Polytope of Type {93,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {93,4}*1488
if this polytope has a name.
Group : SmallGroup(1488,209)
Rank : 3
Schlafli Type : {93,4}
Number of vertices, edges, etc : 186, 372, 8
Order of s0s1s2 : 186
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {93,4}*744
4-fold quotients : {93,2}*372
12-fold quotients : {31,2}*124
31-fold quotients : {3,4}*48
62-fold quotients : {3,4}*24
124-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,121)( 6,122)( 7,124)( 8,123)( 9,117)( 10,118)( 11,120)
( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)
( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)
( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)
( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)
( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)
( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)
( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)(127,252)
(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)(135,368)
(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)(143,360)
(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)(151,352)
(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)(159,344)
(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)(167,336)
(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)(175,328)
(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)(183,320)
(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)(191,312)
(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)(199,304)
(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)(207,296)
(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)(215,288)
(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)(223,280)
(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)(231,272)
(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)(239,264)
(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)(247,256)
(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)(382,490)
(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)(390,482)
(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)(398,474)
(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)(406,466)
(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)(414,458)
(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)(422,450)
(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)
(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)(498,622)
(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)(506,738)
(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)(514,730)
(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)(522,722)
(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)(530,714)
(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)(538,706)
(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)(546,698)
(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)(554,690)
(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)(562,682)
(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)(570,674)
(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)(578,666)
(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)(586,658)
(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)(594,650)
(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)(602,642)
(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)(610,634)
(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)(618,626)
(619,628)(620,627);;
s1 := ( 1,129)( 2,132)( 3,131)( 4,130)( 5,125)( 6,128)( 7,127)( 8,126)
( 9,245)( 10,248)( 11,247)( 12,246)( 13,241)( 14,244)( 15,243)( 16,242)
( 17,237)( 18,240)( 19,239)( 20,238)( 21,233)( 22,236)( 23,235)( 24,234)
( 25,229)( 26,232)( 27,231)( 28,230)( 29,225)( 30,228)( 31,227)( 32,226)
( 33,221)( 34,224)( 35,223)( 36,222)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,213)( 42,216)( 43,215)( 44,214)( 45,209)( 46,212)( 47,211)( 48,210)
( 49,205)( 50,208)( 51,207)( 52,206)( 53,201)( 54,204)( 55,203)( 56,202)
( 57,197)( 58,200)( 59,199)( 60,198)( 61,193)( 62,196)( 63,195)( 64,194)
( 65,189)( 66,192)( 67,191)( 68,190)( 69,185)( 70,188)( 71,187)( 72,186)
( 73,181)( 74,184)( 75,183)( 76,182)( 77,177)( 78,180)( 79,179)( 80,178)
( 81,173)( 82,176)( 83,175)( 84,174)( 85,169)( 86,172)( 87,171)( 88,170)
( 89,165)( 90,168)( 91,167)( 92,166)( 93,161)( 94,164)( 95,163)( 96,162)
( 97,157)( 98,160)( 99,159)(100,158)(101,153)(102,156)(103,155)(104,154)
(105,149)(106,152)(107,151)(108,150)(109,145)(110,148)(111,147)(112,146)
(113,141)(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)(120,138)
(121,133)(122,136)(123,135)(124,134)(249,253)(250,256)(251,255)(252,254)
(257,369)(258,372)(259,371)(260,370)(261,365)(262,368)(263,367)(264,366)
(265,361)(266,364)(267,363)(268,362)(269,357)(270,360)(271,359)(272,358)
(273,353)(274,356)(275,355)(276,354)(277,349)(278,352)(279,351)(280,350)
(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)(288,342)
(289,337)(290,340)(291,339)(292,338)(293,333)(294,336)(295,335)(296,334)
(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)(304,326)
(305,321)(306,324)(307,323)(308,322)(309,317)(310,320)(311,319)(312,318)
(314,316)(373,501)(374,504)(375,503)(376,502)(377,497)(378,500)(379,499)
(380,498)(381,617)(382,620)(383,619)(384,618)(385,613)(386,616)(387,615)
(388,614)(389,609)(390,612)(391,611)(392,610)(393,605)(394,608)(395,607)
(396,606)(397,601)(398,604)(399,603)(400,602)(401,597)(402,600)(403,599)
(404,598)(405,593)(406,596)(407,595)(408,594)(409,589)(410,592)(411,591)
(412,590)(413,585)(414,588)(415,587)(416,586)(417,581)(418,584)(419,583)
(420,582)(421,577)(422,580)(423,579)(424,578)(425,573)(426,576)(427,575)
(428,574)(429,569)(430,572)(431,571)(432,570)(433,565)(434,568)(435,567)
(436,566)(437,561)(438,564)(439,563)(440,562)(441,557)(442,560)(443,559)
(444,558)(445,553)(446,556)(447,555)(448,554)(449,549)(450,552)(451,551)
(452,550)(453,545)(454,548)(455,547)(456,546)(457,541)(458,544)(459,543)
(460,542)(461,537)(462,540)(463,539)(464,538)(465,533)(466,536)(467,535)
(468,534)(469,529)(470,532)(471,531)(472,530)(473,525)(474,528)(475,527)
(476,526)(477,521)(478,524)(479,523)(480,522)(481,517)(482,520)(483,519)
(484,518)(485,513)(486,516)(487,515)(488,514)(489,509)(490,512)(491,511)
(492,510)(493,505)(494,508)(495,507)(496,506)(621,625)(622,628)(623,627)
(624,626)(629,741)(630,744)(631,743)(632,742)(633,737)(634,740)(635,739)
(636,738)(637,733)(638,736)(639,735)(640,734)(641,729)(642,732)(643,731)
(644,730)(645,725)(646,728)(647,727)(648,726)(649,721)(650,724)(651,723)
(652,722)(653,717)(654,720)(655,719)(656,718)(657,713)(658,716)(659,715)
(660,714)(661,709)(662,712)(663,711)(664,710)(665,705)(666,708)(667,707)
(668,706)(669,701)(670,704)(671,703)(672,702)(673,697)(674,700)(675,699)
(676,698)(677,693)(678,696)(679,695)(680,694)(681,689)(682,692)(683,691)
(684,690)(686,688);;
s2 := ( 1,374)( 2,373)( 3,376)( 4,375)( 5,378)( 6,377)( 7,380)( 8,379)
( 9,382)( 10,381)( 11,384)( 12,383)( 13,386)( 14,385)( 15,388)( 16,387)
( 17,390)( 18,389)( 19,392)( 20,391)( 21,394)( 22,393)( 23,396)( 24,395)
( 25,398)( 26,397)( 27,400)( 28,399)( 29,402)( 30,401)( 31,404)( 32,403)
( 33,406)( 34,405)( 35,408)( 36,407)( 37,410)( 38,409)( 39,412)( 40,411)
( 41,414)( 42,413)( 43,416)( 44,415)( 45,418)( 46,417)( 47,420)( 48,419)
( 49,422)( 50,421)( 51,424)( 52,423)( 53,426)( 54,425)( 55,428)( 56,427)
( 57,430)( 58,429)( 59,432)( 60,431)( 61,434)( 62,433)( 63,436)( 64,435)
( 65,438)( 66,437)( 67,440)( 68,439)( 69,442)( 70,441)( 71,444)( 72,443)
( 73,446)( 74,445)( 75,448)( 76,447)( 77,450)( 78,449)( 79,452)( 80,451)
( 81,454)( 82,453)( 83,456)( 84,455)( 85,458)( 86,457)( 87,460)( 88,459)
( 89,462)( 90,461)( 91,464)( 92,463)( 93,466)( 94,465)( 95,468)( 96,467)
( 97,470)( 98,469)( 99,472)(100,471)(101,474)(102,473)(103,476)(104,475)
(105,478)(106,477)(107,480)(108,479)(109,482)(110,481)(111,484)(112,483)
(113,486)(114,485)(115,488)(116,487)(117,490)(118,489)(119,492)(120,491)
(121,494)(122,493)(123,496)(124,495)(125,498)(126,497)(127,500)(128,499)
(129,502)(130,501)(131,504)(132,503)(133,506)(134,505)(135,508)(136,507)
(137,510)(138,509)(139,512)(140,511)(141,514)(142,513)(143,516)(144,515)
(145,518)(146,517)(147,520)(148,519)(149,522)(150,521)(151,524)(152,523)
(153,526)(154,525)(155,528)(156,527)(157,530)(158,529)(159,532)(160,531)
(161,534)(162,533)(163,536)(164,535)(165,538)(166,537)(167,540)(168,539)
(169,542)(170,541)(171,544)(172,543)(173,546)(174,545)(175,548)(176,547)
(177,550)(178,549)(179,552)(180,551)(181,554)(182,553)(183,556)(184,555)
(185,558)(186,557)(187,560)(188,559)(189,562)(190,561)(191,564)(192,563)
(193,566)(194,565)(195,568)(196,567)(197,570)(198,569)(199,572)(200,571)
(201,574)(202,573)(203,576)(204,575)(205,578)(206,577)(207,580)(208,579)
(209,582)(210,581)(211,584)(212,583)(213,586)(214,585)(215,588)(216,587)
(217,590)(218,589)(219,592)(220,591)(221,594)(222,593)(223,596)(224,595)
(225,598)(226,597)(227,600)(228,599)(229,602)(230,601)(231,604)(232,603)
(233,606)(234,605)(235,608)(236,607)(237,610)(238,609)(239,612)(240,611)
(241,614)(242,613)(243,616)(244,615)(245,618)(246,617)(247,620)(248,619)
(249,622)(250,621)(251,624)(252,623)(253,626)(254,625)(255,628)(256,627)
(257,630)(258,629)(259,632)(260,631)(261,634)(262,633)(263,636)(264,635)
(265,638)(266,637)(267,640)(268,639)(269,642)(270,641)(271,644)(272,643)
(273,646)(274,645)(275,648)(276,647)(277,650)(278,649)(279,652)(280,651)
(281,654)(282,653)(283,656)(284,655)(285,658)(286,657)(287,660)(288,659)
(289,662)(290,661)(291,664)(292,663)(293,666)(294,665)(295,668)(296,667)
(297,670)(298,669)(299,672)(300,671)(301,674)(302,673)(303,676)(304,675)
(305,678)(306,677)(307,680)(308,679)(309,682)(310,681)(311,684)(312,683)
(313,686)(314,685)(315,688)(316,687)(317,690)(318,689)(319,692)(320,691)
(321,694)(322,693)(323,696)(324,695)(325,698)(326,697)(327,700)(328,699)
(329,702)(330,701)(331,704)(332,703)(333,706)(334,705)(335,708)(336,707)
(337,710)(338,709)(339,712)(340,711)(341,714)(342,713)(343,716)(344,715)
(345,718)(346,717)(347,720)(348,719)(349,722)(350,721)(351,724)(352,723)
(353,726)(354,725)(355,728)(356,727)(357,730)(358,729)(359,732)(360,731)
(361,734)(362,733)(363,736)(364,735)(365,738)(366,737)(367,740)(368,739)
(369,742)(370,741)(371,744)(372,743);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(744)!( 3, 4)( 5,121)( 6,122)( 7,124)( 8,123)( 9,117)( 10,118)
( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)
( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)
( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)
( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)
( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)
( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)
(127,252)(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)
(135,368)(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)
(143,360)(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)
(151,352)(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)
(159,344)(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)
(167,336)(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)
(175,328)(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)
(183,320)(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)
(191,312)(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)
(199,304)(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)
(207,296)(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)
(215,288)(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)
(223,280)(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)
(231,272)(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)
(239,264)(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)
(247,256)(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)
(382,490)(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)
(390,482)(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)
(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)
(406,466)(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)
(414,458)(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)
(422,450)(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)
(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)
(498,622)(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)
(506,738)(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)
(514,730)(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)
(522,722)(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)
(530,714)(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)
(538,706)(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)
(546,698)(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)
(554,690)(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)
(562,682)(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)
(570,674)(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)
(578,666)(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)
(586,658)(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)
(594,650)(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)
(602,642)(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)
(610,634)(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)
(618,626)(619,628)(620,627);
s1 := Sym(744)!( 1,129)( 2,132)( 3,131)( 4,130)( 5,125)( 6,128)( 7,127)
( 8,126)( 9,245)( 10,248)( 11,247)( 12,246)( 13,241)( 14,244)( 15,243)
( 16,242)( 17,237)( 18,240)( 19,239)( 20,238)( 21,233)( 22,236)( 23,235)
( 24,234)( 25,229)( 26,232)( 27,231)( 28,230)( 29,225)( 30,228)( 31,227)
( 32,226)( 33,221)( 34,224)( 35,223)( 36,222)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,213)( 42,216)( 43,215)( 44,214)( 45,209)( 46,212)( 47,211)
( 48,210)( 49,205)( 50,208)( 51,207)( 52,206)( 53,201)( 54,204)( 55,203)
( 56,202)( 57,197)( 58,200)( 59,199)( 60,198)( 61,193)( 62,196)( 63,195)
( 64,194)( 65,189)( 66,192)( 67,191)( 68,190)( 69,185)( 70,188)( 71,187)
( 72,186)( 73,181)( 74,184)( 75,183)( 76,182)( 77,177)( 78,180)( 79,179)
( 80,178)( 81,173)( 82,176)( 83,175)( 84,174)( 85,169)( 86,172)( 87,171)
( 88,170)( 89,165)( 90,168)( 91,167)( 92,166)( 93,161)( 94,164)( 95,163)
( 96,162)( 97,157)( 98,160)( 99,159)(100,158)(101,153)(102,156)(103,155)
(104,154)(105,149)(106,152)(107,151)(108,150)(109,145)(110,148)(111,147)
(112,146)(113,141)(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)
(120,138)(121,133)(122,136)(123,135)(124,134)(249,253)(250,256)(251,255)
(252,254)(257,369)(258,372)(259,371)(260,370)(261,365)(262,368)(263,367)
(264,366)(265,361)(266,364)(267,363)(268,362)(269,357)(270,360)(271,359)
(272,358)(273,353)(274,356)(275,355)(276,354)(277,349)(278,352)(279,351)
(280,350)(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)
(288,342)(289,337)(290,340)(291,339)(292,338)(293,333)(294,336)(295,335)
(296,334)(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)
(304,326)(305,321)(306,324)(307,323)(308,322)(309,317)(310,320)(311,319)
(312,318)(314,316)(373,501)(374,504)(375,503)(376,502)(377,497)(378,500)
(379,499)(380,498)(381,617)(382,620)(383,619)(384,618)(385,613)(386,616)
(387,615)(388,614)(389,609)(390,612)(391,611)(392,610)(393,605)(394,608)
(395,607)(396,606)(397,601)(398,604)(399,603)(400,602)(401,597)(402,600)
(403,599)(404,598)(405,593)(406,596)(407,595)(408,594)(409,589)(410,592)
(411,591)(412,590)(413,585)(414,588)(415,587)(416,586)(417,581)(418,584)
(419,583)(420,582)(421,577)(422,580)(423,579)(424,578)(425,573)(426,576)
(427,575)(428,574)(429,569)(430,572)(431,571)(432,570)(433,565)(434,568)
(435,567)(436,566)(437,561)(438,564)(439,563)(440,562)(441,557)(442,560)
(443,559)(444,558)(445,553)(446,556)(447,555)(448,554)(449,549)(450,552)
(451,551)(452,550)(453,545)(454,548)(455,547)(456,546)(457,541)(458,544)
(459,543)(460,542)(461,537)(462,540)(463,539)(464,538)(465,533)(466,536)
(467,535)(468,534)(469,529)(470,532)(471,531)(472,530)(473,525)(474,528)
(475,527)(476,526)(477,521)(478,524)(479,523)(480,522)(481,517)(482,520)
(483,519)(484,518)(485,513)(486,516)(487,515)(488,514)(489,509)(490,512)
(491,511)(492,510)(493,505)(494,508)(495,507)(496,506)(621,625)(622,628)
(623,627)(624,626)(629,741)(630,744)(631,743)(632,742)(633,737)(634,740)
(635,739)(636,738)(637,733)(638,736)(639,735)(640,734)(641,729)(642,732)
(643,731)(644,730)(645,725)(646,728)(647,727)(648,726)(649,721)(650,724)
(651,723)(652,722)(653,717)(654,720)(655,719)(656,718)(657,713)(658,716)
(659,715)(660,714)(661,709)(662,712)(663,711)(664,710)(665,705)(666,708)
(667,707)(668,706)(669,701)(670,704)(671,703)(672,702)(673,697)(674,700)
(675,699)(676,698)(677,693)(678,696)(679,695)(680,694)(681,689)(682,692)
(683,691)(684,690)(686,688);
s2 := Sym(744)!( 1,374)( 2,373)( 3,376)( 4,375)( 5,378)( 6,377)( 7,380)
( 8,379)( 9,382)( 10,381)( 11,384)( 12,383)( 13,386)( 14,385)( 15,388)
( 16,387)( 17,390)( 18,389)( 19,392)( 20,391)( 21,394)( 22,393)( 23,396)
( 24,395)( 25,398)( 26,397)( 27,400)( 28,399)( 29,402)( 30,401)( 31,404)
( 32,403)( 33,406)( 34,405)( 35,408)( 36,407)( 37,410)( 38,409)( 39,412)
( 40,411)( 41,414)( 42,413)( 43,416)( 44,415)( 45,418)( 46,417)( 47,420)
( 48,419)( 49,422)( 50,421)( 51,424)( 52,423)( 53,426)( 54,425)( 55,428)
( 56,427)( 57,430)( 58,429)( 59,432)( 60,431)( 61,434)( 62,433)( 63,436)
( 64,435)( 65,438)( 66,437)( 67,440)( 68,439)( 69,442)( 70,441)( 71,444)
( 72,443)( 73,446)( 74,445)( 75,448)( 76,447)( 77,450)( 78,449)( 79,452)
( 80,451)( 81,454)( 82,453)( 83,456)( 84,455)( 85,458)( 86,457)( 87,460)
( 88,459)( 89,462)( 90,461)( 91,464)( 92,463)( 93,466)( 94,465)( 95,468)
( 96,467)( 97,470)( 98,469)( 99,472)(100,471)(101,474)(102,473)(103,476)
(104,475)(105,478)(106,477)(107,480)(108,479)(109,482)(110,481)(111,484)
(112,483)(113,486)(114,485)(115,488)(116,487)(117,490)(118,489)(119,492)
(120,491)(121,494)(122,493)(123,496)(124,495)(125,498)(126,497)(127,500)
(128,499)(129,502)(130,501)(131,504)(132,503)(133,506)(134,505)(135,508)
(136,507)(137,510)(138,509)(139,512)(140,511)(141,514)(142,513)(143,516)
(144,515)(145,518)(146,517)(147,520)(148,519)(149,522)(150,521)(151,524)
(152,523)(153,526)(154,525)(155,528)(156,527)(157,530)(158,529)(159,532)
(160,531)(161,534)(162,533)(163,536)(164,535)(165,538)(166,537)(167,540)
(168,539)(169,542)(170,541)(171,544)(172,543)(173,546)(174,545)(175,548)
(176,547)(177,550)(178,549)(179,552)(180,551)(181,554)(182,553)(183,556)
(184,555)(185,558)(186,557)(187,560)(188,559)(189,562)(190,561)(191,564)
(192,563)(193,566)(194,565)(195,568)(196,567)(197,570)(198,569)(199,572)
(200,571)(201,574)(202,573)(203,576)(204,575)(205,578)(206,577)(207,580)
(208,579)(209,582)(210,581)(211,584)(212,583)(213,586)(214,585)(215,588)
(216,587)(217,590)(218,589)(219,592)(220,591)(221,594)(222,593)(223,596)
(224,595)(225,598)(226,597)(227,600)(228,599)(229,602)(230,601)(231,604)
(232,603)(233,606)(234,605)(235,608)(236,607)(237,610)(238,609)(239,612)
(240,611)(241,614)(242,613)(243,616)(244,615)(245,618)(246,617)(247,620)
(248,619)(249,622)(250,621)(251,624)(252,623)(253,626)(254,625)(255,628)
(256,627)(257,630)(258,629)(259,632)(260,631)(261,634)(262,633)(263,636)
(264,635)(265,638)(266,637)(267,640)(268,639)(269,642)(270,641)(271,644)
(272,643)(273,646)(274,645)(275,648)(276,647)(277,650)(278,649)(279,652)
(280,651)(281,654)(282,653)(283,656)(284,655)(285,658)(286,657)(287,660)
(288,659)(289,662)(290,661)(291,664)(292,663)(293,666)(294,665)(295,668)
(296,667)(297,670)(298,669)(299,672)(300,671)(301,674)(302,673)(303,676)
(304,675)(305,678)(306,677)(307,680)(308,679)(309,682)(310,681)(311,684)
(312,683)(313,686)(314,685)(315,688)(316,687)(317,690)(318,689)(319,692)
(320,691)(321,694)(322,693)(323,696)(324,695)(325,698)(326,697)(327,700)
(328,699)(329,702)(330,701)(331,704)(332,703)(333,706)(334,705)(335,708)
(336,707)(337,710)(338,709)(339,712)(340,711)(341,714)(342,713)(343,716)
(344,715)(345,718)(346,717)(347,720)(348,719)(349,722)(350,721)(351,724)
(352,723)(353,726)(354,725)(355,728)(356,727)(357,730)(358,729)(359,732)
(360,731)(361,734)(362,733)(363,736)(364,735)(365,738)(366,737)(367,740)
(368,739)(369,742)(370,741)(371,744)(372,743);
poly := sub<Sym(744)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope