Polytope of Type {4,117}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,117}*1872
if this polytope has a name.
Group : SmallGroup(1872,542)
Rank : 3
Schlafli Type : {4,117}
Number of vertices, edges, etc : 8, 468, 234
Order of s₀s₁s₂ : 234
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,117}*936
   3-fold quotients : {4,39}*624
   4-fold quotients : {2,117}*468
   6-fold quotients : {4,39}*312
   12-fold quotients : {2,39}*156
   13-fold quotients : {4,9}*144
   26-fold quotients : {4,9}*72
   36-fold quotients : {2,13}*52
   39-fold quotients : {4,3}*48
   52-fold quotients : {2,9}*36
   78-fold quotients : {4,3}*24
   156-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,471)(  2,472)(  3,469)(  4,470)(  5,475)(  6,476)(  7,473)(  8,474)
(  9,479)( 10,480)( 11,477)( 12,478)( 13,483)( 14,484)( 15,481)( 16,482)
( 17,487)( 18,488)( 19,485)( 20,486)( 21,491)( 22,492)( 23,489)( 24,490)
( 25,495)( 26,496)( 27,493)( 28,494)( 29,499)( 30,500)( 31,497)( 32,498)
( 33,503)( 34,504)( 35,501)( 36,502)( 37,507)( 38,508)( 39,505)( 40,506)
( 41,511)( 42,512)( 43,509)( 44,510)( 45,515)( 46,516)( 47,513)( 48,514)
( 49,519)( 50,520)( 51,517)( 52,518)( 53,523)( 54,524)( 55,521)( 56,522)
( 57,527)( 58,528)( 59,525)( 60,526)( 61,531)( 62,532)( 63,529)( 64,530)
( 65,535)( 66,536)( 67,533)( 68,534)( 69,539)( 70,540)( 71,537)( 72,538)
( 73,543)( 74,544)( 75,541)( 76,542)( 77,547)( 78,548)( 79,545)( 80,546)
( 81,551)( 82,552)( 83,549)( 84,550)( 85,555)( 86,556)( 87,553)( 88,554)
( 89,559)( 90,560)( 91,557)( 92,558)( 93,563)( 94,564)( 95,561)( 96,562)
( 97,567)( 98,568)( 99,565)(100,566)(101,571)(102,572)(103,569)(104,570)
(105,575)(106,576)(107,573)(108,574)(109,579)(110,580)(111,577)(112,578)
(113,583)(114,584)(115,581)(116,582)(117,587)(118,588)(119,585)(120,586)
(121,591)(122,592)(123,589)(124,590)(125,595)(126,596)(127,593)(128,594)
(129,599)(130,600)(131,597)(132,598)(133,603)(134,604)(135,601)(136,602)
(137,607)(138,608)(139,605)(140,606)(141,611)(142,612)(143,609)(144,610)
(145,615)(146,616)(147,613)(148,614)(149,619)(150,620)(151,617)(152,618)
(153,623)(154,624)(155,621)(156,622)(157,627)(158,628)(159,625)(160,626)
(161,631)(162,632)(163,629)(164,630)(165,635)(166,636)(167,633)(168,634)
(169,639)(170,640)(171,637)(172,638)(173,643)(174,644)(175,641)(176,642)
(177,647)(178,648)(179,645)(180,646)(181,651)(182,652)(183,649)(184,650)
(185,655)(186,656)(187,653)(188,654)(189,659)(190,660)(191,657)(192,658)
(193,663)(194,664)(195,661)(196,662)(197,667)(198,668)(199,665)(200,666)
(201,671)(202,672)(203,669)(204,670)(205,675)(206,676)(207,673)(208,674)
(209,679)(210,680)(211,677)(212,678)(213,683)(214,684)(215,681)(216,682)
(217,687)(218,688)(219,685)(220,686)(221,691)(222,692)(223,689)(224,690)
(225,695)(226,696)(227,693)(228,694)(229,699)(230,700)(231,697)(232,698)
(233,703)(234,704)(235,701)(236,702)(237,707)(238,708)(239,705)(240,706)
(241,711)(242,712)(243,709)(244,710)(245,715)(246,716)(247,713)(248,714)
(249,719)(250,720)(251,717)(252,718)(253,723)(254,724)(255,721)(256,722)
(257,727)(258,728)(259,725)(260,726)(261,731)(262,732)(263,729)(264,730)
(265,735)(266,736)(267,733)(268,734)(269,739)(270,740)(271,737)(272,738)
(273,743)(274,744)(275,741)(276,742)(277,747)(278,748)(279,745)(280,746)
(281,751)(282,752)(283,749)(284,750)(285,755)(286,756)(287,753)(288,754)
(289,759)(290,760)(291,757)(292,758)(293,763)(294,764)(295,761)(296,762)
(297,767)(298,768)(299,765)(300,766)(301,771)(302,772)(303,769)(304,770)
(305,775)(306,776)(307,773)(308,774)(309,779)(310,780)(311,777)(312,778)
(313,783)(314,784)(315,781)(316,782)(317,787)(318,788)(319,785)(320,786)
(321,791)(322,792)(323,789)(324,790)(325,795)(326,796)(327,793)(328,794)
(329,799)(330,800)(331,797)(332,798)(333,803)(334,804)(335,801)(336,802)
(337,807)(338,808)(339,805)(340,806)(341,811)(342,812)(343,809)(344,810)
(345,815)(346,816)(347,813)(348,814)(349,819)(350,820)(351,817)(352,818)
(353,823)(354,824)(355,821)(356,822)(357,827)(358,828)(359,825)(360,826)
(361,831)(362,832)(363,829)(364,830)(365,835)(366,836)(367,833)(368,834)
(369,839)(370,840)(371,837)(372,838)(373,843)(374,844)(375,841)(376,842)
(377,847)(378,848)(379,845)(380,846)(381,851)(382,852)(383,849)(384,850)
(385,855)(386,856)(387,853)(388,854)(389,859)(390,860)(391,857)(392,858)
(393,863)(394,864)(395,861)(396,862)(397,867)(398,868)(399,865)(400,866)
(401,871)(402,872)(403,869)(404,870)(405,875)(406,876)(407,873)(408,874)
(409,879)(410,880)(411,877)(412,878)(413,883)(414,884)(415,881)(416,882)
(417,887)(418,888)(419,885)(420,886)(421,891)(422,892)(423,889)(424,890)
(425,895)(426,896)(427,893)(428,894)(429,899)(430,900)(431,897)(432,898)
(433,903)(434,904)(435,901)(436,902)(437,907)(438,908)(439,905)(440,906)
(441,911)(442,912)(443,909)(444,910)(445,915)(446,916)(447,913)(448,914)
(449,919)(450,920)(451,917)(452,918)(453,923)(454,924)(455,921)(456,922)
(457,927)(458,928)(459,925)(460,926)(461,931)(462,932)(463,929)(464,930)
(465,935)(466,936)(467,933)(468,934);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13,145)( 14,146)( 15,148)
( 16,147)( 17,153)( 18,154)( 19,156)( 20,155)( 21,149)( 22,150)( 23,152)
( 24,151)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)
( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)( 39,124)
( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)
( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)( 55,120)
( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61, 97)( 62, 98)( 63,100)
( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)
( 72,103)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(157,321)(158,322)(159,324)
(160,323)(161,317)(162,318)(163,320)(164,319)(165,313)(166,314)(167,316)
(168,315)(169,465)(170,466)(171,468)(172,467)(173,461)(174,462)(175,464)
(176,463)(177,457)(178,458)(179,460)(180,459)(181,453)(182,454)(183,456)
(184,455)(185,449)(186,450)(187,452)(188,451)(189,445)(190,446)(191,448)
(192,447)(193,441)(194,442)(195,444)(196,443)(197,437)(198,438)(199,440)
(200,439)(201,433)(202,434)(203,436)(204,435)(205,429)(206,430)(207,432)
(208,431)(209,425)(210,426)(211,428)(212,427)(213,421)(214,422)(215,424)
(216,423)(217,417)(218,418)(219,420)(220,419)(221,413)(222,414)(223,416)
(224,415)(225,409)(226,410)(227,412)(228,411)(229,405)(230,406)(231,408)
(232,407)(233,401)(234,402)(235,404)(236,403)(237,397)(238,398)(239,400)
(240,399)(241,393)(242,394)(243,396)(244,395)(245,389)(246,390)(247,392)
(248,391)(249,385)(250,386)(251,388)(252,387)(253,381)(254,382)(255,384)
(256,383)(257,377)(258,378)(259,380)(260,379)(261,373)(262,374)(263,376)
(264,375)(265,369)(266,370)(267,372)(268,371)(269,365)(270,366)(271,368)
(272,367)(273,361)(274,362)(275,364)(276,363)(277,357)(278,358)(279,360)
(280,359)(281,353)(282,354)(283,356)(284,355)(285,349)(286,350)(287,352)
(288,351)(289,345)(290,346)(291,348)(292,347)(293,341)(294,342)(295,344)
(296,343)(297,337)(298,338)(299,340)(300,339)(301,333)(302,334)(303,336)
(304,335)(305,329)(306,330)(307,332)(308,331)(309,325)(310,326)(311,328)
(312,327)(471,472)(473,477)(474,478)(475,480)(476,479)(481,613)(482,614)
(483,616)(484,615)(485,621)(486,622)(487,624)(488,623)(489,617)(490,618)
(491,620)(492,619)(493,601)(494,602)(495,604)(496,603)(497,609)(498,610)
(499,612)(500,611)(501,605)(502,606)(503,608)(504,607)(505,589)(506,590)
(507,592)(508,591)(509,597)(510,598)(511,600)(512,599)(513,593)(514,594)
(515,596)(516,595)(517,577)(518,578)(519,580)(520,579)(521,585)(522,586)
(523,588)(524,587)(525,581)(526,582)(527,584)(528,583)(529,565)(530,566)
(531,568)(532,567)(533,573)(534,574)(535,576)(536,575)(537,569)(538,570)
(539,572)(540,571)(541,553)(542,554)(543,556)(544,555)(545,561)(546,562)
(547,564)(548,563)(549,557)(550,558)(551,560)(552,559)(625,789)(626,790)
(627,792)(628,791)(629,785)(630,786)(631,788)(632,787)(633,781)(634,782)
(635,784)(636,783)(637,933)(638,934)(639,936)(640,935)(641,929)(642,930)
(643,932)(644,931)(645,925)(646,926)(647,928)(648,927)(649,921)(650,922)
(651,924)(652,923)(653,917)(654,918)(655,920)(656,919)(657,913)(658,914)
(659,916)(660,915)(661,909)(662,910)(663,912)(664,911)(665,905)(666,906)
(667,908)(668,907)(669,901)(670,902)(671,904)(672,903)(673,897)(674,898)
(675,900)(676,899)(677,893)(678,894)(679,896)(680,895)(681,889)(682,890)
(683,892)(684,891)(685,885)(686,886)(687,888)(688,887)(689,881)(690,882)
(691,884)(692,883)(693,877)(694,878)(695,880)(696,879)(697,873)(698,874)
(699,876)(700,875)(701,869)(702,870)(703,872)(704,871)(705,865)(706,866)
(707,868)(708,867)(709,861)(710,862)(711,864)(712,863)(713,857)(714,858)
(715,860)(716,859)(717,853)(718,854)(719,856)(720,855)(721,849)(722,850)
(723,852)(724,851)(725,845)(726,846)(727,848)(728,847)(729,841)(730,842)
(731,844)(732,843)(733,837)(734,838)(735,840)(736,839)(737,833)(738,834)
(739,836)(740,835)(741,829)(742,830)(743,832)(744,831)(745,825)(746,826)
(747,828)(748,827)(749,821)(750,822)(751,824)(752,823)(753,817)(754,818)
(755,820)(756,819)(757,813)(758,814)(759,816)(760,815)(761,809)(762,810)
(763,812)(764,811)(765,805)(766,806)(767,808)(768,807)(769,801)(770,802)
(771,804)(772,803)(773,797)(774,798)(775,800)(776,799)(777,793)(778,794)
(779,796)(780,795);;
s2 := (  1,169)(  2,172)(  3,171)(  4,170)(  5,177)(  6,180)(  7,179)(  8,178)
(  9,173)( 10,176)( 11,175)( 12,174)( 13,157)( 14,160)( 15,159)( 16,158)
( 17,165)( 18,168)( 19,167)( 20,166)( 21,161)( 22,164)( 23,163)( 24,162)
( 25,301)( 26,304)( 27,303)( 28,302)( 29,309)( 30,312)( 31,311)( 32,310)
( 33,305)( 34,308)( 35,307)( 36,306)( 37,289)( 38,292)( 39,291)( 40,290)
( 41,297)( 42,300)( 43,299)( 44,298)( 45,293)( 46,296)( 47,295)( 48,294)
( 49,277)( 50,280)( 51,279)( 52,278)( 53,285)( 54,288)( 55,287)( 56,286)
( 57,281)( 58,284)( 59,283)( 60,282)( 61,265)( 62,268)( 63,267)( 64,266)
( 65,273)( 66,276)( 67,275)( 68,274)( 69,269)( 70,272)( 71,271)( 72,270)
( 73,253)( 74,256)( 75,255)( 76,254)( 77,261)( 78,264)( 79,263)( 80,262)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,241)( 86,244)( 87,243)( 88,242)
( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)( 96,246)
( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)(104,238)
(105,233)(106,236)(107,235)(108,234)(109,217)(110,220)(111,219)(112,218)
(113,225)(114,228)(115,227)(116,226)(117,221)(118,224)(119,223)(120,222)
(121,205)(122,208)(123,207)(124,206)(125,213)(126,216)(127,215)(128,214)
(129,209)(130,212)(131,211)(132,210)(133,193)(134,196)(135,195)(136,194)
(137,201)(138,204)(139,203)(140,202)(141,197)(142,200)(143,199)(144,198)
(145,181)(146,184)(147,183)(148,182)(149,189)(150,192)(151,191)(152,190)
(153,185)(154,188)(155,187)(156,186)(313,333)(314,336)(315,335)(316,334)
(317,329)(318,332)(319,331)(320,330)(321,325)(322,328)(323,327)(324,326)
(337,465)(338,468)(339,467)(340,466)(341,461)(342,464)(343,463)(344,462)
(345,457)(346,460)(347,459)(348,458)(349,453)(350,456)(351,455)(352,454)
(353,449)(354,452)(355,451)(356,450)(357,445)(358,448)(359,447)(360,446)
(361,441)(362,444)(363,443)(364,442)(365,437)(366,440)(367,439)(368,438)
(369,433)(370,436)(371,435)(372,434)(373,429)(374,432)(375,431)(376,430)
(377,425)(378,428)(379,427)(380,426)(381,421)(382,424)(383,423)(384,422)
(385,417)(386,420)(387,419)(388,418)(389,413)(390,416)(391,415)(392,414)
(393,409)(394,412)(395,411)(396,410)(397,405)(398,408)(399,407)(400,406)
(402,404)(469,637)(470,640)(471,639)(472,638)(473,645)(474,648)(475,647)
(476,646)(477,641)(478,644)(479,643)(480,642)(481,625)(482,628)(483,627)
(484,626)(485,633)(486,636)(487,635)(488,634)(489,629)(490,632)(491,631)
(492,630)(493,769)(494,772)(495,771)(496,770)(497,777)(498,780)(499,779)
(500,778)(501,773)(502,776)(503,775)(504,774)(505,757)(506,760)(507,759)
(508,758)(509,765)(510,768)(511,767)(512,766)(513,761)(514,764)(515,763)
(516,762)(517,745)(518,748)(519,747)(520,746)(521,753)(522,756)(523,755)
(524,754)(525,749)(526,752)(527,751)(528,750)(529,733)(530,736)(531,735)
(532,734)(533,741)(534,744)(535,743)(536,742)(537,737)(538,740)(539,739)
(540,738)(541,721)(542,724)(543,723)(544,722)(545,729)(546,732)(547,731)
(548,730)(549,725)(550,728)(551,727)(552,726)(553,709)(554,712)(555,711)
(556,710)(557,717)(558,720)(559,719)(560,718)(561,713)(562,716)(563,715)
(564,714)(565,697)(566,700)(567,699)(568,698)(569,705)(570,708)(571,707)
(572,706)(573,701)(574,704)(575,703)(576,702)(577,685)(578,688)(579,687)
(580,686)(581,693)(582,696)(583,695)(584,694)(585,689)(586,692)(587,691)
(588,690)(589,673)(590,676)(591,675)(592,674)(593,681)(594,684)(595,683)
(596,682)(597,677)(598,680)(599,679)(600,678)(601,661)(602,664)(603,663)
(604,662)(605,669)(606,672)(607,671)(608,670)(609,665)(610,668)(611,667)
(612,666)(613,649)(614,652)(615,651)(616,650)(617,657)(618,660)(619,659)
(620,658)(621,653)(622,656)(623,655)(624,654)(781,801)(782,804)(783,803)
(784,802)(785,797)(786,800)(787,799)(788,798)(789,793)(790,796)(791,795)
(792,794)(805,933)(806,936)(807,935)(808,934)(809,929)(810,932)(811,931)
(812,930)(813,925)(814,928)(815,927)(816,926)(817,921)(818,924)(819,923)
(820,922)(821,917)(822,920)(823,919)(824,918)(825,913)(826,916)(827,915)
(828,914)(829,909)(830,912)(831,911)(832,910)(833,905)(834,908)(835,907)
(836,906)(837,901)(838,904)(839,903)(840,902)(841,897)(842,900)(843,899)
(844,898)(845,893)(846,896)(847,895)(848,894)(849,889)(850,892)(851,891)
(852,890)(853,885)(854,888)(855,887)(856,886)(857,881)(858,884)(859,883)
(860,882)(861,877)(862,880)(863,879)(864,878)(865,873)(866,876)(867,875)
(868,874)(870,872);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(936)!(  1,471)(  2,472)(  3,469)(  4,470)(  5,475)(  6,476)(  7,473)
(  8,474)(  9,479)( 10,480)( 11,477)( 12,478)( 13,483)( 14,484)( 15,481)
( 16,482)( 17,487)( 18,488)( 19,485)( 20,486)( 21,491)( 22,492)( 23,489)
( 24,490)( 25,495)( 26,496)( 27,493)( 28,494)( 29,499)( 30,500)( 31,497)
( 32,498)( 33,503)( 34,504)( 35,501)( 36,502)( 37,507)( 38,508)( 39,505)
( 40,506)( 41,511)( 42,512)( 43,509)( 44,510)( 45,515)( 46,516)( 47,513)
( 48,514)( 49,519)( 50,520)( 51,517)( 52,518)( 53,523)( 54,524)( 55,521)
( 56,522)( 57,527)( 58,528)( 59,525)( 60,526)( 61,531)( 62,532)( 63,529)
( 64,530)( 65,535)( 66,536)( 67,533)( 68,534)( 69,539)( 70,540)( 71,537)
( 72,538)( 73,543)( 74,544)( 75,541)( 76,542)( 77,547)( 78,548)( 79,545)
( 80,546)( 81,551)( 82,552)( 83,549)( 84,550)( 85,555)( 86,556)( 87,553)
( 88,554)( 89,559)( 90,560)( 91,557)( 92,558)( 93,563)( 94,564)( 95,561)
( 96,562)( 97,567)( 98,568)( 99,565)(100,566)(101,571)(102,572)(103,569)
(104,570)(105,575)(106,576)(107,573)(108,574)(109,579)(110,580)(111,577)
(112,578)(113,583)(114,584)(115,581)(116,582)(117,587)(118,588)(119,585)
(120,586)(121,591)(122,592)(123,589)(124,590)(125,595)(126,596)(127,593)
(128,594)(129,599)(130,600)(131,597)(132,598)(133,603)(134,604)(135,601)
(136,602)(137,607)(138,608)(139,605)(140,606)(141,611)(142,612)(143,609)
(144,610)(145,615)(146,616)(147,613)(148,614)(149,619)(150,620)(151,617)
(152,618)(153,623)(154,624)(155,621)(156,622)(157,627)(158,628)(159,625)
(160,626)(161,631)(162,632)(163,629)(164,630)(165,635)(166,636)(167,633)
(168,634)(169,639)(170,640)(171,637)(172,638)(173,643)(174,644)(175,641)
(176,642)(177,647)(178,648)(179,645)(180,646)(181,651)(182,652)(183,649)
(184,650)(185,655)(186,656)(187,653)(188,654)(189,659)(190,660)(191,657)
(192,658)(193,663)(194,664)(195,661)(196,662)(197,667)(198,668)(199,665)
(200,666)(201,671)(202,672)(203,669)(204,670)(205,675)(206,676)(207,673)
(208,674)(209,679)(210,680)(211,677)(212,678)(213,683)(214,684)(215,681)
(216,682)(217,687)(218,688)(219,685)(220,686)(221,691)(222,692)(223,689)
(224,690)(225,695)(226,696)(227,693)(228,694)(229,699)(230,700)(231,697)
(232,698)(233,703)(234,704)(235,701)(236,702)(237,707)(238,708)(239,705)
(240,706)(241,711)(242,712)(243,709)(244,710)(245,715)(246,716)(247,713)
(248,714)(249,719)(250,720)(251,717)(252,718)(253,723)(254,724)(255,721)
(256,722)(257,727)(258,728)(259,725)(260,726)(261,731)(262,732)(263,729)
(264,730)(265,735)(266,736)(267,733)(268,734)(269,739)(270,740)(271,737)
(272,738)(273,743)(274,744)(275,741)(276,742)(277,747)(278,748)(279,745)
(280,746)(281,751)(282,752)(283,749)(284,750)(285,755)(286,756)(287,753)
(288,754)(289,759)(290,760)(291,757)(292,758)(293,763)(294,764)(295,761)
(296,762)(297,767)(298,768)(299,765)(300,766)(301,771)(302,772)(303,769)
(304,770)(305,775)(306,776)(307,773)(308,774)(309,779)(310,780)(311,777)
(312,778)(313,783)(314,784)(315,781)(316,782)(317,787)(318,788)(319,785)
(320,786)(321,791)(322,792)(323,789)(324,790)(325,795)(326,796)(327,793)
(328,794)(329,799)(330,800)(331,797)(332,798)(333,803)(334,804)(335,801)
(336,802)(337,807)(338,808)(339,805)(340,806)(341,811)(342,812)(343,809)
(344,810)(345,815)(346,816)(347,813)(348,814)(349,819)(350,820)(351,817)
(352,818)(353,823)(354,824)(355,821)(356,822)(357,827)(358,828)(359,825)
(360,826)(361,831)(362,832)(363,829)(364,830)(365,835)(366,836)(367,833)
(368,834)(369,839)(370,840)(371,837)(372,838)(373,843)(374,844)(375,841)
(376,842)(377,847)(378,848)(379,845)(380,846)(381,851)(382,852)(383,849)
(384,850)(385,855)(386,856)(387,853)(388,854)(389,859)(390,860)(391,857)
(392,858)(393,863)(394,864)(395,861)(396,862)(397,867)(398,868)(399,865)
(400,866)(401,871)(402,872)(403,869)(404,870)(405,875)(406,876)(407,873)
(408,874)(409,879)(410,880)(411,877)(412,878)(413,883)(414,884)(415,881)
(416,882)(417,887)(418,888)(419,885)(420,886)(421,891)(422,892)(423,889)
(424,890)(425,895)(426,896)(427,893)(428,894)(429,899)(430,900)(431,897)
(432,898)(433,903)(434,904)(435,901)(436,902)(437,907)(438,908)(439,905)
(440,906)(441,911)(442,912)(443,909)(444,910)(445,915)(446,916)(447,913)
(448,914)(449,919)(450,920)(451,917)(452,918)(453,923)(454,924)(455,921)
(456,922)(457,927)(458,928)(459,925)(460,926)(461,931)(462,932)(463,929)
(464,930)(465,935)(466,936)(467,933)(468,934);
s1 := Sym(936)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13,145)( 14,146)
( 15,148)( 16,147)( 17,153)( 18,154)( 19,156)( 20,155)( 21,149)( 22,150)
( 23,152)( 24,151)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)
( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)
( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)
( 47,128)( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)
( 55,120)( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61, 97)( 62, 98)
( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)
( 71,104)( 72,103)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)
( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(157,321)(158,322)
(159,324)(160,323)(161,317)(162,318)(163,320)(164,319)(165,313)(166,314)
(167,316)(168,315)(169,465)(170,466)(171,468)(172,467)(173,461)(174,462)
(175,464)(176,463)(177,457)(178,458)(179,460)(180,459)(181,453)(182,454)
(183,456)(184,455)(185,449)(186,450)(187,452)(188,451)(189,445)(190,446)
(191,448)(192,447)(193,441)(194,442)(195,444)(196,443)(197,437)(198,438)
(199,440)(200,439)(201,433)(202,434)(203,436)(204,435)(205,429)(206,430)
(207,432)(208,431)(209,425)(210,426)(211,428)(212,427)(213,421)(214,422)
(215,424)(216,423)(217,417)(218,418)(219,420)(220,419)(221,413)(222,414)
(223,416)(224,415)(225,409)(226,410)(227,412)(228,411)(229,405)(230,406)
(231,408)(232,407)(233,401)(234,402)(235,404)(236,403)(237,397)(238,398)
(239,400)(240,399)(241,393)(242,394)(243,396)(244,395)(245,389)(246,390)
(247,392)(248,391)(249,385)(250,386)(251,388)(252,387)(253,381)(254,382)
(255,384)(256,383)(257,377)(258,378)(259,380)(260,379)(261,373)(262,374)
(263,376)(264,375)(265,369)(266,370)(267,372)(268,371)(269,365)(270,366)
(271,368)(272,367)(273,361)(274,362)(275,364)(276,363)(277,357)(278,358)
(279,360)(280,359)(281,353)(282,354)(283,356)(284,355)(285,349)(286,350)
(287,352)(288,351)(289,345)(290,346)(291,348)(292,347)(293,341)(294,342)
(295,344)(296,343)(297,337)(298,338)(299,340)(300,339)(301,333)(302,334)
(303,336)(304,335)(305,329)(306,330)(307,332)(308,331)(309,325)(310,326)
(311,328)(312,327)(471,472)(473,477)(474,478)(475,480)(476,479)(481,613)
(482,614)(483,616)(484,615)(485,621)(486,622)(487,624)(488,623)(489,617)
(490,618)(491,620)(492,619)(493,601)(494,602)(495,604)(496,603)(497,609)
(498,610)(499,612)(500,611)(501,605)(502,606)(503,608)(504,607)(505,589)
(506,590)(507,592)(508,591)(509,597)(510,598)(511,600)(512,599)(513,593)
(514,594)(515,596)(516,595)(517,577)(518,578)(519,580)(520,579)(521,585)
(522,586)(523,588)(524,587)(525,581)(526,582)(527,584)(528,583)(529,565)
(530,566)(531,568)(532,567)(533,573)(534,574)(535,576)(536,575)(537,569)
(538,570)(539,572)(540,571)(541,553)(542,554)(543,556)(544,555)(545,561)
(546,562)(547,564)(548,563)(549,557)(550,558)(551,560)(552,559)(625,789)
(626,790)(627,792)(628,791)(629,785)(630,786)(631,788)(632,787)(633,781)
(634,782)(635,784)(636,783)(637,933)(638,934)(639,936)(640,935)(641,929)
(642,930)(643,932)(644,931)(645,925)(646,926)(647,928)(648,927)(649,921)
(650,922)(651,924)(652,923)(653,917)(654,918)(655,920)(656,919)(657,913)
(658,914)(659,916)(660,915)(661,909)(662,910)(663,912)(664,911)(665,905)
(666,906)(667,908)(668,907)(669,901)(670,902)(671,904)(672,903)(673,897)
(674,898)(675,900)(676,899)(677,893)(678,894)(679,896)(680,895)(681,889)
(682,890)(683,892)(684,891)(685,885)(686,886)(687,888)(688,887)(689,881)
(690,882)(691,884)(692,883)(693,877)(694,878)(695,880)(696,879)(697,873)
(698,874)(699,876)(700,875)(701,869)(702,870)(703,872)(704,871)(705,865)
(706,866)(707,868)(708,867)(709,861)(710,862)(711,864)(712,863)(713,857)
(714,858)(715,860)(716,859)(717,853)(718,854)(719,856)(720,855)(721,849)
(722,850)(723,852)(724,851)(725,845)(726,846)(727,848)(728,847)(729,841)
(730,842)(731,844)(732,843)(733,837)(734,838)(735,840)(736,839)(737,833)
(738,834)(739,836)(740,835)(741,829)(742,830)(743,832)(744,831)(745,825)
(746,826)(747,828)(748,827)(749,821)(750,822)(751,824)(752,823)(753,817)
(754,818)(755,820)(756,819)(757,813)(758,814)(759,816)(760,815)(761,809)
(762,810)(763,812)(764,811)(765,805)(766,806)(767,808)(768,807)(769,801)
(770,802)(771,804)(772,803)(773,797)(774,798)(775,800)(776,799)(777,793)
(778,794)(779,796)(780,795);
s2 := Sym(936)!(  1,169)(  2,172)(  3,171)(  4,170)(  5,177)(  6,180)(  7,179)
(  8,178)(  9,173)( 10,176)( 11,175)( 12,174)( 13,157)( 14,160)( 15,159)
( 16,158)( 17,165)( 18,168)( 19,167)( 20,166)( 21,161)( 22,164)( 23,163)
( 24,162)( 25,301)( 26,304)( 27,303)( 28,302)( 29,309)( 30,312)( 31,311)
( 32,310)( 33,305)( 34,308)( 35,307)( 36,306)( 37,289)( 38,292)( 39,291)
( 40,290)( 41,297)( 42,300)( 43,299)( 44,298)( 45,293)( 46,296)( 47,295)
( 48,294)( 49,277)( 50,280)( 51,279)( 52,278)( 53,285)( 54,288)( 55,287)
( 56,286)( 57,281)( 58,284)( 59,283)( 60,282)( 61,265)( 62,268)( 63,267)
( 64,266)( 65,273)( 66,276)( 67,275)( 68,274)( 69,269)( 70,272)( 71,271)
( 72,270)( 73,253)( 74,256)( 75,255)( 76,254)( 77,261)( 78,264)( 79,263)
( 80,262)( 81,257)( 82,260)( 83,259)( 84,258)( 85,241)( 86,244)( 87,243)
( 88,242)( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)
( 96,246)( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)
(104,238)(105,233)(106,236)(107,235)(108,234)(109,217)(110,220)(111,219)
(112,218)(113,225)(114,228)(115,227)(116,226)(117,221)(118,224)(119,223)
(120,222)(121,205)(122,208)(123,207)(124,206)(125,213)(126,216)(127,215)
(128,214)(129,209)(130,212)(131,211)(132,210)(133,193)(134,196)(135,195)
(136,194)(137,201)(138,204)(139,203)(140,202)(141,197)(142,200)(143,199)
(144,198)(145,181)(146,184)(147,183)(148,182)(149,189)(150,192)(151,191)
(152,190)(153,185)(154,188)(155,187)(156,186)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(321,325)(322,328)(323,327)
(324,326)(337,465)(338,468)(339,467)(340,466)(341,461)(342,464)(343,463)
(344,462)(345,457)(346,460)(347,459)(348,458)(349,453)(350,456)(351,455)
(352,454)(353,449)(354,452)(355,451)(356,450)(357,445)(358,448)(359,447)
(360,446)(361,441)(362,444)(363,443)(364,442)(365,437)(366,440)(367,439)
(368,438)(369,433)(370,436)(371,435)(372,434)(373,429)(374,432)(375,431)
(376,430)(377,425)(378,428)(379,427)(380,426)(381,421)(382,424)(383,423)
(384,422)(385,417)(386,420)(387,419)(388,418)(389,413)(390,416)(391,415)
(392,414)(393,409)(394,412)(395,411)(396,410)(397,405)(398,408)(399,407)
(400,406)(402,404)(469,637)(470,640)(471,639)(472,638)(473,645)(474,648)
(475,647)(476,646)(477,641)(478,644)(479,643)(480,642)(481,625)(482,628)
(483,627)(484,626)(485,633)(486,636)(487,635)(488,634)(489,629)(490,632)
(491,631)(492,630)(493,769)(494,772)(495,771)(496,770)(497,777)(498,780)
(499,779)(500,778)(501,773)(502,776)(503,775)(504,774)(505,757)(506,760)
(507,759)(508,758)(509,765)(510,768)(511,767)(512,766)(513,761)(514,764)
(515,763)(516,762)(517,745)(518,748)(519,747)(520,746)(521,753)(522,756)
(523,755)(524,754)(525,749)(526,752)(527,751)(528,750)(529,733)(530,736)
(531,735)(532,734)(533,741)(534,744)(535,743)(536,742)(537,737)(538,740)
(539,739)(540,738)(541,721)(542,724)(543,723)(544,722)(545,729)(546,732)
(547,731)(548,730)(549,725)(550,728)(551,727)(552,726)(553,709)(554,712)
(555,711)(556,710)(557,717)(558,720)(559,719)(560,718)(561,713)(562,716)
(563,715)(564,714)(565,697)(566,700)(567,699)(568,698)(569,705)(570,708)
(571,707)(572,706)(573,701)(574,704)(575,703)(576,702)(577,685)(578,688)
(579,687)(580,686)(581,693)(582,696)(583,695)(584,694)(585,689)(586,692)
(587,691)(588,690)(589,673)(590,676)(591,675)(592,674)(593,681)(594,684)
(595,683)(596,682)(597,677)(598,680)(599,679)(600,678)(601,661)(602,664)
(603,663)(604,662)(605,669)(606,672)(607,671)(608,670)(609,665)(610,668)
(611,667)(612,666)(613,649)(614,652)(615,651)(616,650)(617,657)(618,660)
(619,659)(620,658)(621,653)(622,656)(623,655)(624,654)(781,801)(782,804)
(783,803)(784,802)(785,797)(786,800)(787,799)(788,798)(789,793)(790,796)
(791,795)(792,794)(805,933)(806,936)(807,935)(808,934)(809,929)(810,932)
(811,931)(812,930)(813,925)(814,928)(815,927)(816,926)(817,921)(818,924)
(819,923)(820,922)(821,917)(822,920)(823,919)(824,918)(825,913)(826,916)
(827,915)(828,914)(829,909)(830,912)(831,911)(832,910)(833,905)(834,908)
(835,907)(836,906)(837,901)(838,904)(839,903)(840,902)(841,897)(842,900)
(843,899)(844,898)(845,893)(846,896)(847,895)(848,894)(849,889)(850,892)
(851,891)(852,890)(853,885)(854,888)(855,887)(856,886)(857,881)(858,884)
(859,883)(860,882)(861,877)(862,880)(863,879)(864,878)(865,873)(866,876)
(867,875)(868,874)(870,872);
poly := sub<Sym(936)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope