Polytope of Type {236,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {236,4}*1888
Also Known As : {236,4|2}. if this polytope has another name.
Group : SmallGroup(1888,116)
Rank : 3
Schlafli Type : {236,4}
Number of vertices, edges, etc : 236, 472, 4
Order of s₀s₁s₂ : 236
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {236,2}*944, {118,4}*944
   4-fold quotients : {118,2}*472
   8-fold quotients : {59,2}*236
   59-fold quotients : {4,4}*32
   118-fold quotients : {2,4}*16, {4,2}*16
   236-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,237)(  2,295)(  3,294)(  4,293)(  5,292)(  6,291)(  7,290)(  8,289)
(  9,288)( 10,287)( 11,286)( 12,285)( 13,284)( 14,283)( 15,282)( 16,281)
( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,275)( 23,274)( 24,273)
( 25,272)( 26,271)( 27,270)( 28,269)( 29,268)( 30,267)( 31,266)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,261)( 37,260)( 38,259)( 39,258)( 40,257)
( 41,256)( 42,255)( 43,254)( 44,253)( 45,252)( 46,251)( 47,250)( 48,249)
( 49,248)( 50,247)( 51,246)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)
( 57,240)( 58,239)( 59,238)( 60,296)( 61,354)( 62,353)( 63,352)( 64,351)
( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,344)( 72,343)
( 73,342)( 74,341)( 75,340)( 76,339)( 77,338)( 78,337)( 79,336)( 80,335)
( 81,334)( 82,333)( 83,332)( 84,331)( 85,330)( 86,329)( 87,328)( 88,327)
( 89,326)( 90,325)( 91,324)( 92,323)( 93,322)( 94,321)( 95,320)( 96,319)
( 97,318)( 98,317)( 99,316)(100,315)(101,314)(102,313)(103,312)(104,311)
(105,310)(106,309)(107,308)(108,307)(109,306)(110,305)(111,304)(112,303)
(113,302)(114,301)(115,300)(116,299)(117,298)(118,297)(119,355)(120,413)
(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)(128,405)
(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)(136,397)
(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)(144,389)
(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)(152,381)
(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)(160,373)
(161,372)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)(168,365)
(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)(176,357)
(177,356)(178,414)(179,472)(180,471)(181,470)(182,469)(183,468)(184,467)
(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)(192,459)
(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)(200,451)
(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)(208,443)
(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)(216,435)
(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)(224,427)
(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)(232,419)
(233,418)(234,417)(235,416)(236,415)(473,709)(474,767)(475,766)(476,765)
(477,764)(478,763)(479,762)(480,761)(481,760)(482,759)(483,758)(484,757)
(485,756)(486,755)(487,754)(488,753)(489,752)(490,751)(491,750)(492,749)
(493,748)(494,747)(495,746)(496,745)(497,744)(498,743)(499,742)(500,741)
(501,740)(502,739)(503,738)(504,737)(505,736)(506,735)(507,734)(508,733)
(509,732)(510,731)(511,730)(512,729)(513,728)(514,727)(515,726)(516,725)
(517,724)(518,723)(519,722)(520,721)(521,720)(522,719)(523,718)(524,717)
(525,716)(526,715)(527,714)(528,713)(529,712)(530,711)(531,710)(532,768)
(533,826)(534,825)(535,824)(536,823)(537,822)(538,821)(539,820)(540,819)
(541,818)(542,817)(543,816)(544,815)(545,814)(546,813)(547,812)(548,811)
(549,810)(550,809)(551,808)(552,807)(553,806)(554,805)(555,804)(556,803)
(557,802)(558,801)(559,800)(560,799)(561,798)(562,797)(563,796)(564,795)
(565,794)(566,793)(567,792)(568,791)(569,790)(570,789)(571,788)(572,787)
(573,786)(574,785)(575,784)(576,783)(577,782)(578,781)(579,780)(580,779)
(581,778)(582,777)(583,776)(584,775)(585,774)(586,773)(587,772)(588,771)
(589,770)(590,769)(591,827)(592,885)(593,884)(594,883)(595,882)(596,881)
(597,880)(598,879)(599,878)(600,877)(601,876)(602,875)(603,874)(604,873)
(605,872)(606,871)(607,870)(608,869)(609,868)(610,867)(611,866)(612,865)
(613,864)(614,863)(615,862)(616,861)(617,860)(618,859)(619,858)(620,857)
(621,856)(622,855)(623,854)(624,853)(625,852)(626,851)(627,850)(628,849)
(629,848)(630,847)(631,846)(632,845)(633,844)(634,843)(635,842)(636,841)
(637,840)(638,839)(639,838)(640,837)(641,836)(642,835)(643,834)(644,833)
(645,832)(646,831)(647,830)(648,829)(649,828)(650,886)(651,944)(652,943)
(653,942)(654,941)(655,940)(656,939)(657,938)(658,937)(659,936)(660,935)
(661,934)(662,933)(663,932)(664,931)(665,930)(666,929)(667,928)(668,927)
(669,926)(670,925)(671,924)(672,923)(673,922)(674,921)(675,920)(676,919)
(677,918)(678,917)(679,916)(680,915)(681,914)(682,913)(683,912)(684,911)
(685,910)(686,909)(687,908)(688,907)(689,906)(690,905)(691,904)(692,903)
(693,902)(694,901)(695,900)(696,899)(697,898)(698,897)(699,896)(700,895)
(701,894)(702,893)(703,892)(704,891)(705,890)(706,889)(707,888)(708,887);;
s1 := (  1,  2)(  3, 59)(  4, 58)(  5, 57)(  6, 56)(  7, 55)(  8, 54)(  9, 53)
( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)( 17, 45)
( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)( 25, 37)
( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60, 61)( 62,118)( 63,117)
( 64,116)( 65,115)( 66,114)( 67,113)( 68,112)( 69,111)( 70,110)( 71,109)
( 72,108)( 73,107)( 74,106)( 75,105)( 76,104)( 77,103)( 78,102)( 79,101)
( 80,100)( 81, 99)( 82, 98)( 83, 97)( 84, 96)( 85, 95)( 86, 94)( 87, 93)
( 88, 92)( 89, 91)(119,120)(121,177)(122,176)(123,175)(124,174)(125,173)
(126,172)(127,171)(128,170)(129,169)(130,168)(131,167)(132,166)(133,165)
(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)(141,157)
(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)(178,179)
(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)(186,230)(187,229)
(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)(194,222)(195,221)
(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)
(204,212)(205,211)(206,210)(207,209)(237,297)(238,296)(239,354)(240,353)
(241,352)(242,351)(243,350)(244,349)(245,348)(246,347)(247,346)(248,345)
(249,344)(250,343)(251,342)(252,341)(253,340)(254,339)(255,338)(256,337)
(257,336)(258,335)(259,334)(260,333)(261,332)(262,331)(263,330)(264,329)
(265,328)(266,327)(267,326)(268,325)(269,324)(270,323)(271,322)(272,321)
(273,320)(274,319)(275,318)(276,317)(277,316)(278,315)(279,314)(280,313)
(281,312)(282,311)(283,310)(284,309)(285,308)(286,307)(287,306)(288,305)
(289,304)(290,303)(291,302)(292,301)(293,300)(294,299)(295,298)(355,415)
(356,414)(357,472)(358,471)(359,470)(360,469)(361,468)(362,467)(363,466)
(364,465)(365,464)(366,463)(367,462)(368,461)(369,460)(370,459)(371,458)
(372,457)(373,456)(374,455)(375,454)(376,453)(377,452)(378,451)(379,450)
(380,449)(381,448)(382,447)(383,446)(384,445)(385,444)(386,443)(387,442)
(388,441)(389,440)(390,439)(391,438)(392,437)(393,436)(394,435)(395,434)
(396,433)(397,432)(398,431)(399,430)(400,429)(401,428)(402,427)(403,426)
(404,425)(405,424)(406,423)(407,422)(408,421)(409,420)(410,419)(411,418)
(412,417)(413,416)(473,592)(474,591)(475,649)(476,648)(477,647)(478,646)
(479,645)(480,644)(481,643)(482,642)(483,641)(484,640)(485,639)(486,638)
(487,637)(488,636)(489,635)(490,634)(491,633)(492,632)(493,631)(494,630)
(495,629)(496,628)(497,627)(498,626)(499,625)(500,624)(501,623)(502,622)
(503,621)(504,620)(505,619)(506,618)(507,617)(508,616)(509,615)(510,614)
(511,613)(512,612)(513,611)(514,610)(515,609)(516,608)(517,607)(518,606)
(519,605)(520,604)(521,603)(522,602)(523,601)(524,600)(525,599)(526,598)
(527,597)(528,596)(529,595)(530,594)(531,593)(532,651)(533,650)(534,708)
(535,707)(536,706)(537,705)(538,704)(539,703)(540,702)(541,701)(542,700)
(543,699)(544,698)(545,697)(546,696)(547,695)(548,694)(549,693)(550,692)
(551,691)(552,690)(553,689)(554,688)(555,687)(556,686)(557,685)(558,684)
(559,683)(560,682)(561,681)(562,680)(563,679)(564,678)(565,677)(566,676)
(567,675)(568,674)(569,673)(570,672)(571,671)(572,670)(573,669)(574,668)
(575,667)(576,666)(577,665)(578,664)(579,663)(580,662)(581,661)(582,660)
(583,659)(584,658)(585,657)(586,656)(587,655)(588,654)(589,653)(590,652)
(709,887)(710,886)(711,944)(712,943)(713,942)(714,941)(715,940)(716,939)
(717,938)(718,937)(719,936)(720,935)(721,934)(722,933)(723,932)(724,931)
(725,930)(726,929)(727,928)(728,927)(729,926)(730,925)(731,924)(732,923)
(733,922)(734,921)(735,920)(736,919)(737,918)(738,917)(739,916)(740,915)
(741,914)(742,913)(743,912)(744,911)(745,910)(746,909)(747,908)(748,907)
(749,906)(750,905)(751,904)(752,903)(753,902)(754,901)(755,900)(756,899)
(757,898)(758,897)(759,896)(760,895)(761,894)(762,893)(763,892)(764,891)
(765,890)(766,889)(767,888)(768,828)(769,827)(770,885)(771,884)(772,883)
(773,882)(774,881)(775,880)(776,879)(777,878)(778,877)(779,876)(780,875)
(781,874)(782,873)(783,872)(784,871)(785,870)(786,869)(787,868)(788,867)
(789,866)(790,865)(791,864)(792,863)(793,862)(794,861)(795,860)(796,859)
(797,858)(798,857)(799,856)(800,855)(801,854)(802,853)(803,852)(804,851)
(805,850)(806,849)(807,848)(808,847)(809,846)(810,845)(811,844)(812,843)
(813,842)(814,841)(815,840)(816,839)(817,838)(818,837)(819,836)(820,835)
(821,834)(822,833)(823,832)(824,831)(825,830)(826,829);;
s2 := (  1,473)(  2,474)(  3,475)(  4,476)(  5,477)(  6,478)(  7,479)(  8,480)
(  9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)
( 17,489)( 18,490)( 19,491)( 20,492)( 21,493)( 22,494)( 23,495)( 24,496)
( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)
( 33,505)( 34,506)( 35,507)( 36,508)( 37,509)( 38,510)( 39,511)( 40,512)
( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)
( 49,521)( 50,522)( 51,523)( 52,524)( 53,525)( 54,526)( 55,527)( 56,528)
( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)
( 65,537)( 66,538)( 67,539)( 68,540)( 69,541)( 70,542)( 71,543)( 72,544)
( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)
( 81,553)( 82,554)( 83,555)( 84,556)( 85,557)( 86,558)( 87,559)( 88,560)
( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)
( 97,569)( 98,570)( 99,571)(100,572)(101,573)(102,574)(103,575)(104,576)
(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)
(113,585)(114,586)(115,587)(116,588)(117,589)(118,590)(119,591)(120,592)
(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)
(129,601)(130,602)(131,603)(132,604)(133,605)(134,606)(135,607)(136,608)
(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)
(145,617)(146,618)(147,619)(148,620)(149,621)(150,622)(151,623)(152,624)
(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)
(161,633)(162,634)(163,635)(164,636)(165,637)(166,638)(167,639)(168,640)
(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)
(177,649)(178,650)(179,651)(180,652)(181,653)(182,654)(183,655)(184,656)
(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)
(193,665)(194,666)(195,667)(196,668)(197,669)(198,670)(199,671)(200,672)
(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)
(209,681)(210,682)(211,683)(212,684)(213,685)(214,686)(215,687)(216,688)
(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)
(225,697)(226,698)(227,699)(228,700)(229,701)(230,702)(231,703)(232,704)
(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)
(241,713)(242,714)(243,715)(244,716)(245,717)(246,718)(247,719)(248,720)
(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)
(257,729)(258,730)(259,731)(260,732)(261,733)(262,734)(263,735)(264,736)
(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)
(273,745)(274,746)(275,747)(276,748)(277,749)(278,750)(279,751)(280,752)
(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)
(289,761)(290,762)(291,763)(292,764)(293,765)(294,766)(295,767)(296,768)
(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)
(305,777)(306,778)(307,779)(308,780)(309,781)(310,782)(311,783)(312,784)
(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)
(321,793)(322,794)(323,795)(324,796)(325,797)(326,798)(327,799)(328,800)
(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)
(337,809)(338,810)(339,811)(340,812)(341,813)(342,814)(343,815)(344,816)
(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)
(353,825)(354,826)(355,827)(356,828)(357,829)(358,830)(359,831)(360,832)
(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)
(369,841)(370,842)(371,843)(372,844)(373,845)(374,846)(375,847)(376,848)
(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)
(385,857)(386,858)(387,859)(388,860)(389,861)(390,862)(391,863)(392,864)
(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)
(401,873)(402,874)(403,875)(404,876)(405,877)(406,878)(407,879)(408,880)
(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)
(417,889)(418,890)(419,891)(420,892)(421,893)(422,894)(423,895)(424,896)
(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)
(433,905)(434,906)(435,907)(436,908)(437,909)(438,910)(439,911)(440,912)
(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)
(449,921)(450,922)(451,923)(452,924)(453,925)(454,926)(455,927)(456,928)
(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)
(465,937)(466,938)(467,939)(468,940)(469,941)(470,942)(471,943)(472,944);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(944)!(  1,237)(  2,295)(  3,294)(  4,293)(  5,292)(  6,291)(  7,290)
(  8,289)(  9,288)( 10,287)( 11,286)( 12,285)( 13,284)( 14,283)( 15,282)
( 16,281)( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,275)( 23,274)
( 24,273)( 25,272)( 26,271)( 27,270)( 28,269)( 29,268)( 30,267)( 31,266)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,261)( 37,260)( 38,259)( 39,258)
( 40,257)( 41,256)( 42,255)( 43,254)( 44,253)( 45,252)( 46,251)( 47,250)
( 48,249)( 49,248)( 50,247)( 51,246)( 52,245)( 53,244)( 54,243)( 55,242)
( 56,241)( 57,240)( 58,239)( 59,238)( 60,296)( 61,354)( 62,353)( 63,352)
( 64,351)( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,344)
( 72,343)( 73,342)( 74,341)( 75,340)( 76,339)( 77,338)( 78,337)( 79,336)
( 80,335)( 81,334)( 82,333)( 83,332)( 84,331)( 85,330)( 86,329)( 87,328)
( 88,327)( 89,326)( 90,325)( 91,324)( 92,323)( 93,322)( 94,321)( 95,320)
( 96,319)( 97,318)( 98,317)( 99,316)(100,315)(101,314)(102,313)(103,312)
(104,311)(105,310)(106,309)(107,308)(108,307)(109,306)(110,305)(111,304)
(112,303)(113,302)(114,301)(115,300)(116,299)(117,298)(118,297)(119,355)
(120,413)(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)
(128,405)(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)
(136,397)(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)
(144,389)(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)
(152,381)(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)
(160,373)(161,372)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)
(168,365)(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)
(176,357)(177,356)(178,414)(179,472)(180,471)(181,470)(182,469)(183,468)
(184,467)(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)
(192,459)(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)
(200,451)(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)
(208,443)(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)
(216,435)(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)
(224,427)(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)
(232,419)(233,418)(234,417)(235,416)(236,415)(473,709)(474,767)(475,766)
(476,765)(477,764)(478,763)(479,762)(480,761)(481,760)(482,759)(483,758)
(484,757)(485,756)(486,755)(487,754)(488,753)(489,752)(490,751)(491,750)
(492,749)(493,748)(494,747)(495,746)(496,745)(497,744)(498,743)(499,742)
(500,741)(501,740)(502,739)(503,738)(504,737)(505,736)(506,735)(507,734)
(508,733)(509,732)(510,731)(511,730)(512,729)(513,728)(514,727)(515,726)
(516,725)(517,724)(518,723)(519,722)(520,721)(521,720)(522,719)(523,718)
(524,717)(525,716)(526,715)(527,714)(528,713)(529,712)(530,711)(531,710)
(532,768)(533,826)(534,825)(535,824)(536,823)(537,822)(538,821)(539,820)
(540,819)(541,818)(542,817)(543,816)(544,815)(545,814)(546,813)(547,812)
(548,811)(549,810)(550,809)(551,808)(552,807)(553,806)(554,805)(555,804)
(556,803)(557,802)(558,801)(559,800)(560,799)(561,798)(562,797)(563,796)
(564,795)(565,794)(566,793)(567,792)(568,791)(569,790)(570,789)(571,788)
(572,787)(573,786)(574,785)(575,784)(576,783)(577,782)(578,781)(579,780)
(580,779)(581,778)(582,777)(583,776)(584,775)(585,774)(586,773)(587,772)
(588,771)(589,770)(590,769)(591,827)(592,885)(593,884)(594,883)(595,882)
(596,881)(597,880)(598,879)(599,878)(600,877)(601,876)(602,875)(603,874)
(604,873)(605,872)(606,871)(607,870)(608,869)(609,868)(610,867)(611,866)
(612,865)(613,864)(614,863)(615,862)(616,861)(617,860)(618,859)(619,858)
(620,857)(621,856)(622,855)(623,854)(624,853)(625,852)(626,851)(627,850)
(628,849)(629,848)(630,847)(631,846)(632,845)(633,844)(634,843)(635,842)
(636,841)(637,840)(638,839)(639,838)(640,837)(641,836)(642,835)(643,834)
(644,833)(645,832)(646,831)(647,830)(648,829)(649,828)(650,886)(651,944)
(652,943)(653,942)(654,941)(655,940)(656,939)(657,938)(658,937)(659,936)
(660,935)(661,934)(662,933)(663,932)(664,931)(665,930)(666,929)(667,928)
(668,927)(669,926)(670,925)(671,924)(672,923)(673,922)(674,921)(675,920)
(676,919)(677,918)(678,917)(679,916)(680,915)(681,914)(682,913)(683,912)
(684,911)(685,910)(686,909)(687,908)(688,907)(689,906)(690,905)(691,904)
(692,903)(693,902)(694,901)(695,900)(696,899)(697,898)(698,897)(699,896)
(700,895)(701,894)(702,893)(703,892)(704,891)(705,890)(706,889)(707,888)
(708,887);
s1 := Sym(944)!(  1,  2)(  3, 59)(  4, 58)(  5, 57)(  6, 56)(  7, 55)(  8, 54)
(  9, 53)( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60, 61)( 62,118)
( 63,117)( 64,116)( 65,115)( 66,114)( 67,113)( 68,112)( 69,111)( 70,110)
( 71,109)( 72,108)( 73,107)( 74,106)( 75,105)( 76,104)( 77,103)( 78,102)
( 79,101)( 80,100)( 81, 99)( 82, 98)( 83, 97)( 84, 96)( 85, 95)( 86, 94)
( 87, 93)( 88, 92)( 89, 91)(119,120)(121,177)(122,176)(123,175)(124,174)
(125,173)(126,172)(127,171)(128,170)(129,169)(130,168)(131,167)(132,166)
(133,165)(134,164)(135,163)(136,162)(137,161)(138,160)(139,159)(140,158)
(141,157)(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)
(178,179)(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)(186,230)
(187,229)(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)(194,222)
(195,221)(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)
(203,213)(204,212)(205,211)(206,210)(207,209)(237,297)(238,296)(239,354)
(240,353)(241,352)(242,351)(243,350)(244,349)(245,348)(246,347)(247,346)
(248,345)(249,344)(250,343)(251,342)(252,341)(253,340)(254,339)(255,338)
(256,337)(257,336)(258,335)(259,334)(260,333)(261,332)(262,331)(263,330)
(264,329)(265,328)(266,327)(267,326)(268,325)(269,324)(270,323)(271,322)
(272,321)(273,320)(274,319)(275,318)(276,317)(277,316)(278,315)(279,314)
(280,313)(281,312)(282,311)(283,310)(284,309)(285,308)(286,307)(287,306)
(288,305)(289,304)(290,303)(291,302)(292,301)(293,300)(294,299)(295,298)
(355,415)(356,414)(357,472)(358,471)(359,470)(360,469)(361,468)(362,467)
(363,466)(364,465)(365,464)(366,463)(367,462)(368,461)(369,460)(370,459)
(371,458)(372,457)(373,456)(374,455)(375,454)(376,453)(377,452)(378,451)
(379,450)(380,449)(381,448)(382,447)(383,446)(384,445)(385,444)(386,443)
(387,442)(388,441)(389,440)(390,439)(391,438)(392,437)(393,436)(394,435)
(395,434)(396,433)(397,432)(398,431)(399,430)(400,429)(401,428)(402,427)
(403,426)(404,425)(405,424)(406,423)(407,422)(408,421)(409,420)(410,419)
(411,418)(412,417)(413,416)(473,592)(474,591)(475,649)(476,648)(477,647)
(478,646)(479,645)(480,644)(481,643)(482,642)(483,641)(484,640)(485,639)
(486,638)(487,637)(488,636)(489,635)(490,634)(491,633)(492,632)(493,631)
(494,630)(495,629)(496,628)(497,627)(498,626)(499,625)(500,624)(501,623)
(502,622)(503,621)(504,620)(505,619)(506,618)(507,617)(508,616)(509,615)
(510,614)(511,613)(512,612)(513,611)(514,610)(515,609)(516,608)(517,607)
(518,606)(519,605)(520,604)(521,603)(522,602)(523,601)(524,600)(525,599)
(526,598)(527,597)(528,596)(529,595)(530,594)(531,593)(532,651)(533,650)
(534,708)(535,707)(536,706)(537,705)(538,704)(539,703)(540,702)(541,701)
(542,700)(543,699)(544,698)(545,697)(546,696)(547,695)(548,694)(549,693)
(550,692)(551,691)(552,690)(553,689)(554,688)(555,687)(556,686)(557,685)
(558,684)(559,683)(560,682)(561,681)(562,680)(563,679)(564,678)(565,677)
(566,676)(567,675)(568,674)(569,673)(570,672)(571,671)(572,670)(573,669)
(574,668)(575,667)(576,666)(577,665)(578,664)(579,663)(580,662)(581,661)
(582,660)(583,659)(584,658)(585,657)(586,656)(587,655)(588,654)(589,653)
(590,652)(709,887)(710,886)(711,944)(712,943)(713,942)(714,941)(715,940)
(716,939)(717,938)(718,937)(719,936)(720,935)(721,934)(722,933)(723,932)
(724,931)(725,930)(726,929)(727,928)(728,927)(729,926)(730,925)(731,924)
(732,923)(733,922)(734,921)(735,920)(736,919)(737,918)(738,917)(739,916)
(740,915)(741,914)(742,913)(743,912)(744,911)(745,910)(746,909)(747,908)
(748,907)(749,906)(750,905)(751,904)(752,903)(753,902)(754,901)(755,900)
(756,899)(757,898)(758,897)(759,896)(760,895)(761,894)(762,893)(763,892)
(764,891)(765,890)(766,889)(767,888)(768,828)(769,827)(770,885)(771,884)
(772,883)(773,882)(774,881)(775,880)(776,879)(777,878)(778,877)(779,876)
(780,875)(781,874)(782,873)(783,872)(784,871)(785,870)(786,869)(787,868)
(788,867)(789,866)(790,865)(791,864)(792,863)(793,862)(794,861)(795,860)
(796,859)(797,858)(798,857)(799,856)(800,855)(801,854)(802,853)(803,852)
(804,851)(805,850)(806,849)(807,848)(808,847)(809,846)(810,845)(811,844)
(812,843)(813,842)(814,841)(815,840)(816,839)(817,838)(818,837)(819,836)
(820,835)(821,834)(822,833)(823,832)(824,831)(825,830)(826,829);
s2 := Sym(944)!(  1,473)(  2,474)(  3,475)(  4,476)(  5,477)(  6,478)(  7,479)
(  8,480)(  9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)
( 16,488)( 17,489)( 18,490)( 19,491)( 20,492)( 21,493)( 22,494)( 23,495)
( 24,496)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)
( 32,504)( 33,505)( 34,506)( 35,507)( 36,508)( 37,509)( 38,510)( 39,511)
( 40,512)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)
( 48,520)( 49,521)( 50,522)( 51,523)( 52,524)( 53,525)( 54,526)( 55,527)
( 56,528)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)
( 64,536)( 65,537)( 66,538)( 67,539)( 68,540)( 69,541)( 70,542)( 71,543)
( 72,544)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)
( 80,552)( 81,553)( 82,554)( 83,555)( 84,556)( 85,557)( 86,558)( 87,559)
( 88,560)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)
( 96,568)( 97,569)( 98,570)( 99,571)(100,572)(101,573)(102,574)(103,575)
(104,576)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)
(112,584)(113,585)(114,586)(115,587)(116,588)(117,589)(118,590)(119,591)
(120,592)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)
(128,600)(129,601)(130,602)(131,603)(132,604)(133,605)(134,606)(135,607)
(136,608)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)
(144,616)(145,617)(146,618)(147,619)(148,620)(149,621)(150,622)(151,623)
(152,624)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)
(160,632)(161,633)(162,634)(163,635)(164,636)(165,637)(166,638)(167,639)
(168,640)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)
(176,648)(177,649)(178,650)(179,651)(180,652)(181,653)(182,654)(183,655)
(184,656)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)
(192,664)(193,665)(194,666)(195,667)(196,668)(197,669)(198,670)(199,671)
(200,672)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)
(208,680)(209,681)(210,682)(211,683)(212,684)(213,685)(214,686)(215,687)
(216,688)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)
(224,696)(225,697)(226,698)(227,699)(228,700)(229,701)(230,702)(231,703)
(232,704)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)
(240,712)(241,713)(242,714)(243,715)(244,716)(245,717)(246,718)(247,719)
(248,720)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)
(256,728)(257,729)(258,730)(259,731)(260,732)(261,733)(262,734)(263,735)
(264,736)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)
(272,744)(273,745)(274,746)(275,747)(276,748)(277,749)(278,750)(279,751)
(280,752)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)
(288,760)(289,761)(290,762)(291,763)(292,764)(293,765)(294,766)(295,767)
(296,768)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)
(304,776)(305,777)(306,778)(307,779)(308,780)(309,781)(310,782)(311,783)
(312,784)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)
(320,792)(321,793)(322,794)(323,795)(324,796)(325,797)(326,798)(327,799)
(328,800)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)
(336,808)(337,809)(338,810)(339,811)(340,812)(341,813)(342,814)(343,815)
(344,816)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)
(352,824)(353,825)(354,826)(355,827)(356,828)(357,829)(358,830)(359,831)
(360,832)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)
(368,840)(369,841)(370,842)(371,843)(372,844)(373,845)(374,846)(375,847)
(376,848)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)
(384,856)(385,857)(386,858)(387,859)(388,860)(389,861)(390,862)(391,863)
(392,864)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)
(400,872)(401,873)(402,874)(403,875)(404,876)(405,877)(406,878)(407,879)
(408,880)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)
(416,888)(417,889)(418,890)(419,891)(420,892)(421,893)(422,894)(423,895)
(424,896)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)
(432,904)(433,905)(434,906)(435,907)(436,908)(437,909)(438,910)(439,911)
(440,912)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)
(448,920)(449,921)(450,922)(451,923)(452,924)(453,925)(454,926)(455,927)
(456,928)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)
(464,936)(465,937)(466,938)(467,939)(468,940)(469,941)(470,942)(471,943)
(472,944);
poly := sub<Sym(944)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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