Polytope of Type {123,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope