Polytope of Type {4,244}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,244}*1952
Also Known As : {4,244|2}. if this polytope has another name.
Group : SmallGroup(1952,116)
Rank : 3
Schlafli Type : {4,244}
Number of vertices, edges, etc : 4, 488, 244
Order of s₀s₁s₂ : 244
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 : {2,244}*976, {4,122}*976
   4-fold quotients : {2,122}*488
   8-fold quotients : {2,61}*244
   61-fold quotients : {4,4}*32
   122-fold quotients : {2,4}*16, {4,2}*16
   244-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,489)(  2,490)(  3,491)(  4,492)(  5,493)(  6,494)(  7,495)(  8,496)
(  9,497)( 10,498)( 11,499)( 12,500)( 13,501)( 14,502)( 15,503)( 16,504)
( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)( 24,512)
( 25,513)( 26,514)( 27,515)( 28,516)( 29,517)( 30,518)( 31,519)( 32,520)
( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)
( 41,529)( 42,530)( 43,531)( 44,532)( 45,533)( 46,534)( 47,535)( 48,536)
( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)
( 57,545)( 58,546)( 59,547)( 60,548)( 61,549)( 62,550)( 63,551)( 64,552)
( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)
( 73,561)( 74,562)( 75,563)( 76,564)( 77,565)( 78,566)( 79,567)( 80,568)
( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)
( 89,577)( 90,578)( 91,579)( 92,580)( 93,581)( 94,582)( 95,583)( 96,584)
( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)
(105,593)(106,594)(107,595)(108,596)(109,597)(110,598)(111,599)(112,600)
(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)
(121,609)(122,610)(123,611)(124,612)(125,613)(126,614)(127,615)(128,616)
(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)
(137,625)(138,626)(139,627)(140,628)(141,629)(142,630)(143,631)(144,632)
(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)
(153,641)(154,642)(155,643)(156,644)(157,645)(158,646)(159,647)(160,648)
(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)
(169,657)(170,658)(171,659)(172,660)(173,661)(174,662)(175,663)(176,664)
(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)
(185,673)(186,674)(187,675)(188,676)(189,677)(190,678)(191,679)(192,680)
(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)
(201,689)(202,690)(203,691)(204,692)(205,693)(206,694)(207,695)(208,696)
(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)
(217,705)(218,706)(219,707)(220,708)(221,709)(222,710)(223,711)(224,712)
(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)
(233,721)(234,722)(235,723)(236,724)(237,725)(238,726)(239,727)(240,728)
(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)
(249,737)(250,738)(251,739)(252,740)(253,741)(254,742)(255,743)(256,744)
(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)
(265,753)(266,754)(267,755)(268,756)(269,757)(270,758)(271,759)(272,760)
(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)
(281,769)(282,770)(283,771)(284,772)(285,773)(286,774)(287,775)(288,776)
(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)
(297,785)(298,786)(299,787)(300,788)(301,789)(302,790)(303,791)(304,792)
(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)
(313,801)(314,802)(315,803)(316,804)(317,805)(318,806)(319,807)(320,808)
(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)
(329,817)(330,818)(331,819)(332,820)(333,821)(334,822)(335,823)(336,824)
(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)
(345,833)(346,834)(347,835)(348,836)(349,837)(350,838)(351,839)(352,840)
(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)
(361,849)(362,850)(363,851)(364,852)(365,853)(366,854)(367,855)(368,856)
(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)
(377,865)(378,866)(379,867)(380,868)(381,869)(382,870)(383,871)(384,872)
(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)
(393,881)(394,882)(395,883)(396,884)(397,885)(398,886)(399,887)(400,888)
(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)
(409,897)(410,898)(411,899)(412,900)(413,901)(414,902)(415,903)(416,904)
(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)
(425,913)(426,914)(427,915)(428,916)(429,917)(430,918)(431,919)(432,920)
(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)
(441,929)(442,930)(443,931)(444,932)(445,933)(446,934)(447,935)(448,936)
(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)
(457,945)(458,946)(459,947)(460,948)(461,949)(462,950)(463,951)(464,952)
(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)
(473,961)(474,962)(475,963)(476,964)(477,965)(478,966)(479,967)(480,968)
(481,969)(482,970)(483,971)(484,972)(485,973)(486,974)(487,975)(488,976);;
s1 := (  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)(  9, 54)
( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)
( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)( 25, 38)
( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)( 64,121)
( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)
( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)( 80,105)
( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)
( 89, 96)( 90, 95)( 91, 94)( 92, 93)(124,183)(125,182)(126,181)(127,180)
(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172)
(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)
(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)
(152,155)(153,154)(185,244)(186,243)(187,242)(188,241)(189,240)(190,239)
(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)(198,231)
(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)(206,223)
(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)(214,215)
(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)(251,361)(252,360)
(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)(259,353)(260,352)
(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)(267,345)(268,344)
(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)(275,337)(276,336)
(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)(283,329)(284,328)
(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)(291,321)(292,320)
(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)(299,313)(300,312)
(301,311)(302,310)(303,309)(304,308)(305,307)(367,428)(368,488)(369,487)
(370,486)(371,485)(372,484)(373,483)(374,482)(375,481)(376,480)(377,479)
(378,478)(379,477)(380,476)(381,475)(382,474)(383,473)(384,472)(385,471)
(386,470)(387,469)(388,468)(389,467)(390,466)(391,465)(392,464)(393,463)
(394,462)(395,461)(396,460)(397,459)(398,458)(399,457)(400,456)(401,455)
(402,454)(403,453)(404,452)(405,451)(406,450)(407,449)(408,448)(409,447)
(410,446)(411,445)(412,444)(413,443)(414,442)(415,441)(416,440)(417,439)
(418,438)(419,437)(420,436)(421,435)(422,434)(423,433)(424,432)(425,431)
(426,430)(427,429)(489,611)(490,671)(491,670)(492,669)(493,668)(494,667)
(495,666)(496,665)(497,664)(498,663)(499,662)(500,661)(501,660)(502,659)
(503,658)(504,657)(505,656)(506,655)(507,654)(508,653)(509,652)(510,651)
(511,650)(512,649)(513,648)(514,647)(515,646)(516,645)(517,644)(518,643)
(519,642)(520,641)(521,640)(522,639)(523,638)(524,637)(525,636)(526,635)
(527,634)(528,633)(529,632)(530,631)(531,630)(532,629)(533,628)(534,627)
(535,626)(536,625)(537,624)(538,623)(539,622)(540,621)(541,620)(542,619)
(543,618)(544,617)(545,616)(546,615)(547,614)(548,613)(549,612)(550,672)
(551,732)(552,731)(553,730)(554,729)(555,728)(556,727)(557,726)(558,725)
(559,724)(560,723)(561,722)(562,721)(563,720)(564,719)(565,718)(566,717)
(567,716)(568,715)(569,714)(570,713)(571,712)(572,711)(573,710)(574,709)
(575,708)(576,707)(577,706)(578,705)(579,704)(580,703)(581,702)(582,701)
(583,700)(584,699)(585,698)(586,697)(587,696)(588,695)(589,694)(590,693)
(591,692)(592,691)(593,690)(594,689)(595,688)(596,687)(597,686)(598,685)
(599,684)(600,683)(601,682)(602,681)(603,680)(604,679)(605,678)(606,677)
(607,676)(608,675)(609,674)(610,673)(733,916)(734,976)(735,975)(736,974)
(737,973)(738,972)(739,971)(740,970)(741,969)(742,968)(743,967)(744,966)
(745,965)(746,964)(747,963)(748,962)(749,961)(750,960)(751,959)(752,958)
(753,957)(754,956)(755,955)(756,954)(757,953)(758,952)(759,951)(760,950)
(761,949)(762,948)(763,947)(764,946)(765,945)(766,944)(767,943)(768,942)
(769,941)(770,940)(771,939)(772,938)(773,937)(774,936)(775,935)(776,934)
(777,933)(778,932)(779,931)(780,930)(781,929)(782,928)(783,927)(784,926)
(785,925)(786,924)(787,923)(788,922)(789,921)(790,920)(791,919)(792,918)
(793,917)(794,855)(795,915)(796,914)(797,913)(798,912)(799,911)(800,910)
(801,909)(802,908)(803,907)(804,906)(805,905)(806,904)(807,903)(808,902)
(809,901)(810,900)(811,899)(812,898)(813,897)(814,896)(815,895)(816,894)
(817,893)(818,892)(819,891)(820,890)(821,889)(822,888)(823,887)(824,886)
(825,885)(826,884)(827,883)(828,882)(829,881)(830,880)(831,879)(832,878)
(833,877)(834,876)(835,875)(836,874)(837,873)(838,872)(839,871)(840,870)
(841,869)(842,868)(843,867)(844,866)(845,865)(846,864)(847,863)(848,862)
(849,861)(850,860)(851,859)(852,858)(853,857)(854,856);;
s2 := (  1,246)(  2,245)(  3,305)(  4,304)(  5,303)(  6,302)(  7,301)(  8,300)
(  9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)
( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)( 24,284)
( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)( 32,276)
( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)( 40,268)
( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)( 48,260)
( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)( 56,252)
( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,307)( 63,306)( 64,366)
( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)( 72,358)
( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)( 80,350)
( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)( 88,342)
( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)( 96,334)
( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)(112,318)
(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)(120,310)
(121,309)(122,308)(123,368)(124,367)(125,427)(126,426)(127,425)(128,424)
(129,423)(130,422)(131,421)(132,420)(133,419)(134,418)(135,417)(136,416)
(137,415)(138,414)(139,413)(140,412)(141,411)(142,410)(143,409)(144,408)
(145,407)(146,406)(147,405)(148,404)(149,403)(150,402)(151,401)(152,400)
(153,399)(154,398)(155,397)(156,396)(157,395)(158,394)(159,393)(160,392)
(161,391)(162,390)(163,389)(164,388)(165,387)(166,386)(167,385)(168,384)
(169,383)(170,382)(171,381)(172,380)(173,379)(174,378)(175,377)(176,376)
(177,375)(178,374)(179,373)(180,372)(181,371)(182,370)(183,369)(184,429)
(185,428)(186,488)(187,487)(188,486)(189,485)(190,484)(191,483)(192,482)
(193,481)(194,480)(195,479)(196,478)(197,477)(198,476)(199,475)(200,474)
(201,473)(202,472)(203,471)(204,470)(205,469)(206,468)(207,467)(208,466)
(209,465)(210,464)(211,463)(212,462)(213,461)(214,460)(215,459)(216,458)
(217,457)(218,456)(219,455)(220,454)(221,453)(222,452)(223,451)(224,450)
(225,449)(226,448)(227,447)(228,446)(229,445)(230,444)(231,443)(232,442)
(233,441)(234,440)(235,439)(236,438)(237,437)(238,436)(239,435)(240,434)
(241,433)(242,432)(243,431)(244,430)(489,734)(490,733)(491,793)(492,792)
(493,791)(494,790)(495,789)(496,788)(497,787)(498,786)(499,785)(500,784)
(501,783)(502,782)(503,781)(504,780)(505,779)(506,778)(507,777)(508,776)
(509,775)(510,774)(511,773)(512,772)(513,771)(514,770)(515,769)(516,768)
(517,767)(518,766)(519,765)(520,764)(521,763)(522,762)(523,761)(524,760)
(525,759)(526,758)(527,757)(528,756)(529,755)(530,754)(531,753)(532,752)
(533,751)(534,750)(535,749)(536,748)(537,747)(538,746)(539,745)(540,744)
(541,743)(542,742)(543,741)(544,740)(545,739)(546,738)(547,737)(548,736)
(549,735)(550,795)(551,794)(552,854)(553,853)(554,852)(555,851)(556,850)
(557,849)(558,848)(559,847)(560,846)(561,845)(562,844)(563,843)(564,842)
(565,841)(566,840)(567,839)(568,838)(569,837)(570,836)(571,835)(572,834)
(573,833)(574,832)(575,831)(576,830)(577,829)(578,828)(579,827)(580,826)
(581,825)(582,824)(583,823)(584,822)(585,821)(586,820)(587,819)(588,818)
(589,817)(590,816)(591,815)(592,814)(593,813)(594,812)(595,811)(596,810)
(597,809)(598,808)(599,807)(600,806)(601,805)(602,804)(603,803)(604,802)
(605,801)(606,800)(607,799)(608,798)(609,797)(610,796)(611,856)(612,855)
(613,915)(614,914)(615,913)(616,912)(617,911)(618,910)(619,909)(620,908)
(621,907)(622,906)(623,905)(624,904)(625,903)(626,902)(627,901)(628,900)
(629,899)(630,898)(631,897)(632,896)(633,895)(634,894)(635,893)(636,892)
(637,891)(638,890)(639,889)(640,888)(641,887)(642,886)(643,885)(644,884)
(645,883)(646,882)(647,881)(648,880)(649,879)(650,878)(651,877)(652,876)
(653,875)(654,874)(655,873)(656,872)(657,871)(658,870)(659,869)(660,868)
(661,867)(662,866)(663,865)(664,864)(665,863)(666,862)(667,861)(668,860)
(669,859)(670,858)(671,857)(672,917)(673,916)(674,976)(675,975)(676,974)
(677,973)(678,972)(679,971)(680,970)(681,969)(682,968)(683,967)(684,966)
(685,965)(686,964)(687,963)(688,962)(689,961)(690,960)(691,959)(692,958)
(693,957)(694,956)(695,955)(696,954)(697,953)(698,952)(699,951)(700,950)
(701,949)(702,948)(703,947)(704,946)(705,945)(706,944)(707,943)(708,942)
(709,941)(710,940)(711,939)(712,938)(713,937)(714,936)(715,935)(716,934)
(717,933)(718,932)(719,931)(720,930)(721,929)(722,928)(723,927)(724,926)
(725,925)(726,924)(727,923)(728,922)(729,921)(730,920)(731,919)(732,918);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(976)!(  1,489)(  2,490)(  3,491)(  4,492)(  5,493)(  6,494)(  7,495)
(  8,496)(  9,497)( 10,498)( 11,499)( 12,500)( 13,501)( 14,502)( 15,503)
( 16,504)( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)
( 24,512)( 25,513)( 26,514)( 27,515)( 28,516)( 29,517)( 30,518)( 31,519)
( 32,520)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)
( 40,528)( 41,529)( 42,530)( 43,531)( 44,532)( 45,533)( 46,534)( 47,535)
( 48,536)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)
( 56,544)( 57,545)( 58,546)( 59,547)( 60,548)( 61,549)( 62,550)( 63,551)
( 64,552)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)
( 72,560)( 73,561)( 74,562)( 75,563)( 76,564)( 77,565)( 78,566)( 79,567)
( 80,568)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)
( 88,576)( 89,577)( 90,578)( 91,579)( 92,580)( 93,581)( 94,582)( 95,583)
( 96,584)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)
(104,592)(105,593)(106,594)(107,595)(108,596)(109,597)(110,598)(111,599)
(112,600)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)
(120,608)(121,609)(122,610)(123,611)(124,612)(125,613)(126,614)(127,615)
(128,616)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)
(136,624)(137,625)(138,626)(139,627)(140,628)(141,629)(142,630)(143,631)
(144,632)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)
(152,640)(153,641)(154,642)(155,643)(156,644)(157,645)(158,646)(159,647)
(160,648)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)
(168,656)(169,657)(170,658)(171,659)(172,660)(173,661)(174,662)(175,663)
(176,664)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)
(184,672)(185,673)(186,674)(187,675)(188,676)(189,677)(190,678)(191,679)
(192,680)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)
(200,688)(201,689)(202,690)(203,691)(204,692)(205,693)(206,694)(207,695)
(208,696)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)
(216,704)(217,705)(218,706)(219,707)(220,708)(221,709)(222,710)(223,711)
(224,712)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)
(232,720)(233,721)(234,722)(235,723)(236,724)(237,725)(238,726)(239,727)
(240,728)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)
(248,736)(249,737)(250,738)(251,739)(252,740)(253,741)(254,742)(255,743)
(256,744)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)
(264,752)(265,753)(266,754)(267,755)(268,756)(269,757)(270,758)(271,759)
(272,760)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)
(280,768)(281,769)(282,770)(283,771)(284,772)(285,773)(286,774)(287,775)
(288,776)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)
(296,784)(297,785)(298,786)(299,787)(300,788)(301,789)(302,790)(303,791)
(304,792)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)
(312,800)(313,801)(314,802)(315,803)(316,804)(317,805)(318,806)(319,807)
(320,808)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)
(328,816)(329,817)(330,818)(331,819)(332,820)(333,821)(334,822)(335,823)
(336,824)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)
(344,832)(345,833)(346,834)(347,835)(348,836)(349,837)(350,838)(351,839)
(352,840)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)
(360,848)(361,849)(362,850)(363,851)(364,852)(365,853)(366,854)(367,855)
(368,856)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)
(376,864)(377,865)(378,866)(379,867)(380,868)(381,869)(382,870)(383,871)
(384,872)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)
(392,880)(393,881)(394,882)(395,883)(396,884)(397,885)(398,886)(399,887)
(400,888)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)
(408,896)(409,897)(410,898)(411,899)(412,900)(413,901)(414,902)(415,903)
(416,904)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)
(424,912)(425,913)(426,914)(427,915)(428,916)(429,917)(430,918)(431,919)
(432,920)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)
(440,928)(441,929)(442,930)(443,931)(444,932)(445,933)(446,934)(447,935)
(448,936)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)
(456,944)(457,945)(458,946)(459,947)(460,948)(461,949)(462,950)(463,951)
(464,952)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)
(472,960)(473,961)(474,962)(475,963)(476,964)(477,965)(478,966)(479,967)
(480,968)(481,969)(482,970)(483,971)(484,972)(485,973)(486,974)(487,975)
(488,976);
s1 := Sym(976)!(  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)
(  9, 54)( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)
( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)
( 64,121)( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)
( 72,113)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)
( 80,105)( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)
( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(124,183)(125,182)(126,181)
(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)
(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)
(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)
(151,156)(152,155)(153,154)(185,244)(186,243)(187,242)(188,241)(189,240)
(190,239)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)
(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)
(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)
(214,215)(245,306)(246,366)(247,365)(248,364)(249,363)(250,362)(251,361)
(252,360)(253,359)(254,358)(255,357)(256,356)(257,355)(258,354)(259,353)
(260,352)(261,351)(262,350)(263,349)(264,348)(265,347)(266,346)(267,345)
(268,344)(269,343)(270,342)(271,341)(272,340)(273,339)(274,338)(275,337)
(276,336)(277,335)(278,334)(279,333)(280,332)(281,331)(282,330)(283,329)
(284,328)(285,327)(286,326)(287,325)(288,324)(289,323)(290,322)(291,321)
(292,320)(293,319)(294,318)(295,317)(296,316)(297,315)(298,314)(299,313)
(300,312)(301,311)(302,310)(303,309)(304,308)(305,307)(367,428)(368,488)
(369,487)(370,486)(371,485)(372,484)(373,483)(374,482)(375,481)(376,480)
(377,479)(378,478)(379,477)(380,476)(381,475)(382,474)(383,473)(384,472)
(385,471)(386,470)(387,469)(388,468)(389,467)(390,466)(391,465)(392,464)
(393,463)(394,462)(395,461)(396,460)(397,459)(398,458)(399,457)(400,456)
(401,455)(402,454)(403,453)(404,452)(405,451)(406,450)(407,449)(408,448)
(409,447)(410,446)(411,445)(412,444)(413,443)(414,442)(415,441)(416,440)
(417,439)(418,438)(419,437)(420,436)(421,435)(422,434)(423,433)(424,432)
(425,431)(426,430)(427,429)(489,611)(490,671)(491,670)(492,669)(493,668)
(494,667)(495,666)(496,665)(497,664)(498,663)(499,662)(500,661)(501,660)
(502,659)(503,658)(504,657)(505,656)(506,655)(507,654)(508,653)(509,652)
(510,651)(511,650)(512,649)(513,648)(514,647)(515,646)(516,645)(517,644)
(518,643)(519,642)(520,641)(521,640)(522,639)(523,638)(524,637)(525,636)
(526,635)(527,634)(528,633)(529,632)(530,631)(531,630)(532,629)(533,628)
(534,627)(535,626)(536,625)(537,624)(538,623)(539,622)(540,621)(541,620)
(542,619)(543,618)(544,617)(545,616)(546,615)(547,614)(548,613)(549,612)
(550,672)(551,732)(552,731)(553,730)(554,729)(555,728)(556,727)(557,726)
(558,725)(559,724)(560,723)(561,722)(562,721)(563,720)(564,719)(565,718)
(566,717)(567,716)(568,715)(569,714)(570,713)(571,712)(572,711)(573,710)
(574,709)(575,708)(576,707)(577,706)(578,705)(579,704)(580,703)(581,702)
(582,701)(583,700)(584,699)(585,698)(586,697)(587,696)(588,695)(589,694)
(590,693)(591,692)(592,691)(593,690)(594,689)(595,688)(596,687)(597,686)
(598,685)(599,684)(600,683)(601,682)(602,681)(603,680)(604,679)(605,678)
(606,677)(607,676)(608,675)(609,674)(610,673)(733,916)(734,976)(735,975)
(736,974)(737,973)(738,972)(739,971)(740,970)(741,969)(742,968)(743,967)
(744,966)(745,965)(746,964)(747,963)(748,962)(749,961)(750,960)(751,959)
(752,958)(753,957)(754,956)(755,955)(756,954)(757,953)(758,952)(759,951)
(760,950)(761,949)(762,948)(763,947)(764,946)(765,945)(766,944)(767,943)
(768,942)(769,941)(770,940)(771,939)(772,938)(773,937)(774,936)(775,935)
(776,934)(777,933)(778,932)(779,931)(780,930)(781,929)(782,928)(783,927)
(784,926)(785,925)(786,924)(787,923)(788,922)(789,921)(790,920)(791,919)
(792,918)(793,917)(794,855)(795,915)(796,914)(797,913)(798,912)(799,911)
(800,910)(801,909)(802,908)(803,907)(804,906)(805,905)(806,904)(807,903)
(808,902)(809,901)(810,900)(811,899)(812,898)(813,897)(814,896)(815,895)
(816,894)(817,893)(818,892)(819,891)(820,890)(821,889)(822,888)(823,887)
(824,886)(825,885)(826,884)(827,883)(828,882)(829,881)(830,880)(831,879)
(832,878)(833,877)(834,876)(835,875)(836,874)(837,873)(838,872)(839,871)
(840,870)(841,869)(842,868)(843,867)(844,866)(845,865)(846,864)(847,863)
(848,862)(849,861)(850,860)(851,859)(852,858)(853,857)(854,856);
s2 := Sym(976)!(  1,246)(  2,245)(  3,305)(  4,304)(  5,303)(  6,302)(  7,301)
(  8,300)(  9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)
( 16,292)( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)
( 24,284)( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)
( 32,276)( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)
( 40,268)( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)
( 48,260)( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)
( 56,252)( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,307)( 63,306)
( 64,366)( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)
( 72,358)( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)
( 80,350)( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)
( 88,342)( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)
( 96,334)( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)
(112,318)(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)
(120,310)(121,309)(122,308)(123,368)(124,367)(125,427)(126,426)(127,425)
(128,424)(129,423)(130,422)(131,421)(132,420)(133,419)(134,418)(135,417)
(136,416)(137,415)(138,414)(139,413)(140,412)(141,411)(142,410)(143,409)
(144,408)(145,407)(146,406)(147,405)(148,404)(149,403)(150,402)(151,401)
(152,400)(153,399)(154,398)(155,397)(156,396)(157,395)(158,394)(159,393)
(160,392)(161,391)(162,390)(163,389)(164,388)(165,387)(166,386)(167,385)
(168,384)(169,383)(170,382)(171,381)(172,380)(173,379)(174,378)(175,377)
(176,376)(177,375)(178,374)(179,373)(180,372)(181,371)(182,370)(183,369)
(184,429)(185,428)(186,488)(187,487)(188,486)(189,485)(190,484)(191,483)
(192,482)(193,481)(194,480)(195,479)(196,478)(197,477)(198,476)(199,475)
(200,474)(201,473)(202,472)(203,471)(204,470)(205,469)(206,468)(207,467)
(208,466)(209,465)(210,464)(211,463)(212,462)(213,461)(214,460)(215,459)
(216,458)(217,457)(218,456)(219,455)(220,454)(221,453)(222,452)(223,451)
(224,450)(225,449)(226,448)(227,447)(228,446)(229,445)(230,444)(231,443)
(232,442)(233,441)(234,440)(235,439)(236,438)(237,437)(238,436)(239,435)
(240,434)(241,433)(242,432)(243,431)(244,430)(489,734)(490,733)(491,793)
(492,792)(493,791)(494,790)(495,789)(496,788)(497,787)(498,786)(499,785)
(500,784)(501,783)(502,782)(503,781)(504,780)(505,779)(506,778)(507,777)
(508,776)(509,775)(510,774)(511,773)(512,772)(513,771)(514,770)(515,769)
(516,768)(517,767)(518,766)(519,765)(520,764)(521,763)(522,762)(523,761)
(524,760)(525,759)(526,758)(527,757)(528,756)(529,755)(530,754)(531,753)
(532,752)(533,751)(534,750)(535,749)(536,748)(537,747)(538,746)(539,745)
(540,744)(541,743)(542,742)(543,741)(544,740)(545,739)(546,738)(547,737)
(548,736)(549,735)(550,795)(551,794)(552,854)(553,853)(554,852)(555,851)
(556,850)(557,849)(558,848)(559,847)(560,846)(561,845)(562,844)(563,843)
(564,842)(565,841)(566,840)(567,839)(568,838)(569,837)(570,836)(571,835)
(572,834)(573,833)(574,832)(575,831)(576,830)(577,829)(578,828)(579,827)
(580,826)(581,825)(582,824)(583,823)(584,822)(585,821)(586,820)(587,819)
(588,818)(589,817)(590,816)(591,815)(592,814)(593,813)(594,812)(595,811)
(596,810)(597,809)(598,808)(599,807)(600,806)(601,805)(602,804)(603,803)
(604,802)(605,801)(606,800)(607,799)(608,798)(609,797)(610,796)(611,856)
(612,855)(613,915)(614,914)(615,913)(616,912)(617,911)(618,910)(619,909)
(620,908)(621,907)(622,906)(623,905)(624,904)(625,903)(626,902)(627,901)
(628,900)(629,899)(630,898)(631,897)(632,896)(633,895)(634,894)(635,893)
(636,892)(637,891)(638,890)(639,889)(640,888)(641,887)(642,886)(643,885)
(644,884)(645,883)(646,882)(647,881)(648,880)(649,879)(650,878)(651,877)
(652,876)(653,875)(654,874)(655,873)(656,872)(657,871)(658,870)(659,869)
(660,868)(661,867)(662,866)(663,865)(664,864)(665,863)(666,862)(667,861)
(668,860)(669,859)(670,858)(671,857)(672,917)(673,916)(674,976)(675,975)
(676,974)(677,973)(678,972)(679,971)(680,970)(681,969)(682,968)(683,967)
(684,966)(685,965)(686,964)(687,963)(688,962)(689,961)(690,960)(691,959)
(692,958)(693,957)(694,956)(695,955)(696,954)(697,953)(698,952)(699,951)
(700,950)(701,949)(702,948)(703,947)(704,946)(705,945)(706,944)(707,943)
(708,942)(709,941)(710,940)(711,939)(712,938)(713,937)(714,936)(715,935)
(716,934)(717,933)(718,932)(719,931)(720,930)(721,929)(722,928)(723,927)
(724,926)(725,925)(726,924)(727,923)(728,922)(729,921)(730,920)(731,919)
(732,918);
poly := sub<Sym(976)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope