Polytope of Type {4,236}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,236}*1888
Also Known As : {4,236|2}. if this polytope has another name.
Group : SmallGroup(1888,116)
Rank : 3
Schlafli Type : {4,236}
Number of vertices, edges, etc : 4, 472, 236
Order of s₀s₁s₂ : 236
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {2,236}*944, {4,118}*944
   4-fold quotients : {2,118}*472
   8-fold quotients : {2,59}*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 := (  1,473)(  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);;
s1 := (  2, 59)(  3, 58)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 53)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)( 17, 44)
( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)( 25, 36)
( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 61,118)( 62,117)( 63,116)
( 64,115)( 65,114)( 66,113)( 67,112)( 68,111)( 69,110)( 70,109)( 71,108)
( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,101)( 79,100)
( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)
( 88, 91)( 89, 90)(120,177)(121,176)(122,175)(123,174)(124,173)(125,172)
(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)(133,164)
(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)(141,156)
(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(179,236)
(180,235)(181,234)(182,233)(183,232)(184,231)(185,230)(186,229)(187,228)
(188,227)(189,226)(190,225)(191,224)(192,223)(193,222)(194,221)(195,220)
(196,219)(197,218)(198,217)(199,216)(200,215)(201,214)(202,213)(203,212)
(204,211)(205,210)(206,209)(207,208)(237,296)(238,354)(239,353)(240,352)
(241,351)(242,350)(243,349)(244,348)(245,347)(246,346)(247,345)(248,344)
(249,343)(250,342)(251,341)(252,340)(253,339)(254,338)(255,337)(256,336)
(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)(263,329)(264,328)
(265,327)(266,326)(267,325)(268,324)(269,323)(270,322)(271,321)(272,320)
(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)(279,313)(280,312)
(281,311)(282,310)(283,309)(284,308)(285,307)(286,306)(287,305)(288,304)
(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)(355,414)
(356,472)(357,471)(358,470)(359,469)(360,468)(361,467)(362,466)(363,465)
(364,464)(365,463)(366,462)(367,461)(368,460)(369,459)(370,458)(371,457)
(372,456)(373,455)(374,454)(375,453)(376,452)(377,451)(378,450)(379,449)
(380,448)(381,447)(382,446)(383,445)(384,444)(385,443)(386,442)(387,441)
(388,440)(389,439)(390,438)(391,437)(392,436)(393,435)(394,434)(395,433)
(396,432)(397,431)(398,430)(399,429)(400,428)(401,427)(402,426)(403,425)
(404,424)(405,423)(406,422)(407,421)(408,420)(409,419)(410,418)(411,417)
(412,416)(413,415)(473,591)(474,649)(475,648)(476,647)(477,646)(478,645)
(479,644)(480,643)(481,642)(482,641)(483,640)(484,639)(485,638)(486,637)
(487,636)(488,635)(489,634)(490,633)(491,632)(492,631)(493,630)(494,629)
(495,628)(496,627)(497,626)(498,625)(499,624)(500,623)(501,622)(502,621)
(503,620)(504,619)(505,618)(506,617)(507,616)(508,615)(509,614)(510,613)
(511,612)(512,611)(513,610)(514,609)(515,608)(516,607)(517,606)(518,605)
(519,604)(520,603)(521,602)(522,601)(523,600)(524,599)(525,598)(526,597)
(527,596)(528,595)(529,594)(530,593)(531,592)(532,650)(533,708)(534,707)
(535,706)(536,705)(537,704)(538,703)(539,702)(540,701)(541,700)(542,699)
(543,698)(544,697)(545,696)(546,695)(547,694)(548,693)(549,692)(550,691)
(551,690)(552,689)(553,688)(554,687)(555,686)(556,685)(557,684)(558,683)
(559,682)(560,681)(561,680)(562,679)(563,678)(564,677)(565,676)(566,675)
(567,674)(568,673)(569,672)(570,671)(571,670)(572,669)(573,668)(574,667)
(575,666)(576,665)(577,664)(578,663)(579,662)(580,661)(581,660)(582,659)
(583,658)(584,657)(585,656)(586,655)(587,654)(588,653)(589,652)(590,651)
(709,886)(710,944)(711,943)(712,942)(713,941)(714,940)(715,939)(716,938)
(717,937)(718,936)(719,935)(720,934)(721,933)(722,932)(723,931)(724,930)
(725,929)(726,928)(727,927)(728,926)(729,925)(730,924)(731,923)(732,922)
(733,921)(734,920)(735,919)(736,918)(737,917)(738,916)(739,915)(740,914)
(741,913)(742,912)(743,911)(744,910)(745,909)(746,908)(747,907)(748,906)
(749,905)(750,904)(751,903)(752,902)(753,901)(754,900)(755,899)(756,898)
(757,897)(758,896)(759,895)(760,894)(761,893)(762,892)(763,891)(764,890)
(765,889)(766,888)(767,887)(768,827)(769,885)(770,884)(771,883)(772,882)
(773,881)(774,880)(775,879)(776,878)(777,877)(778,876)(779,875)(780,874)
(781,873)(782,872)(783,871)(784,870)(785,869)(786,868)(787,867)(788,866)
(789,865)(790,864)(791,863)(792,862)(793,861)(794,860)(795,859)(796,858)
(797,857)(798,856)(799,855)(800,854)(801,853)(802,852)(803,851)(804,850)
(805,849)(806,848)(807,847)(808,846)(809,845)(810,844)(811,843)(812,842)
(813,841)(814,840)(815,839)(816,838)(817,837)(818,836)(819,835)(820,834)
(821,833)(822,832)(823,831)(824,830)(825,829)(826,828);;
s2 := (  1,238)(  2,237)(  3,295)(  4,294)(  5,293)(  6,292)(  7,291)(  8,290)
(  9,289)( 10,288)( 11,287)( 12,286)( 13,285)( 14,284)( 15,283)( 16,282)
( 17,281)( 18,280)( 19,279)( 20,278)( 21,277)( 22,276)( 23,275)( 24,274)
( 25,273)( 26,272)( 27,271)( 28,270)( 29,269)( 30,268)( 31,267)( 32,266)
( 33,265)( 34,264)( 35,263)( 36,262)( 37,261)( 38,260)( 39,259)( 40,258)
( 41,257)( 42,256)( 43,255)( 44,254)( 45,253)( 46,252)( 47,251)( 48,250)
( 49,249)( 50,248)( 51,247)( 52,246)( 53,245)( 54,244)( 55,243)( 56,242)
( 57,241)( 58,240)( 59,239)( 60,297)( 61,296)( 62,354)( 63,353)( 64,352)
( 65,351)( 66,350)( 67,349)( 68,348)( 69,347)( 70,346)( 71,345)( 72,344)
( 73,343)( 74,342)( 75,341)( 76,340)( 77,339)( 78,338)( 79,337)( 80,336)
( 81,335)( 82,334)( 83,333)( 84,332)( 85,331)( 86,330)( 87,329)( 88,328)
( 89,327)( 90,326)( 91,325)( 92,324)( 93,323)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,317)(100,316)(101,315)(102,314)(103,313)(104,312)
(105,311)(106,310)(107,309)(108,308)(109,307)(110,306)(111,305)(112,304)
(113,303)(114,302)(115,301)(116,300)(117,299)(118,298)(119,356)(120,355)
(121,413)(122,412)(123,411)(124,410)(125,409)(126,408)(127,407)(128,406)
(129,405)(130,404)(131,403)(132,402)(133,401)(134,400)(135,399)(136,398)
(137,397)(138,396)(139,395)(140,394)(141,393)(142,392)(143,391)(144,390)
(145,389)(146,388)(147,387)(148,386)(149,385)(150,384)(151,383)(152,382)
(153,381)(154,380)(155,379)(156,378)(157,377)(158,376)(159,375)(160,374)
(161,373)(162,372)(163,371)(164,370)(165,369)(166,368)(167,367)(168,366)
(169,365)(170,364)(171,363)(172,362)(173,361)(174,360)(175,359)(176,358)
(177,357)(178,415)(179,414)(180,472)(181,471)(182,470)(183,469)(184,468)
(185,467)(186,466)(187,465)(188,464)(189,463)(190,462)(191,461)(192,460)
(193,459)(194,458)(195,457)(196,456)(197,455)(198,454)(199,453)(200,452)
(201,451)(202,450)(203,449)(204,448)(205,447)(206,446)(207,445)(208,444)
(209,443)(210,442)(211,441)(212,440)(213,439)(214,438)(215,437)(216,436)
(217,435)(218,434)(219,433)(220,432)(221,431)(222,430)(223,429)(224,428)
(225,427)(226,426)(227,425)(228,424)(229,423)(230,422)(231,421)(232,420)
(233,419)(234,418)(235,417)(236,416)(473,710)(474,709)(475,767)(476,766)
(477,765)(478,764)(479,763)(480,762)(481,761)(482,760)(483,759)(484,758)
(485,757)(486,756)(487,755)(488,754)(489,753)(490,752)(491,751)(492,750)
(493,749)(494,748)(495,747)(496,746)(497,745)(498,744)(499,743)(500,742)
(501,741)(502,740)(503,739)(504,738)(505,737)(506,736)(507,735)(508,734)
(509,733)(510,732)(511,731)(512,730)(513,729)(514,728)(515,727)(516,726)
(517,725)(518,724)(519,723)(520,722)(521,721)(522,720)(523,719)(524,718)
(525,717)(526,716)(527,715)(528,714)(529,713)(530,712)(531,711)(532,769)
(533,768)(534,826)(535,825)(536,824)(537,823)(538,822)(539,821)(540,820)
(541,819)(542,818)(543,817)(544,816)(545,815)(546,814)(547,813)(548,812)
(549,811)(550,810)(551,809)(552,808)(553,807)(554,806)(555,805)(556,804)
(557,803)(558,802)(559,801)(560,800)(561,799)(562,798)(563,797)(564,796)
(565,795)(566,794)(567,793)(568,792)(569,791)(570,790)(571,789)(572,788)
(573,787)(574,786)(575,785)(576,784)(577,783)(578,782)(579,781)(580,780)
(581,779)(582,778)(583,777)(584,776)(585,775)(586,774)(587,773)(588,772)
(589,771)(590,770)(591,828)(592,827)(593,885)(594,884)(595,883)(596,882)
(597,881)(598,880)(599,879)(600,878)(601,877)(602,876)(603,875)(604,874)
(605,873)(606,872)(607,871)(608,870)(609,869)(610,868)(611,867)(612,866)
(613,865)(614,864)(615,863)(616,862)(617,861)(618,860)(619,859)(620,858)
(621,857)(622,856)(623,855)(624,854)(625,853)(626,852)(627,851)(628,850)
(629,849)(630,848)(631,847)(632,846)(633,845)(634,844)(635,843)(636,842)
(637,841)(638,840)(639,839)(640,838)(641,837)(642,836)(643,835)(644,834)
(645,833)(646,832)(647,831)(648,830)(649,829)(650,887)(651,886)(652,944)
(653,943)(654,942)(655,941)(656,940)(657,939)(658,938)(659,937)(660,936)
(661,935)(662,934)(663,933)(664,932)(665,931)(666,930)(667,929)(668,928)
(669,927)(670,926)(671,925)(672,924)(673,923)(674,922)(675,921)(676,920)
(677,919)(678,918)(679,917)(680,916)(681,915)(682,914)(683,913)(684,912)
(685,911)(686,910)(687,909)(688,908)(689,907)(690,906)(691,905)(692,904)
(693,903)(694,902)(695,901)(696,900)(697,899)(698,898)(699,897)(700,896)
(701,895)(702,894)(703,893)(704,892)(705,891)(706,890)(707,889)(708,888);;
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*s0*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope