Polytope of Type {234,4}

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