1 * x.8^-1, x.1 * x.6 * x.4^-1, x.4 * x.1 * x.5^-1, x.2 * x.8 * x.6, (x.2 * 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 : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 98)(14, 99)(15, 97)(16, 102)(17, 107)(18, 105)(19, 106)(20, 101)(21, 100)(22, 108)(23, 104)(24, 103)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 93)(38, 94)(39, 95)(40, 96)(41, 85)(42, 86)(43, 87)(44, 88)(45, 89)(46, 90)(47, 91)(48, 92)(49, 67)(50, 65)(51, 66)(52, 61)(53, 72)(54, 68)(55, 64)(56, 63)(57, 70)(58, 71)(59, 69)(60, 62)(73, 168)(74, 164)(75, 160)(76, 159)(77, 166)(78, 167)(79, 165)(80, 158)(81, 163)(82, 161)(83, 162)(84, 157)(109, 123)(110, 121)(111, 122)(112, 129)(113, 128)(114, 124)(115, 132)(116, 131)(117, 126)(118, 127)(119, 125)(120, 130)(145, 156)(146, 152)(147, 148)(149, 154)(150, 155)(151, 153) MAP : A3.1277 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) : <24, 12> 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.5^3, x.4 * x.5^-1 * x.3, x.5 * x.3 * x.5^-1 * x.1, (x.3 * x.2)^2, x.4^4 > 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 : 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, 21)(2, 22)(3, 23)(4, 24)(5, 9)(6, 10)(7, 11)(8, 12)(13, 17)(14, 18)(15, 19)(16, 20)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1278 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) : <24, 12> 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.5^3, x.4 * x.5^-1 * x.3, x.4^-1 * x.5^-1 * x.1 * x.3, x.5 * x.3 * x.5^-1 * x.2, x.4^4 > 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 : 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, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(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, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1280 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) : <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.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.4^-1 * x.2 * x.4 * x.1, (x.3 * x.1)^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 : 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, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(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, 163)(147, 161)(148, 154)(149, 159)(150, 157)(151, 158)(152, 165)(153, 164)(155, 156)(160, 166)(167, 168) MAP : A3.1283 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) : <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.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, (x.4 * x.1)^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 : 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, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(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, 163)(147, 161)(148, 154)(149, 159)(150, 157)(151, 158)(152, 165)(153, 164)(155, 156)(160, 166)(167, 168) MAP : A3.1286 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, {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.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^3, u.7^3, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1 > CTG (small) : <12, 3> 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.4 * x.6, x.3^3, x.7^3, x.5 * x.6^-1 * x.8, x.3^-1 * x.4^-1 * x.1, x.2 * x.7 * x.3^-1, x.1 * x.6 * x.7^-1, x.7 * x.2 * x.8^-1, (x.2 * x.1)^2, x.3 * x.6 * x.7 * x.1 > 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, 3) #DARTS : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 67)(26, 65)(27, 66)(28, 61)(29, 72)(30, 68)(31, 64)(32, 63)(33, 70)(34, 71)(35, 69)(36, 62)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 136)(50, 144)(51, 140)(52, 139)(53, 134)(54, 135)(55, 133)(56, 138)(57, 143)(58, 141)(59, 142)(60, 137)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 166)(86, 167)(87, 165)(88, 158)(89, 163)(90, 161)(91, 162)(92, 157)(93, 168)(94, 164)(95, 160)(96, 159)(97, 107)(98, 105)(99, 106)(100, 101)(102, 108)(103, 104)(109, 148)(110, 156)(111, 152)(112, 151)(113, 146)(114, 147)(115, 145)(116, 150)(117, 155)(118, 153)(119, 154)(120, 149) MAP : A3.1291 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) 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.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> 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.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > 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, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 8)(2, 12)(3, 4)(5, 11)(6, 15)(7, 9)(10, 13)(14, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 66)(50, 70)(51, 78)(52, 71)(53, 79)(54, 75)(55, 77)(56, 69)(57, 67)(58, 73)(59, 65)(60, 72)(61, 80)(62, 74)(63, 76)(64, 68)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1296 NOTES : type I, chiral, QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) 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.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> 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.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > 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, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 109)(34, 105)(35, 100)(36, 112)(37, 110)(38, 106)(39, 107)(40, 103)(41, 101)(42, 97)(43, 108)(44, 104)(45, 102)(46, 98)(47, 99)(48, 111)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1306 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > 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, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 47)(18, 44)(19, 45)(20, 43)(21, 42)(22, 48)(23, 46)(24, 41)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 96)(34, 93)(35, 92)(36, 90)(37, 91)(38, 95)(39, 89)(40, 94)(49, 51)(50, 54)(52, 56)(53, 55)(57, 109)(58, 112)(59, 111)(60, 105)(61, 110)(62, 108)(63, 106)(64, 107)(65, 66)(67, 70)(68, 71)(69, 72)(73, 104)(74, 101)(75, 100)(76, 98)(77, 99)(78, 103)(79, 97)(80, 102) MAP : A3.1327 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.3^4, u.7^4 > CTG (small) : <8, 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.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > 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, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 44)(18, 47)(19, 48)(20, 46)(21, 41)(22, 45)(23, 43)(24, 42)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 93)(34, 96)(35, 95)(36, 89)(37, 94)(38, 92)(39, 90)(40, 91)(49, 50)(51, 54)(52, 55)(53, 56)(57, 112)(58, 109)(59, 108)(60, 106)(61, 107)(62, 111)(63, 105)(64, 110)(65, 66)(67, 70)(68, 71)(69, 72)(73, 101)(74, 104)(75, 103)(76, 97)(77, 102)(78, 100)(79, 98)(80, 99) MAP : A3.1351 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.6^4, u.8^4 > CTG (small) : <8, 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.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * 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, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 18)(19, 22)(20, 23)(21, 24)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 47)(34, 44)(35, 45)(36, 43)(37, 42)(38, 48)(39, 46)(40, 41)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1352 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, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 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.6^4, u.8^4 > CTG (small) : <8, 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^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > 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, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 18)(19, 22)(20, 23)(21, 24)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 48)(34, 45)(35, 44)(36, 42)(37, 43)(38, 47)(39, 41)(40, 46)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1378 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) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.4^3, x.2^3, x.1 * x.2^-1 * x.4, x.3^3, x.2 * x.4 * x.3, (x.3 * x.4^-1)^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 : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 73)(10, 74)(11, 75)(12, 76)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 46)(26, 47)(27, 45)(28, 38)(29, 43)(30, 41)(31, 42)(32, 37)(33, 48)(34, 44)(35, 40)(36, 39)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72) MAP : A3.1382 NOTES : type I, non-biCayley, reflexible, isomorphic to Dual({3,8}), QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 2, 2 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.5^2, u.6^2, u.3^3, u.4^3, u.1 * u.2^-1 * u.4^-1, u.2 * u.3^-1 * u.5 * u.1^-1 * u.6 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.5^2, x.6^2, x.4 * x.2^-2, x.3^3, x.4^3, x.1 * x.2^-1 * x.4^-1, x.4 * x.3 * x.5, x.2 * x.5 * x.3^-1, x.4 * x.3^-1 * x.6 * x.3^-1, x.5 * x.2 * x.6 * x.2^-1, x.2 * x.3^-1 * x.5 * x.1^-1 * x.6 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 11, 23, 35, 47)(2, 14, 26, 38, 9, 21, 33, 45)(3, 15, 27, 39, 10, 22, 34, 46)(4, 16, 28, 40, 5, 17, 29, 41)(6, 18, 30, 42, 12, 24, 36, 48)(7, 19, 31, 43, 8, 20, 32, 44)(49, 61, 73, 85, 54, 66, 78, 90)(50, 62, 74, 86, 55, 67, 79, 91)(51, 63, 75, 87, 53, 65, 77, 89)(52, 64, 76, 88, 58, 70, 82, 94)(56, 68, 80, 92, 57, 69, 81, 93)(59, 71, 83, 95, 60, 72, 84, 96) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 44)(26, 40)(27, 48)(28, 47)(29, 42)(30, 43)(31, 41)(32, 46)(33, 39)(34, 37)(35, 38)(36, 45)(61, 75)(62, 73)(63, 74)(64, 81)(65, 80)(66, 76)(67, 84)(68, 83)(69, 78)(70, 79)(71, 77)(72, 82) MAP : A3.1384 NOTES : type I, non-Cayley, chiral, QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 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)^3 > 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^-1 * x.1 * x.2, x.3^4, x.3 * x.4 * x.2 * x.4 * x.3, (x.3 * x.4)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 30, 54, 78, 6, 25, 49, 73)(2, 31, 55, 79, 7, 26, 50, 74)(3, 29, 53, 77, 5, 27, 51, 75)(4, 46, 70, 94, 22, 28, 52, 76)(8, 33, 57, 81, 9, 32, 56, 80)(10, 40, 64, 88, 16, 34, 58, 82)(11, 48, 72, 96, 24, 35, 59, 83)(12, 47, 71, 95, 23, 36, 60, 84)(13, 42, 66, 90, 18, 37, 61, 85)(14, 43, 67, 91, 19, 38, 62, 86)(15, 41, 65, 89, 17, 39, 63, 87)(20, 45, 69, 93, 21, 44, 68, 92) L = (1, 38)(2, 39)(3, 37)(4, 30)(5, 43)(6, 41)(7, 42)(8, 25)(9, 40)(10, 48)(11, 32)(12, 31)(13, 34)(14, 35)(15, 33)(16, 26)(17, 47)(18, 45)(19, 46)(20, 29)(21, 36)(22, 44)(23, 28)(24, 27)(49, 55)(50, 53)(51, 54)(52, 61)(56, 66)(57, 70)(58, 71)(59, 69)(60, 62)(63, 68)(64, 67)(65, 72)(73, 84)(74, 92)(75, 76)(77, 88)(78, 96)(79, 80)(81, 91)(82, 89)(83, 90)(85, 95)(86, 93)(87, 94) MAP : A3.1397 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) : <12, 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.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.5, x.2 * x.5 * x.4, (x.2 * x.1)^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 : 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, 50)(2, 51)(3, 49)(4, 54)(5, 59)(6, 57)(7, 58)(8, 53)(9, 52)(10, 60)(11, 56)(12, 55)(13, 32)(14, 28)(15, 36)(16, 35)(17, 30)(18, 31)(19, 29)(20, 34)(21, 27)(22, 25)(23, 26)(24, 33)(37, 48)(38, 44)(39, 40)(41, 46)(42, 47)(43, 45)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 88)(74, 96)(75, 92)(76, 91)(77, 86)(78, 87)(79, 85)(80, 90)(81, 95)(82, 93)(83, 94)(84, 89)