Created on Sat Sep 04 2010, 03:31:46 CEST GENUS: 2 NUMBER OF MAPS: 17 REFLEXIBLE MAPS: 13 CHIRAL MAPS: 4 #TYPE I: 9 #TYPE II: 8 CAYLEY MAPS: 17 NON-CAYLEY MAPS: 0 MAP : A2.1 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: [ 8, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, (x.2^-3 * x.3^-1)^2, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 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, 243)(50, 251)(51, 260)(52, 259)(53, 241)(54, 244)(55, 242)(56, 266)(57, 261)(58, 263)(59, 257)(60, 262)(61, 271)(62, 269)(63, 270)(64, 265)(65, 284)(66, 281)(67, 258)(68, 282)(69, 275)(70, 283)(71, 267)(72, 268)(73, 250)(74, 252)(75, 254)(76, 249)(77, 276)(78, 274)(79, 273)(80, 278)(81, 248)(82, 264)(83, 255)(84, 256)(85, 246)(86, 247)(87, 245)(88, 277)(89, 287)(90, 286)(91, 253)(92, 285)(93, 272)(94, 288)(95, 280)(96, 279)(97, 200)(98, 216)(99, 207)(100, 208)(101, 198)(102, 199)(103, 197)(104, 229)(105, 202)(106, 204)(107, 206)(108, 201)(109, 228)(110, 226)(111, 225)(112, 230)(113, 239)(114, 238)(115, 205)(116, 237)(117, 224)(118, 240)(119, 232)(120, 231)(121, 213)(122, 215)(123, 209)(124, 214)(125, 223)(126, 221)(127, 222)(128, 217)(129, 195)(130, 203)(131, 212)(132, 211)(133, 193)(134, 196)(135, 194)(136, 218)(137, 236)(138, 233)(139, 210)(140, 234)(141, 227)(142, 235)(143, 219)(144, 220) MAP : A2.7 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: [ 2, 4, 6 ] 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)^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 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, 122)(26, 121)(27, 127)(28, 125)(29, 124)(30, 136)(31, 123)(32, 130)(33, 142)(34, 128)(35, 139)(36, 134)(37, 144)(38, 132)(39, 143)(40, 126)(41, 138)(42, 137)(43, 131)(44, 141)(45, 140)(46, 129)(47, 135)(48, 133)(49, 102)(50, 99)(51, 108)(52, 97)(53, 105)(54, 120)(55, 104)(56, 107)(57, 114)(58, 101)(59, 117)(60, 119)(61, 115)(62, 100)(63, 118)(64, 106)(65, 110)(66, 116)(67, 98)(68, 112)(69, 111)(70, 103)(71, 109)(72, 113) MAP : A2.25 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: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, x.2^-1 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 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, 123)(26, 137)(27, 124)(28, 121)(29, 138)(30, 139)(31, 129)(32, 122)(33, 134)(34, 135)(35, 141)(36, 130)(37, 140)(38, 127)(39, 132)(40, 133)(41, 128)(42, 142)(43, 144)(44, 136)(45, 143)(46, 125)(47, 131)(48, 126)(49, 102)(50, 103)(51, 109)(52, 98)(53, 108)(54, 119)(55, 100)(56, 101)(57, 120)(58, 110)(59, 112)(60, 104)(61, 111)(62, 117)(63, 99)(64, 118)(65, 115)(66, 105)(67, 116)(68, 113)(69, 106)(70, 107)(71, 97)(72, 114) MAP : A2.33 NOTES : type I, reflexible, isomorphic to Med2({3,8}), QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <48, 29> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^8, (x.1^-1 * x.2 * x.1^-2)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 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, 51)(2, 59)(3, 68)(4, 67)(5, 49)(6, 52)(7, 50)(8, 74)(9, 69)(10, 71)(11, 65)(12, 70)(13, 79)(14, 77)(15, 78)(16, 73)(17, 92)(18, 89)(19, 66)(20, 90)(21, 83)(22, 91)(23, 75)(24, 76)(25, 58)(26, 60)(27, 62)(28, 57)(29, 84)(30, 82)(31, 81)(32, 86)(33, 56)(34, 72)(35, 63)(36, 64)(37, 54)(38, 55)(39, 53)(40, 85)(41, 95)(42, 94)(43, 61)(44, 93)(45, 80)(46, 96)(47, 88)(48, 87)(97, 146)(98, 148)(99, 150)(100, 145)(101, 172)(102, 170)(103, 169)(104, 174)(105, 183)(106, 182)(107, 149)(108, 181)(109, 192)(110, 184)(111, 176)(112, 175)(113, 168)(114, 160)(115, 151)(116, 152)(117, 166)(118, 167)(119, 165)(120, 173)(121, 163)(122, 147)(123, 156)(124, 155)(125, 161)(126, 164)(127, 162)(128, 186)(129, 180)(130, 177)(131, 154)(132, 178)(133, 171)(134, 179)(135, 187)(136, 188)(137, 157)(138, 159)(139, 153)(140, 158)(141, 191)(142, 189)(143, 190)(144, 185) MAP : A2.39 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) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1^-1, x.1^-2 * x.2 * x.1^-2 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 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, 29)(3, 30)(4, 37)(5, 35)(6, 42)(7, 45)(8, 43)(9, 28)(10, 32)(11, 25)(12, 27)(13, 46)(14, 48)(15, 38)(16, 41)(17, 31)(18, 36)(19, 47)(20, 39)(21, 40)(22, 33)(23, 34)(24, 44)(49, 75)(50, 89)(51, 76)(52, 73)(53, 90)(54, 91)(55, 81)(56, 74)(57, 86)(58, 87)(59, 93)(60, 82)(61, 92)(62, 79)(63, 84)(64, 85)(65, 80)(66, 94)(67, 96)(68, 88)(69, 95)(70, 77)(71, 83)(72, 78) MAP : A2.43 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: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^6 > CTG (small) : <24, 8> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 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, 30)(2, 27)(3, 36)(4, 25)(5, 33)(6, 48)(7, 32)(8, 35)(9, 42)(10, 29)(11, 45)(12, 47)(13, 43)(14, 28)(15, 46)(16, 34)(17, 38)(18, 44)(19, 26)(20, 40)(21, 39)(22, 31)(23, 37)(24, 41)(49, 75)(50, 78)(51, 80)(52, 81)(53, 73)(54, 82)(55, 84)(56, 77)(57, 79)(58, 83)(59, 74)(60, 76)(61, 89)(62, 95)(63, 85)(64, 96)(65, 92)(66, 86)(67, 93)(68, 87)(69, 88)(70, 90)(71, 94)(72, 91) MAP : A2.46 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: [ 3, 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)^3 > CTG (small) : <12, 4> 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.1)^2, x.4 * x.5 * x.1 * x.2, x.4^-1 * x.5 * x.4 * x.5, (x.2 * x.5)^2, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 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, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70)(73, 75)(74, 83)(76, 80)(77, 84)(78, 79)(81, 82) MAP : A2.51 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: [ 3, 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)^3 > CTG (small) : <12, 4> 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)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 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, 88)(14, 90)(15, 96)(16, 89)(17, 85)(18, 93)(19, 95)(20, 87)(21, 86)(22, 91)(23, 94)(24, 92)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 62)(38, 61)(39, 71)(40, 66)(41, 69)(42, 64)(43, 68)(44, 67)(45, 65)(46, 72)(47, 63)(48, 70) MAP : A2.89 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) : <48, 29> 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.3 * x.2^-2 * x.1 * x.3^-1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #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, 6)(2, 5)(3, 8)(4, 7)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 20)(16, 19)(25, 38)(26, 37)(27, 40)(28, 39)(29, 34)(30, 33)(31, 36)(32, 35)(41, 46)(42, 45)(43, 48)(44, 47)(49, 99)(50, 107)(51, 116)(52, 115)(53, 97)(54, 100)(55, 98)(56, 122)(57, 117)(58, 119)(59, 113)(60, 118)(61, 127)(62, 125)(63, 126)(64, 121)(65, 140)(66, 137)(67, 114)(68, 138)(69, 131)(70, 139)(71, 123)(72, 124)(73, 106)(74, 108)(75, 110)(76, 105)(77, 132)(78, 130)(79, 129)(80, 134)(81, 104)(82, 120)(83, 111)(84, 112)(85, 102)(86, 103)(87, 101)(88, 133)(89, 143)(90, 142)(91, 109)(92, 141)(93, 128)(94, 144)(95, 136)(96, 135)(145, 194)(146, 196)(147, 198)(148, 193)(149, 220)(150, 218)(151, 217)(152, 222)(153, 231)(154, 230)(155, 197)(156, 229)(157, 240)(158, 232)(159, 224)(160, 223)(161, 216)(162, 208)(163, 199)(164, 200)(165, 214)(166, 215)(167, 213)(168, 221)(169, 211)(170, 195)(171, 204)(172, 203)(173, 209)(174, 212)(175, 210)(176, 234)(177, 228)(178, 225)(179, 202)(180, 226)(181, 219)(182, 227)(183, 235)(184, 236)(185, 205)(186, 207)(187, 201)(188, 206)(189, 239)(190, 237)(191, 238)(192, 233) MAP : A2.93 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) : <24, 8> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, (x.3^-1 * x.2)^2, x.3^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 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, 2)(3, 7)(4, 5)(6, 16)(8, 10)(9, 22)(11, 19)(12, 14)(13, 24)(15, 23)(17, 18)(20, 21)(25, 51)(26, 54)(27, 56)(28, 57)(29, 49)(30, 58)(31, 60)(32, 53)(33, 55)(34, 59)(35, 50)(36, 52)(37, 65)(38, 71)(39, 61)(40, 72)(41, 68)(42, 62)(43, 69)(44, 63)(45, 64)(46, 66)(47, 70)(48, 67)(73, 100)(74, 115)(75, 98)(76, 110)(77, 106)(78, 97)(79, 118)(80, 103)(81, 101)(82, 112)(83, 104)(84, 99)(85, 119)(86, 113)(87, 117)(88, 116)(89, 120)(90, 105)(91, 109)(92, 114)(93, 107)(94, 111)(95, 108)(96, 102) MAP : A2.97 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) : <6, 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.5^3, x.6^3, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, 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 : (3, 4, 4, 4, 4) #DARTS : 60 R = (1, 7, 13, 19, 25)(2, 8, 14, 20, 26)(3, 9, 15, 21, 27)(4, 10, 16, 22, 28)(5, 11, 17, 23, 29)(6, 12, 18, 24, 30)(31, 37, 43, 49, 55)(32, 38, 44, 50, 56)(33, 39, 45, 51, 57)(34, 40, 46, 52, 58)(35, 41, 47, 53, 59)(36, 42, 48, 54, 60) L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 35)(8, 33)(9, 36)(10, 32)(11, 34)(12, 31)(13, 21)(14, 23)(15, 22)(16, 19)(17, 24)(18, 20)(25, 26)(27, 29)(28, 30)(37, 38)(39, 41)(40, 42)(43, 52)(44, 54)(45, 49)(46, 51)(47, 50)(48, 53) MAP : A2.99 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) : <24, 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.1 * x.2^-2 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 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, 27)(2, 41)(3, 28)(4, 25)(5, 42)(6, 43)(7, 33)(8, 26)(9, 38)(10, 39)(11, 45)(12, 34)(13, 44)(14, 31)(15, 36)(16, 37)(17, 32)(18, 46)(19, 48)(20, 40)(21, 47)(22, 29)(23, 35)(24, 30)(49, 74)(50, 77)(51, 78)(52, 85)(53, 83)(54, 90)(55, 93)(56, 91)(57, 76)(58, 80)(59, 73)(60, 75)(61, 94)(62, 96)(63, 86)(64, 89)(65, 79)(66, 84)(67, 95)(68, 87)(69, 88)(70, 81)(71, 82)(72, 92)(97, 143)(98, 124)(99, 135)(100, 127)(101, 128)(102, 121)(103, 122)(104, 132)(105, 138)(106, 141)(107, 142)(108, 125)(109, 123)(110, 130)(111, 133)(112, 131)(113, 140)(114, 144)(115, 137)(116, 139)(117, 134)(118, 136)(119, 126)(120, 129) MAP : A2.105 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) : <12, 4> 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.3 * x.4^-2, x.1 * x.3 * x.4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * 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 : 72 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) L = (1, 2)(3, 11)(4, 6)(5, 9)(7, 8)(10, 12)(13, 29)(14, 33)(15, 32)(16, 25)(17, 28)(18, 26)(19, 34)(20, 36)(21, 30)(22, 35)(23, 31)(24, 27)(37, 66)(38, 64)(39, 70)(40, 69)(41, 62)(42, 65)(43, 63)(44, 71)(45, 61)(46, 68)(47, 72)(48, 67)(49, 51)(50, 59)(52, 56)(53, 60)(54, 55)(57, 58) MAP : A2.109 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) : <6, 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.2 * x.1, x.6 * x.3^-1, x.3 * x.7 * x.4^-1, x.6^3, x.3^3, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5 > 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 : 72 R = (1, 7, 13, 19, 25, 31)(2, 8, 14, 20, 26, 32)(3, 9, 15, 21, 27, 33)(4, 10, 16, 22, 28, 34)(5, 11, 17, 23, 29, 35)(6, 12, 18, 24, 30, 36)(37, 43, 49, 55, 61, 67)(38, 44, 50, 56, 62, 68)(39, 45, 51, 57, 63, 69)(40, 46, 52, 58, 64, 70)(41, 47, 53, 59, 65, 71)(42, 48, 54, 60, 66, 72) L = (1, 9)(2, 11)(3, 10)(4, 7)(5, 12)(6, 8)(13, 30)(14, 28)(15, 26)(16, 29)(17, 25)(18, 27)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(31, 32)(33, 35)(34, 36)(37, 69)(38, 71)(39, 70)(40, 67)(41, 72)(42, 68)(43, 44)(45, 47)(46, 48)(49, 65)(50, 63)(51, 66)(52, 62)(53, 64)(54, 61) MAP : A2.111 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) : <12, 4> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4 * x.5^-2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, (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 : 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, 16)(2, 18)(3, 24)(4, 17)(5, 13)(6, 21)(7, 23)(8, 15)(9, 14)(10, 19)(11, 22)(12, 20)(25, 69)(26, 65)(27, 67)(28, 62)(29, 66)(30, 61)(31, 72)(32, 70)(33, 64)(34, 63)(35, 68)(36, 71)(37, 39)(38, 47)(40, 44)(41, 48)(42, 43)(45, 46)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(73, 74)(75, 83)(76, 78)(77, 81)(79, 80)(82, 84) MAP : A2.114 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) : <6, 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.2 * x.1, x.7 * x.3^-1, x.4 * x.5^-1 * x.6, x.5 * x.6^-1 * x.8, x.3^3, x.3^-1 * x.4^-1 * x.1, x.7 * x.2 * x.8^-1, x.7^3, x.3 * x.6 * x.4^-1, x.1 * x.3 * x.6^-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 : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 9)(2, 11)(3, 10)(4, 7)(5, 12)(6, 8)(13, 36)(14, 34)(15, 32)(16, 35)(17, 31)(18, 33)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 71)(26, 69)(27, 72)(28, 68)(29, 70)(30, 67)(37, 38)(39, 41)(40, 42)(43, 81)(44, 83)(45, 82)(46, 79)(47, 84)(48, 80)(49, 50)(51, 53)(52, 54)(55, 77)(56, 75)(57, 78)(58, 74)(59, 76)(60, 73) MAP : A2.116 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) : <6, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6 * x.4^-1, x.6^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.6^3, x.5 * x.6^-1 * x.7^-1, x.8^3, x.4 * x.2 * x.5^-1, x.3 * x.4^-1 * x.8^-1 > 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 : 84 R = (1, 7, 13, 19, 25, 31, 37)(2, 8, 14, 20, 26, 32, 38)(3, 9, 15, 21, 27, 33, 39)(4, 10, 16, 22, 28, 34, 40)(5, 11, 17, 23, 29, 35, 41)(6, 12, 18, 24, 30, 36, 42)(43, 49, 55, 61, 67, 73, 79)(44, 50, 56, 62, 68, 74, 80)(45, 51, 57, 63, 69, 75, 81)(46, 52, 58, 64, 70, 76, 82)(47, 53, 59, 65, 71, 77, 83)(48, 54, 60, 66, 72, 78, 84) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 51)(8, 53)(9, 52)(10, 49)(11, 54)(12, 50)(13, 14)(15, 17)(16, 18)(19, 47)(20, 45)(21, 48)(22, 44)(23, 46)(24, 43)(25, 33)(26, 35)(27, 34)(28, 31)(29, 36)(30, 32)(37, 80)(38, 79)(39, 83)(40, 84)(41, 81)(42, 82)(55, 64)(56, 66)(57, 61)(58, 63)(59, 62)(60, 65)(73, 74)(75, 77)(76, 78)