Polytope of Type {4,123}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,123}*1968
if this polytope has a name.
Group : SmallGroup(1968,193)
Rank : 3
Schlafli Type : {4,123}
Number of vertices, edges, etc : 8, 492, 246
Order of s₀s₁s₂ : 246
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,123}*984
   4-fold quotients : {2,123}*492
   12-fold quotients : {2,41}*164
   41-fold quotients : {4,3}*48
   82-fold quotients : {4,3}*24
   164-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,495)(  2,496)(  3,493)(  4,494)(  5,499)(  6,500)(  7,497)(  8,498)
(  9,503)( 10,504)( 11,501)( 12,502)( 13,507)( 14,508)( 15,505)( 16,506)
( 17,511)( 18,512)( 19,509)( 20,510)( 21,515)( 22,516)( 23,513)( 24,514)
( 25,519)( 26,520)( 27,517)( 28,518)( 29,523)( 30,524)( 31,521)( 32,522)
( 33,527)( 34,528)( 35,525)( 36,526)( 37,531)( 38,532)( 39,529)( 40,530)
( 41,535)( 42,536)( 43,533)( 44,534)( 45,539)( 46,540)( 47,537)( 48,538)
( 49,543)( 50,544)( 51,541)( 52,542)( 53,547)( 54,548)( 55,545)( 56,546)
( 57,551)( 58,552)( 59,549)( 60,550)( 61,555)( 62,556)( 63,553)( 64,554)
( 65,559)( 66,560)( 67,557)( 68,558)( 69,563)( 70,564)( 71,561)( 72,562)
( 73,567)( 74,568)( 75,565)( 76,566)( 77,571)( 78,572)( 79,569)( 80,570)
( 81,575)( 82,576)( 83,573)( 84,574)( 85,579)( 86,580)( 87,577)( 88,578)
( 89,583)( 90,584)( 91,581)( 92,582)( 93,587)( 94,588)( 95,585)( 96,586)
( 97,591)( 98,592)( 99,589)(100,590)(101,595)(102,596)(103,593)(104,594)
(105,599)(106,600)(107,597)(108,598)(109,603)(110,604)(111,601)(112,602)
(113,607)(114,608)(115,605)(116,606)(117,611)(118,612)(119,609)(120,610)
(121,615)(122,616)(123,613)(124,614)(125,619)(126,620)(127,617)(128,618)
(129,623)(130,624)(131,621)(132,622)(133,627)(134,628)(135,625)(136,626)
(137,631)(138,632)(139,629)(140,630)(141,635)(142,636)(143,633)(144,634)
(145,639)(146,640)(147,637)(148,638)(149,643)(150,644)(151,641)(152,642)
(153,647)(154,648)(155,645)(156,646)(157,651)(158,652)(159,649)(160,650)
(161,655)(162,656)(163,653)(164,654)(165,659)(166,660)(167,657)(168,658)
(169,663)(170,664)(171,661)(172,662)(173,667)(174,668)(175,665)(176,666)
(177,671)(178,672)(179,669)(180,670)(181,675)(182,676)(183,673)(184,674)
(185,679)(186,680)(187,677)(188,678)(189,683)(190,684)(191,681)(192,682)
(193,687)(194,688)(195,685)(196,686)(197,691)(198,692)(199,689)(200,690)
(201,695)(202,696)(203,693)(204,694)(205,699)(206,700)(207,697)(208,698)
(209,703)(210,704)(211,701)(212,702)(213,707)(214,708)(215,705)(216,706)
(217,711)(218,712)(219,709)(220,710)(221,715)(222,716)(223,713)(224,714)
(225,719)(226,720)(227,717)(228,718)(229,723)(230,724)(231,721)(232,722)
(233,727)(234,728)(235,725)(236,726)(237,731)(238,732)(239,729)(240,730)
(241,735)(242,736)(243,733)(244,734)(245,739)(246,740)(247,737)(248,738)
(249,743)(250,744)(251,741)(252,742)(253,747)(254,748)(255,745)(256,746)
(257,751)(258,752)(259,749)(260,750)(261,755)(262,756)(263,753)(264,754)
(265,759)(266,760)(267,757)(268,758)(269,763)(270,764)(271,761)(272,762)
(273,767)(274,768)(275,765)(276,766)(277,771)(278,772)(279,769)(280,770)
(281,775)(282,776)(283,773)(284,774)(285,779)(286,780)(287,777)(288,778)
(289,783)(290,784)(291,781)(292,782)(293,787)(294,788)(295,785)(296,786)
(297,791)(298,792)(299,789)(300,790)(301,795)(302,796)(303,793)(304,794)
(305,799)(306,800)(307,797)(308,798)(309,803)(310,804)(311,801)(312,802)
(313,807)(314,808)(315,805)(316,806)(317,811)(318,812)(319,809)(320,810)
(321,815)(322,816)(323,813)(324,814)(325,819)(326,820)(327,817)(328,818)
(329,823)(330,824)(331,821)(332,822)(333,827)(334,828)(335,825)(336,826)
(337,831)(338,832)(339,829)(340,830)(341,835)(342,836)(343,833)(344,834)
(345,839)(346,840)(347,837)(348,838)(349,843)(350,844)(351,841)(352,842)
(353,847)(354,848)(355,845)(356,846)(357,851)(358,852)(359,849)(360,850)
(361,855)(362,856)(363,853)(364,854)(365,859)(366,860)(367,857)(368,858)
(369,863)(370,864)(371,861)(372,862)(373,867)(374,868)(375,865)(376,866)
(377,871)(378,872)(379,869)(380,870)(381,875)(382,876)(383,873)(384,874)
(385,879)(386,880)(387,877)(388,878)(389,883)(390,884)(391,881)(392,882)
(393,887)(394,888)(395,885)(396,886)(397,891)(398,892)(399,889)(400,890)
(401,895)(402,896)(403,893)(404,894)(405,899)(406,900)(407,897)(408,898)
(409,903)(410,904)(411,901)(412,902)(413,907)(414,908)(415,905)(416,906)
(417,911)(418,912)(419,909)(420,910)(421,915)(422,916)(423,913)(424,914)
(425,919)(426,920)(427,917)(428,918)(429,923)(430,924)(431,921)(432,922)
(433,927)(434,928)(435,925)(436,926)(437,931)(438,932)(439,929)(440,930)
(441,935)(442,936)(443,933)(444,934)(445,939)(446,940)(447,937)(448,938)
(449,943)(450,944)(451,941)(452,942)(453,947)(454,948)(455,945)(456,946)
(457,951)(458,952)(459,949)(460,950)(461,955)(462,956)(463,953)(464,954)
(465,959)(466,960)(467,957)(468,958)(469,963)(470,964)(471,961)(472,962)
(473,967)(474,968)(475,965)(476,966)(477,971)(478,972)(479,969)(480,970)
(481,975)(482,976)(483,973)(484,974)(485,979)(486,980)(487,977)(488,978)
(489,983)(490,984)(491,981)(492,982);;
s1 := (  3,  4)(  5,161)(  6,162)(  7,164)(  8,163)(  9,157)( 10,158)( 11,160)
( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)( 19,152)
( 20,151)( 21,145)( 22,146)( 23,148)( 24,147)( 25,141)( 26,142)( 27,144)
( 28,143)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)( 35,136)
( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,125)( 42,126)( 43,128)
( 44,127)( 45,121)( 46,122)( 47,124)( 48,123)( 49,117)( 50,118)( 51,120)
( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 57,109)( 58,110)( 59,112)
( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)
( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 85)( 82, 86)( 83, 88)
( 84, 87)(165,329)(166,330)(167,332)(168,331)(169,489)(170,490)(171,492)
(172,491)(173,485)(174,486)(175,488)(176,487)(177,481)(178,482)(179,484)
(180,483)(181,477)(182,478)(183,480)(184,479)(185,473)(186,474)(187,476)
(188,475)(189,469)(190,470)(191,472)(192,471)(193,465)(194,466)(195,468)
(196,467)(197,461)(198,462)(199,464)(200,463)(201,457)(202,458)(203,460)
(204,459)(205,453)(206,454)(207,456)(208,455)(209,449)(210,450)(211,452)
(212,451)(213,445)(214,446)(215,448)(216,447)(217,441)(218,442)(219,444)
(220,443)(221,437)(222,438)(223,440)(224,439)(225,433)(226,434)(227,436)
(228,435)(229,429)(230,430)(231,432)(232,431)(233,425)(234,426)(235,428)
(236,427)(237,421)(238,422)(239,424)(240,423)(241,417)(242,418)(243,420)
(244,419)(245,413)(246,414)(247,416)(248,415)(249,409)(250,410)(251,412)
(252,411)(253,405)(254,406)(255,408)(256,407)(257,401)(258,402)(259,404)
(260,403)(261,397)(262,398)(263,400)(264,399)(265,393)(266,394)(267,396)
(268,395)(269,389)(270,390)(271,392)(272,391)(273,385)(274,386)(275,388)
(276,387)(277,381)(278,382)(279,384)(280,383)(281,377)(282,378)(283,380)
(284,379)(285,373)(286,374)(287,376)(288,375)(289,369)(290,370)(291,372)
(292,371)(293,365)(294,366)(295,368)(296,367)(297,361)(298,362)(299,364)
(300,363)(301,357)(302,358)(303,360)(304,359)(305,353)(306,354)(307,356)
(308,355)(309,349)(310,350)(311,352)(312,351)(313,345)(314,346)(315,348)
(316,347)(317,341)(318,342)(319,344)(320,343)(321,337)(322,338)(323,340)
(324,339)(325,333)(326,334)(327,336)(328,335)(495,496)(497,653)(498,654)
(499,656)(500,655)(501,649)(502,650)(503,652)(504,651)(505,645)(506,646)
(507,648)(508,647)(509,641)(510,642)(511,644)(512,643)(513,637)(514,638)
(515,640)(516,639)(517,633)(518,634)(519,636)(520,635)(521,629)(522,630)
(523,632)(524,631)(525,625)(526,626)(527,628)(528,627)(529,621)(530,622)
(531,624)(532,623)(533,617)(534,618)(535,620)(536,619)(537,613)(538,614)
(539,616)(540,615)(541,609)(542,610)(543,612)(544,611)(545,605)(546,606)
(547,608)(548,607)(549,601)(550,602)(551,604)(552,603)(553,597)(554,598)
(555,600)(556,599)(557,593)(558,594)(559,596)(560,595)(561,589)(562,590)
(563,592)(564,591)(565,585)(566,586)(567,588)(568,587)(569,581)(570,582)
(571,584)(572,583)(573,577)(574,578)(575,580)(576,579)(657,821)(658,822)
(659,824)(660,823)(661,981)(662,982)(663,984)(664,983)(665,977)(666,978)
(667,980)(668,979)(669,973)(670,974)(671,976)(672,975)(673,969)(674,970)
(675,972)(676,971)(677,965)(678,966)(679,968)(680,967)(681,961)(682,962)
(683,964)(684,963)(685,957)(686,958)(687,960)(688,959)(689,953)(690,954)
(691,956)(692,955)(693,949)(694,950)(695,952)(696,951)(697,945)(698,946)
(699,948)(700,947)(701,941)(702,942)(703,944)(704,943)(705,937)(706,938)
(707,940)(708,939)(709,933)(710,934)(711,936)(712,935)(713,929)(714,930)
(715,932)(716,931)(717,925)(718,926)(719,928)(720,927)(721,921)(722,922)
(723,924)(724,923)(725,917)(726,918)(727,920)(728,919)(729,913)(730,914)
(731,916)(732,915)(733,909)(734,910)(735,912)(736,911)(737,905)(738,906)
(739,908)(740,907)(741,901)(742,902)(743,904)(744,903)(745,897)(746,898)
(747,900)(748,899)(749,893)(750,894)(751,896)(752,895)(753,889)(754,890)
(755,892)(756,891)(757,885)(758,886)(759,888)(760,887)(761,881)(762,882)
(763,884)(764,883)(765,877)(766,878)(767,880)(768,879)(769,873)(770,874)
(771,876)(772,875)(773,869)(774,870)(775,872)(776,871)(777,865)(778,866)
(779,868)(780,867)(781,861)(782,862)(783,864)(784,863)(785,857)(786,858)
(787,860)(788,859)(789,853)(790,854)(791,856)(792,855)(793,849)(794,850)
(795,852)(796,851)(797,845)(798,846)(799,848)(800,847)(801,841)(802,842)
(803,844)(804,843)(805,837)(806,838)(807,840)(808,839)(809,833)(810,834)
(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)(818,826)
(819,828)(820,827);;
s2 := (  1,169)(  2,172)(  3,171)(  4,170)(  5,165)(  6,168)(  7,167)(  8,166)
(  9,325)( 10,328)( 11,327)( 12,326)( 13,321)( 14,324)( 15,323)( 16,322)
( 17,317)( 18,320)( 19,319)( 20,318)( 21,313)( 22,316)( 23,315)( 24,314)
( 25,309)( 26,312)( 27,311)( 28,310)( 29,305)( 30,308)( 31,307)( 32,306)
( 33,301)( 34,304)( 35,303)( 36,302)( 37,297)( 38,300)( 39,299)( 40,298)
( 41,293)( 42,296)( 43,295)( 44,294)( 45,289)( 46,292)( 47,291)( 48,290)
( 49,285)( 50,288)( 51,287)( 52,286)( 53,281)( 54,284)( 55,283)( 56,282)
( 57,277)( 58,280)( 59,279)( 60,278)( 61,273)( 62,276)( 63,275)( 64,274)
( 65,269)( 66,272)( 67,271)( 68,270)( 69,265)( 70,268)( 71,267)( 72,266)
( 73,261)( 74,264)( 75,263)( 76,262)( 77,257)( 78,260)( 79,259)( 80,258)
( 81,253)( 82,256)( 83,255)( 84,254)( 85,249)( 86,252)( 87,251)( 88,250)
( 89,245)( 90,248)( 91,247)( 92,246)( 93,241)( 94,244)( 95,243)( 96,242)
( 97,237)( 98,240)( 99,239)(100,238)(101,233)(102,236)(103,235)(104,234)
(105,229)(106,232)(107,231)(108,230)(109,225)(110,228)(111,227)(112,226)
(113,221)(114,224)(115,223)(116,222)(117,217)(118,220)(119,219)(120,218)
(121,213)(122,216)(123,215)(124,214)(125,209)(126,212)(127,211)(128,210)
(129,205)(130,208)(131,207)(132,206)(133,201)(134,204)(135,203)(136,202)
(137,197)(138,200)(139,199)(140,198)(141,193)(142,196)(143,195)(144,194)
(145,189)(146,192)(147,191)(148,190)(149,185)(150,188)(151,187)(152,186)
(153,181)(154,184)(155,183)(156,182)(157,177)(158,180)(159,179)(160,178)
(161,173)(162,176)(163,175)(164,174)(329,333)(330,336)(331,335)(332,334)
(337,489)(338,492)(339,491)(340,490)(341,485)(342,488)(343,487)(344,486)
(345,481)(346,484)(347,483)(348,482)(349,477)(350,480)(351,479)(352,478)
(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)(360,470)
(361,465)(362,468)(363,467)(364,466)(365,461)(366,464)(367,463)(368,462)
(369,457)(370,460)(371,459)(372,458)(373,453)(374,456)(375,455)(376,454)
(377,449)(378,452)(379,451)(380,450)(381,445)(382,448)(383,447)(384,446)
(385,441)(386,444)(387,443)(388,442)(389,437)(390,440)(391,439)(392,438)
(393,433)(394,436)(395,435)(396,434)(397,429)(398,432)(399,431)(400,430)
(401,425)(402,428)(403,427)(404,426)(405,421)(406,424)(407,423)(408,422)
(409,417)(410,420)(411,419)(412,418)(414,416)(493,661)(494,664)(495,663)
(496,662)(497,657)(498,660)(499,659)(500,658)(501,817)(502,820)(503,819)
(504,818)(505,813)(506,816)(507,815)(508,814)(509,809)(510,812)(511,811)
(512,810)(513,805)(514,808)(515,807)(516,806)(517,801)(518,804)(519,803)
(520,802)(521,797)(522,800)(523,799)(524,798)(525,793)(526,796)(527,795)
(528,794)(529,789)(530,792)(531,791)(532,790)(533,785)(534,788)(535,787)
(536,786)(537,781)(538,784)(539,783)(540,782)(541,777)(542,780)(543,779)
(544,778)(545,773)(546,776)(547,775)(548,774)(549,769)(550,772)(551,771)
(552,770)(553,765)(554,768)(555,767)(556,766)(557,761)(558,764)(559,763)
(560,762)(561,757)(562,760)(563,759)(564,758)(565,753)(566,756)(567,755)
(568,754)(569,749)(570,752)(571,751)(572,750)(573,745)(574,748)(575,747)
(576,746)(577,741)(578,744)(579,743)(580,742)(581,737)(582,740)(583,739)
(584,738)(585,733)(586,736)(587,735)(588,734)(589,729)(590,732)(591,731)
(592,730)(593,725)(594,728)(595,727)(596,726)(597,721)(598,724)(599,723)
(600,722)(601,717)(602,720)(603,719)(604,718)(605,713)(606,716)(607,715)
(608,714)(609,709)(610,712)(611,711)(612,710)(613,705)(614,708)(615,707)
(616,706)(617,701)(618,704)(619,703)(620,702)(621,697)(622,700)(623,699)
(624,698)(625,693)(626,696)(627,695)(628,694)(629,689)(630,692)(631,691)
(632,690)(633,685)(634,688)(635,687)(636,686)(637,681)(638,684)(639,683)
(640,682)(641,677)(642,680)(643,679)(644,678)(645,673)(646,676)(647,675)
(648,674)(649,669)(650,672)(651,671)(652,670)(653,665)(654,668)(655,667)
(656,666)(821,825)(822,828)(823,827)(824,826)(829,981)(830,984)(831,983)
(832,982)(833,977)(834,980)(835,979)(836,978)(837,973)(838,976)(839,975)
(840,974)(841,969)(842,972)(843,971)(844,970)(845,965)(846,968)(847,967)
(848,966)(849,961)(850,964)(851,963)(852,962)(853,957)(854,960)(855,959)
(856,958)(857,953)(858,956)(859,955)(860,954)(861,949)(862,952)(863,951)
(864,950)(865,945)(866,948)(867,947)(868,946)(869,941)(870,944)(871,943)
(872,942)(873,937)(874,940)(875,939)(876,938)(877,933)(878,936)(879,935)
(880,934)(881,929)(882,932)(883,931)(884,930)(885,925)(886,928)(887,927)
(888,926)(889,921)(890,924)(891,923)(892,922)(893,917)(894,920)(895,919)
(896,918)(897,913)(898,916)(899,915)(900,914)(901,909)(902,912)(903,911)
(904,910)(906,908);;
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*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(984)!(  1,495)(  2,496)(  3,493)(  4,494)(  5,499)(  6,500)(  7,497)
(  8,498)(  9,503)( 10,504)( 11,501)( 12,502)( 13,507)( 14,508)( 15,505)
( 16,506)( 17,511)( 18,512)( 19,509)( 20,510)( 21,515)( 22,516)( 23,513)
( 24,514)( 25,519)( 26,520)( 27,517)( 28,518)( 29,523)( 30,524)( 31,521)
( 32,522)( 33,527)( 34,528)( 35,525)( 36,526)( 37,531)( 38,532)( 39,529)
( 40,530)( 41,535)( 42,536)( 43,533)( 44,534)( 45,539)( 46,540)( 47,537)
( 48,538)( 49,543)( 50,544)( 51,541)( 52,542)( 53,547)( 54,548)( 55,545)
( 56,546)( 57,551)( 58,552)( 59,549)( 60,550)( 61,555)( 62,556)( 63,553)
( 64,554)( 65,559)( 66,560)( 67,557)( 68,558)( 69,563)( 70,564)( 71,561)
( 72,562)( 73,567)( 74,568)( 75,565)( 76,566)( 77,571)( 78,572)( 79,569)
( 80,570)( 81,575)( 82,576)( 83,573)( 84,574)( 85,579)( 86,580)( 87,577)
( 88,578)( 89,583)( 90,584)( 91,581)( 92,582)( 93,587)( 94,588)( 95,585)
( 96,586)( 97,591)( 98,592)( 99,589)(100,590)(101,595)(102,596)(103,593)
(104,594)(105,599)(106,600)(107,597)(108,598)(109,603)(110,604)(111,601)
(112,602)(113,607)(114,608)(115,605)(116,606)(117,611)(118,612)(119,609)
(120,610)(121,615)(122,616)(123,613)(124,614)(125,619)(126,620)(127,617)
(128,618)(129,623)(130,624)(131,621)(132,622)(133,627)(134,628)(135,625)
(136,626)(137,631)(138,632)(139,629)(140,630)(141,635)(142,636)(143,633)
(144,634)(145,639)(146,640)(147,637)(148,638)(149,643)(150,644)(151,641)
(152,642)(153,647)(154,648)(155,645)(156,646)(157,651)(158,652)(159,649)
(160,650)(161,655)(162,656)(163,653)(164,654)(165,659)(166,660)(167,657)
(168,658)(169,663)(170,664)(171,661)(172,662)(173,667)(174,668)(175,665)
(176,666)(177,671)(178,672)(179,669)(180,670)(181,675)(182,676)(183,673)
(184,674)(185,679)(186,680)(187,677)(188,678)(189,683)(190,684)(191,681)
(192,682)(193,687)(194,688)(195,685)(196,686)(197,691)(198,692)(199,689)
(200,690)(201,695)(202,696)(203,693)(204,694)(205,699)(206,700)(207,697)
(208,698)(209,703)(210,704)(211,701)(212,702)(213,707)(214,708)(215,705)
(216,706)(217,711)(218,712)(219,709)(220,710)(221,715)(222,716)(223,713)
(224,714)(225,719)(226,720)(227,717)(228,718)(229,723)(230,724)(231,721)
(232,722)(233,727)(234,728)(235,725)(236,726)(237,731)(238,732)(239,729)
(240,730)(241,735)(242,736)(243,733)(244,734)(245,739)(246,740)(247,737)
(248,738)(249,743)(250,744)(251,741)(252,742)(253,747)(254,748)(255,745)
(256,746)(257,751)(258,752)(259,749)(260,750)(261,755)(262,756)(263,753)
(264,754)(265,759)(266,760)(267,757)(268,758)(269,763)(270,764)(271,761)
(272,762)(273,767)(274,768)(275,765)(276,766)(277,771)(278,772)(279,769)
(280,770)(281,775)(282,776)(283,773)(284,774)(285,779)(286,780)(287,777)
(288,778)(289,783)(290,784)(291,781)(292,782)(293,787)(294,788)(295,785)
(296,786)(297,791)(298,792)(299,789)(300,790)(301,795)(302,796)(303,793)
(304,794)(305,799)(306,800)(307,797)(308,798)(309,803)(310,804)(311,801)
(312,802)(313,807)(314,808)(315,805)(316,806)(317,811)(318,812)(319,809)
(320,810)(321,815)(322,816)(323,813)(324,814)(325,819)(326,820)(327,817)
(328,818)(329,823)(330,824)(331,821)(332,822)(333,827)(334,828)(335,825)
(336,826)(337,831)(338,832)(339,829)(340,830)(341,835)(342,836)(343,833)
(344,834)(345,839)(346,840)(347,837)(348,838)(349,843)(350,844)(351,841)
(352,842)(353,847)(354,848)(355,845)(356,846)(357,851)(358,852)(359,849)
(360,850)(361,855)(362,856)(363,853)(364,854)(365,859)(366,860)(367,857)
(368,858)(369,863)(370,864)(371,861)(372,862)(373,867)(374,868)(375,865)
(376,866)(377,871)(378,872)(379,869)(380,870)(381,875)(382,876)(383,873)
(384,874)(385,879)(386,880)(387,877)(388,878)(389,883)(390,884)(391,881)
(392,882)(393,887)(394,888)(395,885)(396,886)(397,891)(398,892)(399,889)
(400,890)(401,895)(402,896)(403,893)(404,894)(405,899)(406,900)(407,897)
(408,898)(409,903)(410,904)(411,901)(412,902)(413,907)(414,908)(415,905)
(416,906)(417,911)(418,912)(419,909)(420,910)(421,915)(422,916)(423,913)
(424,914)(425,919)(426,920)(427,917)(428,918)(429,923)(430,924)(431,921)
(432,922)(433,927)(434,928)(435,925)(436,926)(437,931)(438,932)(439,929)
(440,930)(441,935)(442,936)(443,933)(444,934)(445,939)(446,940)(447,937)
(448,938)(449,943)(450,944)(451,941)(452,942)(453,947)(454,948)(455,945)
(456,946)(457,951)(458,952)(459,949)(460,950)(461,955)(462,956)(463,953)
(464,954)(465,959)(466,960)(467,957)(468,958)(469,963)(470,964)(471,961)
(472,962)(473,967)(474,968)(475,965)(476,966)(477,971)(478,972)(479,969)
(480,970)(481,975)(482,976)(483,973)(484,974)(485,979)(486,980)(487,977)
(488,978)(489,983)(490,984)(491,981)(492,982);
s1 := Sym(984)!(  3,  4)(  5,161)(  6,162)(  7,164)(  8,163)(  9,157)( 10,158)
( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)
( 19,152)( 20,151)( 21,145)( 22,146)( 23,148)( 24,147)( 25,141)( 26,142)
( 27,144)( 28,143)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)
( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,125)( 42,126)
( 43,128)( 44,127)( 45,121)( 46,122)( 47,124)( 48,123)( 49,117)( 50,118)
( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 57,109)( 58,110)
( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)
( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)( 73, 93)( 74, 94)
( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 85)( 82, 86)
( 83, 88)( 84, 87)(165,329)(166,330)(167,332)(168,331)(169,489)(170,490)
(171,492)(172,491)(173,485)(174,486)(175,488)(176,487)(177,481)(178,482)
(179,484)(180,483)(181,477)(182,478)(183,480)(184,479)(185,473)(186,474)
(187,476)(188,475)(189,469)(190,470)(191,472)(192,471)(193,465)(194,466)
(195,468)(196,467)(197,461)(198,462)(199,464)(200,463)(201,457)(202,458)
(203,460)(204,459)(205,453)(206,454)(207,456)(208,455)(209,449)(210,450)
(211,452)(212,451)(213,445)(214,446)(215,448)(216,447)(217,441)(218,442)
(219,444)(220,443)(221,437)(222,438)(223,440)(224,439)(225,433)(226,434)
(227,436)(228,435)(229,429)(230,430)(231,432)(232,431)(233,425)(234,426)
(235,428)(236,427)(237,421)(238,422)(239,424)(240,423)(241,417)(242,418)
(243,420)(244,419)(245,413)(246,414)(247,416)(248,415)(249,409)(250,410)
(251,412)(252,411)(253,405)(254,406)(255,408)(256,407)(257,401)(258,402)
(259,404)(260,403)(261,397)(262,398)(263,400)(264,399)(265,393)(266,394)
(267,396)(268,395)(269,389)(270,390)(271,392)(272,391)(273,385)(274,386)
(275,388)(276,387)(277,381)(278,382)(279,384)(280,383)(281,377)(282,378)
(283,380)(284,379)(285,373)(286,374)(287,376)(288,375)(289,369)(290,370)
(291,372)(292,371)(293,365)(294,366)(295,368)(296,367)(297,361)(298,362)
(299,364)(300,363)(301,357)(302,358)(303,360)(304,359)(305,353)(306,354)
(307,356)(308,355)(309,349)(310,350)(311,352)(312,351)(313,345)(314,346)
(315,348)(316,347)(317,341)(318,342)(319,344)(320,343)(321,337)(322,338)
(323,340)(324,339)(325,333)(326,334)(327,336)(328,335)(495,496)(497,653)
(498,654)(499,656)(500,655)(501,649)(502,650)(503,652)(504,651)(505,645)
(506,646)(507,648)(508,647)(509,641)(510,642)(511,644)(512,643)(513,637)
(514,638)(515,640)(516,639)(517,633)(518,634)(519,636)(520,635)(521,629)
(522,630)(523,632)(524,631)(525,625)(526,626)(527,628)(528,627)(529,621)
(530,622)(531,624)(532,623)(533,617)(534,618)(535,620)(536,619)(537,613)
(538,614)(539,616)(540,615)(541,609)(542,610)(543,612)(544,611)(545,605)
(546,606)(547,608)(548,607)(549,601)(550,602)(551,604)(552,603)(553,597)
(554,598)(555,600)(556,599)(557,593)(558,594)(559,596)(560,595)(561,589)
(562,590)(563,592)(564,591)(565,585)(566,586)(567,588)(568,587)(569,581)
(570,582)(571,584)(572,583)(573,577)(574,578)(575,580)(576,579)(657,821)
(658,822)(659,824)(660,823)(661,981)(662,982)(663,984)(664,983)(665,977)
(666,978)(667,980)(668,979)(669,973)(670,974)(671,976)(672,975)(673,969)
(674,970)(675,972)(676,971)(677,965)(678,966)(679,968)(680,967)(681,961)
(682,962)(683,964)(684,963)(685,957)(686,958)(687,960)(688,959)(689,953)
(690,954)(691,956)(692,955)(693,949)(694,950)(695,952)(696,951)(697,945)
(698,946)(699,948)(700,947)(701,941)(702,942)(703,944)(704,943)(705,937)
(706,938)(707,940)(708,939)(709,933)(710,934)(711,936)(712,935)(713,929)
(714,930)(715,932)(716,931)(717,925)(718,926)(719,928)(720,927)(721,921)
(722,922)(723,924)(724,923)(725,917)(726,918)(727,920)(728,919)(729,913)
(730,914)(731,916)(732,915)(733,909)(734,910)(735,912)(736,911)(737,905)
(738,906)(739,908)(740,907)(741,901)(742,902)(743,904)(744,903)(745,897)
(746,898)(747,900)(748,899)(749,893)(750,894)(751,896)(752,895)(753,889)
(754,890)(755,892)(756,891)(757,885)(758,886)(759,888)(760,887)(761,881)
(762,882)(763,884)(764,883)(765,877)(766,878)(767,880)(768,879)(769,873)
(770,874)(771,876)(772,875)(773,869)(774,870)(775,872)(776,871)(777,865)
(778,866)(779,868)(780,867)(781,861)(782,862)(783,864)(784,863)(785,857)
(786,858)(787,860)(788,859)(789,853)(790,854)(791,856)(792,855)(793,849)
(794,850)(795,852)(796,851)(797,845)(798,846)(799,848)(800,847)(801,841)
(802,842)(803,844)(804,843)(805,837)(806,838)(807,840)(808,839)(809,833)
(810,834)(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)
(818,826)(819,828)(820,827);
s2 := Sym(984)!(  1,169)(  2,172)(  3,171)(  4,170)(  5,165)(  6,168)(  7,167)
(  8,166)(  9,325)( 10,328)( 11,327)( 12,326)( 13,321)( 14,324)( 15,323)
( 16,322)( 17,317)( 18,320)( 19,319)( 20,318)( 21,313)( 22,316)( 23,315)
( 24,314)( 25,309)( 26,312)( 27,311)( 28,310)( 29,305)( 30,308)( 31,307)
( 32,306)( 33,301)( 34,304)( 35,303)( 36,302)( 37,297)( 38,300)( 39,299)
( 40,298)( 41,293)( 42,296)( 43,295)( 44,294)( 45,289)( 46,292)( 47,291)
( 48,290)( 49,285)( 50,288)( 51,287)( 52,286)( 53,281)( 54,284)( 55,283)
( 56,282)( 57,277)( 58,280)( 59,279)( 60,278)( 61,273)( 62,276)( 63,275)
( 64,274)( 65,269)( 66,272)( 67,271)( 68,270)( 69,265)( 70,268)( 71,267)
( 72,266)( 73,261)( 74,264)( 75,263)( 76,262)( 77,257)( 78,260)( 79,259)
( 80,258)( 81,253)( 82,256)( 83,255)( 84,254)( 85,249)( 86,252)( 87,251)
( 88,250)( 89,245)( 90,248)( 91,247)( 92,246)( 93,241)( 94,244)( 95,243)
( 96,242)( 97,237)( 98,240)( 99,239)(100,238)(101,233)(102,236)(103,235)
(104,234)(105,229)(106,232)(107,231)(108,230)(109,225)(110,228)(111,227)
(112,226)(113,221)(114,224)(115,223)(116,222)(117,217)(118,220)(119,219)
(120,218)(121,213)(122,216)(123,215)(124,214)(125,209)(126,212)(127,211)
(128,210)(129,205)(130,208)(131,207)(132,206)(133,201)(134,204)(135,203)
(136,202)(137,197)(138,200)(139,199)(140,198)(141,193)(142,196)(143,195)
(144,194)(145,189)(146,192)(147,191)(148,190)(149,185)(150,188)(151,187)
(152,186)(153,181)(154,184)(155,183)(156,182)(157,177)(158,180)(159,179)
(160,178)(161,173)(162,176)(163,175)(164,174)(329,333)(330,336)(331,335)
(332,334)(337,489)(338,492)(339,491)(340,490)(341,485)(342,488)(343,487)
(344,486)(345,481)(346,484)(347,483)(348,482)(349,477)(350,480)(351,479)
(352,478)(353,473)(354,476)(355,475)(356,474)(357,469)(358,472)(359,471)
(360,470)(361,465)(362,468)(363,467)(364,466)(365,461)(366,464)(367,463)
(368,462)(369,457)(370,460)(371,459)(372,458)(373,453)(374,456)(375,455)
(376,454)(377,449)(378,452)(379,451)(380,450)(381,445)(382,448)(383,447)
(384,446)(385,441)(386,444)(387,443)(388,442)(389,437)(390,440)(391,439)
(392,438)(393,433)(394,436)(395,435)(396,434)(397,429)(398,432)(399,431)
(400,430)(401,425)(402,428)(403,427)(404,426)(405,421)(406,424)(407,423)
(408,422)(409,417)(410,420)(411,419)(412,418)(414,416)(493,661)(494,664)
(495,663)(496,662)(497,657)(498,660)(499,659)(500,658)(501,817)(502,820)
(503,819)(504,818)(505,813)(506,816)(507,815)(508,814)(509,809)(510,812)
(511,811)(512,810)(513,805)(514,808)(515,807)(516,806)(517,801)(518,804)
(519,803)(520,802)(521,797)(522,800)(523,799)(524,798)(525,793)(526,796)
(527,795)(528,794)(529,789)(530,792)(531,791)(532,790)(533,785)(534,788)
(535,787)(536,786)(537,781)(538,784)(539,783)(540,782)(541,777)(542,780)
(543,779)(544,778)(545,773)(546,776)(547,775)(548,774)(549,769)(550,772)
(551,771)(552,770)(553,765)(554,768)(555,767)(556,766)(557,761)(558,764)
(559,763)(560,762)(561,757)(562,760)(563,759)(564,758)(565,753)(566,756)
(567,755)(568,754)(569,749)(570,752)(571,751)(572,750)(573,745)(574,748)
(575,747)(576,746)(577,741)(578,744)(579,743)(580,742)(581,737)(582,740)
(583,739)(584,738)(585,733)(586,736)(587,735)(588,734)(589,729)(590,732)
(591,731)(592,730)(593,725)(594,728)(595,727)(596,726)(597,721)(598,724)
(599,723)(600,722)(601,717)(602,720)(603,719)(604,718)(605,713)(606,716)
(607,715)(608,714)(609,709)(610,712)(611,711)(612,710)(613,705)(614,708)
(615,707)(616,706)(617,701)(618,704)(619,703)(620,702)(621,697)(622,700)
(623,699)(624,698)(625,693)(626,696)(627,695)(628,694)(629,689)(630,692)
(631,691)(632,690)(633,685)(634,688)(635,687)(636,686)(637,681)(638,684)
(639,683)(640,682)(641,677)(642,680)(643,679)(644,678)(645,673)(646,676)
(647,675)(648,674)(649,669)(650,672)(651,671)(652,670)(653,665)(654,668)
(655,667)(656,666)(821,825)(822,828)(823,827)(824,826)(829,981)(830,984)
(831,983)(832,982)(833,977)(834,980)(835,979)(836,978)(837,973)(838,976)
(839,975)(840,974)(841,969)(842,972)(843,971)(844,970)(845,965)(846,968)
(847,967)(848,966)(849,961)(850,964)(851,963)(852,962)(853,957)(854,960)
(855,959)(856,958)(857,953)(858,956)(859,955)(860,954)(861,949)(862,952)
(863,951)(864,950)(865,945)(866,948)(867,947)(868,946)(869,941)(870,944)
(871,943)(872,942)(873,937)(874,940)(875,939)(876,938)(877,933)(878,936)
(879,935)(880,934)(881,929)(882,932)(883,931)(884,930)(885,925)(886,928)
(887,927)(888,926)(889,921)(890,924)(891,923)(892,922)(893,917)(894,920)
(895,919)(896,918)(897,913)(898,916)(899,915)(900,914)(901,909)(902,912)
(903,911)(904,910)(906,908);
poly := sub<Sym(984)|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*s2*s1*s0*s1*s2*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 >;

References : None.
to this polytope