Polytope of Type {8,122}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,122}*1952
Also Known As : {8,122|2}. if this polytope has another name.
Group : SmallGroup(1952,155)
Rank : 3
Schlafli Type : {8,122}
Number of vertices, edges, etc : 8, 488, 122
Order of s₀s₁s₂ : 488
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 : {4,122}*976
   4-fold quotients : {2,122}*488
   8-fold quotients : {2,61}*244
   61-fold quotients : {8,2}*32
   122-fold quotients : {4,2}*16
   244-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope