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Polytope of Type {234,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {234,4}*1872c
if this polytope has a name.
Group : SmallGroup(1872,542)
Rank : 3
Schlafli Type : {234,4}
Number of vertices, edges, etc : 234, 468, 4
Order of s0s1s2 : 117
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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 : {117,4}*936
   3-fold quotients : {78,4}*624c
   6-fold quotients : {39,4}*312
   13-fold quotients : {18,4}*144c
   26-fold quotients : {9,4}*72
   39-fold quotients : {6,4}*48b
   78-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  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);;
s1 := (  1,637)(  2,640)(  3,639)(  4,638)(  5,645)(  6,648)(  7,647)(  8,646)
(  9,641)( 10,644)( 11,643)( 12,642)( 13,625)( 14,628)( 15,627)( 16,626)
( 17,633)( 18,636)( 19,635)( 20,634)( 21,629)( 22,632)( 23,631)( 24,630)
( 25,769)( 26,772)( 27,771)( 28,770)( 29,777)( 30,780)( 31,779)( 32,778)
( 33,773)( 34,776)( 35,775)( 36,774)( 37,757)( 38,760)( 39,759)( 40,758)
( 41,765)( 42,768)( 43,767)( 44,766)( 45,761)( 46,764)( 47,763)( 48,762)
( 49,745)( 50,748)( 51,747)( 52,746)( 53,753)( 54,756)( 55,755)( 56,754)
( 57,749)( 58,752)( 59,751)( 60,750)( 61,733)( 62,736)( 63,735)( 64,734)
( 65,741)( 66,744)( 67,743)( 68,742)( 69,737)( 70,740)( 71,739)( 72,738)
( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)( 80,730)
( 81,725)( 82,728)( 83,727)( 84,726)( 85,709)( 86,712)( 87,711)( 88,710)
( 89,717)( 90,720)( 91,719)( 92,718)( 93,713)( 94,716)( 95,715)( 96,714)
( 97,697)( 98,700)( 99,699)(100,698)(101,705)(102,708)(103,707)(104,706)
(105,701)(106,704)(107,703)(108,702)(109,685)(110,688)(111,687)(112,686)
(113,693)(114,696)(115,695)(116,694)(117,689)(118,692)(119,691)(120,690)
(121,673)(122,676)(123,675)(124,674)(125,681)(126,684)(127,683)(128,682)
(129,677)(130,680)(131,679)(132,678)(133,661)(134,664)(135,663)(136,662)
(137,669)(138,672)(139,671)(140,670)(141,665)(142,668)(143,667)(144,666)
(145,649)(146,652)(147,651)(148,650)(149,657)(150,660)(151,659)(152,658)
(153,653)(154,656)(155,655)(156,654)(157,481)(158,484)(159,483)(160,482)
(161,489)(162,492)(163,491)(164,490)(165,485)(166,488)(167,487)(168,486)
(169,469)(170,472)(171,471)(172,470)(173,477)(174,480)(175,479)(176,478)
(177,473)(178,476)(179,475)(180,474)(181,613)(182,616)(183,615)(184,614)
(185,621)(186,624)(187,623)(188,622)(189,617)(190,620)(191,619)(192,618)
(193,601)(194,604)(195,603)(196,602)(197,609)(198,612)(199,611)(200,610)
(201,605)(202,608)(203,607)(204,606)(205,589)(206,592)(207,591)(208,590)
(209,597)(210,600)(211,599)(212,598)(213,593)(214,596)(215,595)(216,594)
(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)(224,586)
(225,581)(226,584)(227,583)(228,582)(229,565)(230,568)(231,567)(232,566)
(233,573)(234,576)(235,575)(236,574)(237,569)(238,572)(239,571)(240,570)
(241,553)(242,556)(243,555)(244,554)(245,561)(246,564)(247,563)(248,562)
(249,557)(250,560)(251,559)(252,558)(253,541)(254,544)(255,543)(256,542)
(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)
(265,529)(266,532)(267,531)(268,530)(269,537)(270,540)(271,539)(272,538)
(273,533)(274,536)(275,535)(276,534)(277,517)(278,520)(279,519)(280,518)
(281,525)(282,528)(283,527)(284,526)(285,521)(286,524)(287,523)(288,522)
(289,505)(290,508)(291,507)(292,506)(293,513)(294,516)(295,515)(296,514)
(297,509)(298,512)(299,511)(300,510)(301,493)(302,496)(303,495)(304,494)
(305,501)(306,504)(307,503)(308,502)(309,497)(310,500)(311,499)(312,498)
(313,801)(314,804)(315,803)(316,802)(317,797)(318,800)(319,799)(320,798)
(321,793)(322,796)(323,795)(324,794)(325,789)(326,792)(327,791)(328,790)
(329,785)(330,788)(331,787)(332,786)(333,781)(334,784)(335,783)(336,782)
(337,933)(338,936)(339,935)(340,934)(341,929)(342,932)(343,931)(344,930)
(345,925)(346,928)(347,927)(348,926)(349,921)(350,924)(351,923)(352,922)
(353,917)(354,920)(355,919)(356,918)(357,913)(358,916)(359,915)(360,914)
(361,909)(362,912)(363,911)(364,910)(365,905)(366,908)(367,907)(368,906)
(369,901)(370,904)(371,903)(372,902)(373,897)(374,900)(375,899)(376,898)
(377,893)(378,896)(379,895)(380,894)(381,889)(382,892)(383,891)(384,890)
(385,885)(386,888)(387,887)(388,886)(389,881)(390,884)(391,883)(392,882)
(393,877)(394,880)(395,879)(396,878)(397,873)(398,876)(399,875)(400,874)
(401,869)(402,872)(403,871)(404,870)(405,865)(406,868)(407,867)(408,866)
(409,861)(410,864)(411,863)(412,862)(413,857)(414,860)(415,859)(416,858)
(417,853)(418,856)(419,855)(420,854)(421,849)(422,852)(423,851)(424,850)
(425,845)(426,848)(427,847)(428,846)(429,841)(430,844)(431,843)(432,842)
(433,837)(434,840)(435,839)(436,838)(437,833)(438,836)(439,835)(440,834)
(441,829)(442,832)(443,831)(444,830)(445,825)(446,828)(447,827)(448,826)
(449,821)(450,824)(451,823)(452,822)(453,817)(454,820)(455,819)(456,818)
(457,813)(458,816)(459,815)(460,814)(461,809)(462,812)(463,811)(464,810)
(465,805)(466,808)(467,807)(468,806);;
s2 := (  1,470)(  2,469)(  3,472)(  4,471)(  5,474)(  6,473)(  7,476)(  8,475)
(  9,478)( 10,477)( 11,480)( 12,479)( 13,482)( 14,481)( 15,484)( 16,483)
( 17,486)( 18,485)( 19,488)( 20,487)( 21,490)( 22,489)( 23,492)( 24,491)
( 25,494)( 26,493)( 27,496)( 28,495)( 29,498)( 30,497)( 31,500)( 32,499)
( 33,502)( 34,501)( 35,504)( 36,503)( 37,506)( 38,505)( 39,508)( 40,507)
( 41,510)( 42,509)( 43,512)( 44,511)( 45,514)( 46,513)( 47,516)( 48,515)
( 49,518)( 50,517)( 51,520)( 52,519)( 53,522)( 54,521)( 55,524)( 56,523)
( 57,526)( 58,525)( 59,528)( 60,527)( 61,530)( 62,529)( 63,532)( 64,531)
( 65,534)( 66,533)( 67,536)( 68,535)( 69,538)( 70,537)( 71,540)( 72,539)
( 73,542)( 74,541)( 75,544)( 76,543)( 77,546)( 78,545)( 79,548)( 80,547)
( 81,550)( 82,549)( 83,552)( 84,551)( 85,554)( 86,553)( 87,556)( 88,555)
( 89,558)( 90,557)( 91,560)( 92,559)( 93,562)( 94,561)( 95,564)( 96,563)
( 97,566)( 98,565)( 99,568)(100,567)(101,570)(102,569)(103,572)(104,571)
(105,574)(106,573)(107,576)(108,575)(109,578)(110,577)(111,580)(112,579)
(113,582)(114,581)(115,584)(116,583)(117,586)(118,585)(119,588)(120,587)
(121,590)(122,589)(123,592)(124,591)(125,594)(126,593)(127,596)(128,595)
(129,598)(130,597)(131,600)(132,599)(133,602)(134,601)(135,604)(136,603)
(137,606)(138,605)(139,608)(140,607)(141,610)(142,609)(143,612)(144,611)
(145,614)(146,613)(147,616)(148,615)(149,618)(150,617)(151,620)(152,619)
(153,622)(154,621)(155,624)(156,623)(157,626)(158,625)(159,628)(160,627)
(161,630)(162,629)(163,632)(164,631)(165,634)(166,633)(167,636)(168,635)
(169,638)(170,637)(171,640)(172,639)(173,642)(174,641)(175,644)(176,643)
(177,646)(178,645)(179,648)(180,647)(181,650)(182,649)(183,652)(184,651)
(185,654)(186,653)(187,656)(188,655)(189,658)(190,657)(191,660)(192,659)
(193,662)(194,661)(195,664)(196,663)(197,666)(198,665)(199,668)(200,667)
(201,670)(202,669)(203,672)(204,671)(205,674)(206,673)(207,676)(208,675)
(209,678)(210,677)(211,680)(212,679)(213,682)(214,681)(215,684)(216,683)
(217,686)(218,685)(219,688)(220,687)(221,690)(222,689)(223,692)(224,691)
(225,694)(226,693)(227,696)(228,695)(229,698)(230,697)(231,700)(232,699)
(233,702)(234,701)(235,704)(236,703)(237,706)(238,705)(239,708)(240,707)
(241,710)(242,709)(243,712)(244,711)(245,714)(246,713)(247,716)(248,715)
(249,718)(250,717)(251,720)(252,719)(253,722)(254,721)(255,724)(256,723)
(257,726)(258,725)(259,728)(260,727)(261,730)(262,729)(263,732)(264,731)
(265,734)(266,733)(267,736)(268,735)(269,738)(270,737)(271,740)(272,739)
(273,742)(274,741)(275,744)(276,743)(277,746)(278,745)(279,748)(280,747)
(281,750)(282,749)(283,752)(284,751)(285,754)(286,753)(287,756)(288,755)
(289,758)(290,757)(291,760)(292,759)(293,762)(294,761)(295,764)(296,763)
(297,766)(298,765)(299,768)(300,767)(301,770)(302,769)(303,772)(304,771)
(305,774)(306,773)(307,776)(308,775)(309,778)(310,777)(311,780)(312,779)
(313,782)(314,781)(315,784)(316,783)(317,786)(318,785)(319,788)(320,787)
(321,790)(322,789)(323,792)(324,791)(325,794)(326,793)(327,796)(328,795)
(329,798)(330,797)(331,800)(332,799)(333,802)(334,801)(335,804)(336,803)
(337,806)(338,805)(339,808)(340,807)(341,810)(342,809)(343,812)(344,811)
(345,814)(346,813)(347,816)(348,815)(349,818)(350,817)(351,820)(352,819)
(353,822)(354,821)(355,824)(356,823)(357,826)(358,825)(359,828)(360,827)
(361,830)(362,829)(363,832)(364,831)(365,834)(366,833)(367,836)(368,835)
(369,838)(370,837)(371,840)(372,839)(373,842)(374,841)(375,844)(376,843)
(377,846)(378,845)(379,848)(380,847)(381,850)(382,849)(383,852)(384,851)
(385,854)(386,853)(387,856)(388,855)(389,858)(390,857)(391,860)(392,859)
(393,862)(394,861)(395,864)(396,863)(397,866)(398,865)(399,868)(400,867)
(401,870)(402,869)(403,872)(404,871)(405,874)(406,873)(407,876)(408,875)
(409,878)(410,877)(411,880)(412,879)(413,882)(414,881)(415,884)(416,883)
(417,886)(418,885)(419,888)(420,887)(421,890)(422,889)(423,892)(424,891)
(425,894)(426,893)(427,896)(428,895)(429,898)(430,897)(431,900)(432,899)
(433,902)(434,901)(435,904)(436,903)(437,906)(438,905)(439,908)(440,907)
(441,910)(442,909)(443,912)(444,911)(445,914)(446,913)(447,916)(448,915)
(449,918)(450,917)(451,920)(452,919)(453,922)(454,921)(455,924)(456,923)
(457,926)(458,925)(459,928)(460,927)(461,930)(462,929)(463,932)(464,931)
(465,934)(466,933)(467,936)(468,935);;
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*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(936)!(  1,637)(  2,640)(  3,639)(  4,638)(  5,645)(  6,648)(  7,647)
(  8,646)(  9,641)( 10,644)( 11,643)( 12,642)( 13,625)( 14,628)( 15,627)
( 16,626)( 17,633)( 18,636)( 19,635)( 20,634)( 21,629)( 22,632)( 23,631)
( 24,630)( 25,769)( 26,772)( 27,771)( 28,770)( 29,777)( 30,780)( 31,779)
( 32,778)( 33,773)( 34,776)( 35,775)( 36,774)( 37,757)( 38,760)( 39,759)
( 40,758)( 41,765)( 42,768)( 43,767)( 44,766)( 45,761)( 46,764)( 47,763)
( 48,762)( 49,745)( 50,748)( 51,747)( 52,746)( 53,753)( 54,756)( 55,755)
( 56,754)( 57,749)( 58,752)( 59,751)( 60,750)( 61,733)( 62,736)( 63,735)
( 64,734)( 65,741)( 66,744)( 67,743)( 68,742)( 69,737)( 70,740)( 71,739)
( 72,738)( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)
( 80,730)( 81,725)( 82,728)( 83,727)( 84,726)( 85,709)( 86,712)( 87,711)
( 88,710)( 89,717)( 90,720)( 91,719)( 92,718)( 93,713)( 94,716)( 95,715)
( 96,714)( 97,697)( 98,700)( 99,699)(100,698)(101,705)(102,708)(103,707)
(104,706)(105,701)(106,704)(107,703)(108,702)(109,685)(110,688)(111,687)
(112,686)(113,693)(114,696)(115,695)(116,694)(117,689)(118,692)(119,691)
(120,690)(121,673)(122,676)(123,675)(124,674)(125,681)(126,684)(127,683)
(128,682)(129,677)(130,680)(131,679)(132,678)(133,661)(134,664)(135,663)
(136,662)(137,669)(138,672)(139,671)(140,670)(141,665)(142,668)(143,667)
(144,666)(145,649)(146,652)(147,651)(148,650)(149,657)(150,660)(151,659)
(152,658)(153,653)(154,656)(155,655)(156,654)(157,481)(158,484)(159,483)
(160,482)(161,489)(162,492)(163,491)(164,490)(165,485)(166,488)(167,487)
(168,486)(169,469)(170,472)(171,471)(172,470)(173,477)(174,480)(175,479)
(176,478)(177,473)(178,476)(179,475)(180,474)(181,613)(182,616)(183,615)
(184,614)(185,621)(186,624)(187,623)(188,622)(189,617)(190,620)(191,619)
(192,618)(193,601)(194,604)(195,603)(196,602)(197,609)(198,612)(199,611)
(200,610)(201,605)(202,608)(203,607)(204,606)(205,589)(206,592)(207,591)
(208,590)(209,597)(210,600)(211,599)(212,598)(213,593)(214,596)(215,595)
(216,594)(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)
(224,586)(225,581)(226,584)(227,583)(228,582)(229,565)(230,568)(231,567)
(232,566)(233,573)(234,576)(235,575)(236,574)(237,569)(238,572)(239,571)
(240,570)(241,553)(242,556)(243,555)(244,554)(245,561)(246,564)(247,563)
(248,562)(249,557)(250,560)(251,559)(252,558)(253,541)(254,544)(255,543)
(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)
(264,546)(265,529)(266,532)(267,531)(268,530)(269,537)(270,540)(271,539)
(272,538)(273,533)(274,536)(275,535)(276,534)(277,517)(278,520)(279,519)
(280,518)(281,525)(282,528)(283,527)(284,526)(285,521)(286,524)(287,523)
(288,522)(289,505)(290,508)(291,507)(292,506)(293,513)(294,516)(295,515)
(296,514)(297,509)(298,512)(299,511)(300,510)(301,493)(302,496)(303,495)
(304,494)(305,501)(306,504)(307,503)(308,502)(309,497)(310,500)(311,499)
(312,498)(313,801)(314,804)(315,803)(316,802)(317,797)(318,800)(319,799)
(320,798)(321,793)(322,796)(323,795)(324,794)(325,789)(326,792)(327,791)
(328,790)(329,785)(330,788)(331,787)(332,786)(333,781)(334,784)(335,783)
(336,782)(337,933)(338,936)(339,935)(340,934)(341,929)(342,932)(343,931)
(344,930)(345,925)(346,928)(347,927)(348,926)(349,921)(350,924)(351,923)
(352,922)(353,917)(354,920)(355,919)(356,918)(357,913)(358,916)(359,915)
(360,914)(361,909)(362,912)(363,911)(364,910)(365,905)(366,908)(367,907)
(368,906)(369,901)(370,904)(371,903)(372,902)(373,897)(374,900)(375,899)
(376,898)(377,893)(378,896)(379,895)(380,894)(381,889)(382,892)(383,891)
(384,890)(385,885)(386,888)(387,887)(388,886)(389,881)(390,884)(391,883)
(392,882)(393,877)(394,880)(395,879)(396,878)(397,873)(398,876)(399,875)
(400,874)(401,869)(402,872)(403,871)(404,870)(405,865)(406,868)(407,867)
(408,866)(409,861)(410,864)(411,863)(412,862)(413,857)(414,860)(415,859)
(416,858)(417,853)(418,856)(419,855)(420,854)(421,849)(422,852)(423,851)
(424,850)(425,845)(426,848)(427,847)(428,846)(429,841)(430,844)(431,843)
(432,842)(433,837)(434,840)(435,839)(436,838)(437,833)(438,836)(439,835)
(440,834)(441,829)(442,832)(443,831)(444,830)(445,825)(446,828)(447,827)
(448,826)(449,821)(450,824)(451,823)(452,822)(453,817)(454,820)(455,819)
(456,818)(457,813)(458,816)(459,815)(460,814)(461,809)(462,812)(463,811)
(464,810)(465,805)(466,808)(467,807)(468,806);
s2 := Sym(936)!(  1,470)(  2,469)(  3,472)(  4,471)(  5,474)(  6,473)(  7,476)
(  8,475)(  9,478)( 10,477)( 11,480)( 12,479)( 13,482)( 14,481)( 15,484)
( 16,483)( 17,486)( 18,485)( 19,488)( 20,487)( 21,490)( 22,489)( 23,492)
( 24,491)( 25,494)( 26,493)( 27,496)( 28,495)( 29,498)( 30,497)( 31,500)
( 32,499)( 33,502)( 34,501)( 35,504)( 36,503)( 37,506)( 38,505)( 39,508)
( 40,507)( 41,510)( 42,509)( 43,512)( 44,511)( 45,514)( 46,513)( 47,516)
( 48,515)( 49,518)( 50,517)( 51,520)( 52,519)( 53,522)( 54,521)( 55,524)
( 56,523)( 57,526)( 58,525)( 59,528)( 60,527)( 61,530)( 62,529)( 63,532)
( 64,531)( 65,534)( 66,533)( 67,536)( 68,535)( 69,538)( 70,537)( 71,540)
( 72,539)( 73,542)( 74,541)( 75,544)( 76,543)( 77,546)( 78,545)( 79,548)
( 80,547)( 81,550)( 82,549)( 83,552)( 84,551)( 85,554)( 86,553)( 87,556)
( 88,555)( 89,558)( 90,557)( 91,560)( 92,559)( 93,562)( 94,561)( 95,564)
( 96,563)( 97,566)( 98,565)( 99,568)(100,567)(101,570)(102,569)(103,572)
(104,571)(105,574)(106,573)(107,576)(108,575)(109,578)(110,577)(111,580)
(112,579)(113,582)(114,581)(115,584)(116,583)(117,586)(118,585)(119,588)
(120,587)(121,590)(122,589)(123,592)(124,591)(125,594)(126,593)(127,596)
(128,595)(129,598)(130,597)(131,600)(132,599)(133,602)(134,601)(135,604)
(136,603)(137,606)(138,605)(139,608)(140,607)(141,610)(142,609)(143,612)
(144,611)(145,614)(146,613)(147,616)(148,615)(149,618)(150,617)(151,620)
(152,619)(153,622)(154,621)(155,624)(156,623)(157,626)(158,625)(159,628)
(160,627)(161,630)(162,629)(163,632)(164,631)(165,634)(166,633)(167,636)
(168,635)(169,638)(170,637)(171,640)(172,639)(173,642)(174,641)(175,644)
(176,643)(177,646)(178,645)(179,648)(180,647)(181,650)(182,649)(183,652)
(184,651)(185,654)(186,653)(187,656)(188,655)(189,658)(190,657)(191,660)
(192,659)(193,662)(194,661)(195,664)(196,663)(197,666)(198,665)(199,668)
(200,667)(201,670)(202,669)(203,672)(204,671)(205,674)(206,673)(207,676)
(208,675)(209,678)(210,677)(211,680)(212,679)(213,682)(214,681)(215,684)
(216,683)(217,686)(218,685)(219,688)(220,687)(221,690)(222,689)(223,692)
(224,691)(225,694)(226,693)(227,696)(228,695)(229,698)(230,697)(231,700)
(232,699)(233,702)(234,701)(235,704)(236,703)(237,706)(238,705)(239,708)
(240,707)(241,710)(242,709)(243,712)(244,711)(245,714)(246,713)(247,716)
(248,715)(249,718)(250,717)(251,720)(252,719)(253,722)(254,721)(255,724)
(256,723)(257,726)(258,725)(259,728)(260,727)(261,730)(262,729)(263,732)
(264,731)(265,734)(266,733)(267,736)(268,735)(269,738)(270,737)(271,740)
(272,739)(273,742)(274,741)(275,744)(276,743)(277,746)(278,745)(279,748)
(280,747)(281,750)(282,749)(283,752)(284,751)(285,754)(286,753)(287,756)
(288,755)(289,758)(290,757)(291,760)(292,759)(293,762)(294,761)(295,764)
(296,763)(297,766)(298,765)(299,768)(300,767)(301,770)(302,769)(303,772)
(304,771)(305,774)(306,773)(307,776)(308,775)(309,778)(310,777)(311,780)
(312,779)(313,782)(314,781)(315,784)(316,783)(317,786)(318,785)(319,788)
(320,787)(321,790)(322,789)(323,792)(324,791)(325,794)(326,793)(327,796)
(328,795)(329,798)(330,797)(331,800)(332,799)(333,802)(334,801)(335,804)
(336,803)(337,806)(338,805)(339,808)(340,807)(341,810)(342,809)(343,812)
(344,811)(345,814)(346,813)(347,816)(348,815)(349,818)(350,817)(351,820)
(352,819)(353,822)(354,821)(355,824)(356,823)(357,826)(358,825)(359,828)
(360,827)(361,830)(362,829)(363,832)(364,831)(365,834)(366,833)(367,836)
(368,835)(369,838)(370,837)(371,840)(372,839)(373,842)(374,841)(375,844)
(376,843)(377,846)(378,845)(379,848)(380,847)(381,850)(382,849)(383,852)
(384,851)(385,854)(386,853)(387,856)(388,855)(389,858)(390,857)(391,860)
(392,859)(393,862)(394,861)(395,864)(396,863)(397,866)(398,865)(399,868)
(400,867)(401,870)(402,869)(403,872)(404,871)(405,874)(406,873)(407,876)
(408,875)(409,878)(410,877)(411,880)(412,879)(413,882)(414,881)(415,884)
(416,883)(417,886)(418,885)(419,888)(420,887)(421,890)(422,889)(423,892)
(424,891)(425,894)(426,893)(427,896)(428,895)(429,898)(430,897)(431,900)
(432,899)(433,902)(434,901)(435,904)(436,903)(437,906)(438,905)(439,908)
(440,907)(441,910)(442,909)(443,912)(444,911)(445,914)(446,913)(447,916)
(448,915)(449,918)(450,917)(451,920)(452,919)(453,922)(454,921)(455,924)
(456,923)(457,926)(458,925)(459,928)(460,927)(461,930)(462,929)(463,932)
(464,931)(465,934)(466,933)(467,936)(468,935);
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, 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*s2*s1*s0*s2*s1*s0*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 >; 
 
References : None.
to this polytope