Polytope of Type {246,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {246,4}*1968c
if this polytope has a name.
Group : SmallGroup(1968,193)
Rank : 3
Schlafli Type : {246,4}
Number of vertices, edges, etc : 246, 492, 4
Order of s₀s₁s₂ : 123
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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
   41-fold quotients : {6,4}*48b
   82-fold quotients : {3,4}*24
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 := (  1,661)(  2,664)(  3,663)(  4,662)(  5,657)(  6,660)(  7,659)(  8,658)
(  9,817)( 10,820)( 11,819)( 12,818)( 13,813)( 14,816)( 15,815)( 16,814)
( 17,809)( 18,812)( 19,811)( 20,810)( 21,805)( 22,808)( 23,807)( 24,806)
( 25,801)( 26,804)( 27,803)( 28,802)( 29,797)( 30,800)( 31,799)( 32,798)
( 33,793)( 34,796)( 35,795)( 36,794)( 37,789)( 38,792)( 39,791)( 40,790)
( 41,785)( 42,788)( 43,787)( 44,786)( 45,781)( 46,784)( 47,783)( 48,782)
( 49,777)( 50,780)( 51,779)( 52,778)( 53,773)( 54,776)( 55,775)( 56,774)
( 57,769)( 58,772)( 59,771)( 60,770)( 61,765)( 62,768)( 63,767)( 64,766)
( 65,761)( 66,764)( 67,763)( 68,762)( 69,757)( 70,760)( 71,759)( 72,758)
( 73,753)( 74,756)( 75,755)( 76,754)( 77,749)( 78,752)( 79,751)( 80,750)
( 81,745)( 82,748)( 83,747)( 84,746)( 85,741)( 86,744)( 87,743)( 88,742)
( 89,737)( 90,740)( 91,739)( 92,738)( 93,733)( 94,736)( 95,735)( 96,734)
( 97,729)( 98,732)( 99,731)(100,730)(101,725)(102,728)(103,727)(104,726)
(105,721)(106,724)(107,723)(108,722)(109,717)(110,720)(111,719)(112,718)
(113,713)(114,716)(115,715)(116,714)(117,709)(118,712)(119,711)(120,710)
(121,705)(122,708)(123,707)(124,706)(125,701)(126,704)(127,703)(128,702)
(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)(136,694)
(137,689)(138,692)(139,691)(140,690)(141,685)(142,688)(143,687)(144,686)
(145,681)(146,684)(147,683)(148,682)(149,677)(150,680)(151,679)(152,678)
(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)(160,670)
(161,665)(162,668)(163,667)(164,666)(165,497)(166,500)(167,499)(168,498)
(169,493)(170,496)(171,495)(172,494)(173,653)(174,656)(175,655)(176,654)
(177,649)(178,652)(179,651)(180,650)(181,645)(182,648)(183,647)(184,646)
(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)(192,638)
(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)
(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)(208,622)
(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)
(217,609)(218,612)(219,611)(220,610)(221,605)(222,608)(223,607)(224,606)
(225,601)(226,604)(227,603)(228,602)(229,597)(230,600)(231,599)(232,598)
(233,593)(234,596)(235,595)(236,594)(237,589)(238,592)(239,591)(240,590)
(241,585)(242,588)(243,587)(244,586)(245,581)(246,584)(247,583)(248,582)
(249,577)(250,580)(251,579)(252,578)(253,573)(254,576)(255,575)(256,574)
(257,569)(258,572)(259,571)(260,570)(261,565)(262,568)(263,567)(264,566)
(265,561)(266,564)(267,563)(268,562)(269,557)(270,560)(271,559)(272,558)
(273,553)(274,556)(275,555)(276,554)(277,549)(278,552)(279,551)(280,550)
(281,545)(282,548)(283,547)(284,546)(285,541)(286,544)(287,543)(288,542)
(289,537)(290,540)(291,539)(292,538)(293,533)(294,536)(295,535)(296,534)
(297,529)(298,532)(299,531)(300,530)(301,525)(302,528)(303,527)(304,526)
(305,521)(306,524)(307,523)(308,522)(309,517)(310,520)(311,519)(312,518)
(313,513)(314,516)(315,515)(316,514)(317,509)(318,512)(319,511)(320,510)
(321,505)(322,508)(323,507)(324,506)(325,501)(326,504)(327,503)(328,502)
(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)(336,822)
(337,981)(338,984)(339,983)(340,982)(341,977)(342,980)(343,979)(344,978)
(345,973)(346,976)(347,975)(348,974)(349,969)(350,972)(351,971)(352,970)
(353,965)(354,968)(355,967)(356,966)(357,961)(358,964)(359,963)(360,962)
(361,957)(362,960)(363,959)(364,958)(365,953)(366,956)(367,955)(368,954)
(369,949)(370,952)(371,951)(372,950)(373,945)(374,948)(375,947)(376,946)
(377,941)(378,944)(379,943)(380,942)(381,937)(382,940)(383,939)(384,938)
(385,933)(386,936)(387,935)(388,934)(389,929)(390,932)(391,931)(392,930)
(393,925)(394,928)(395,927)(396,926)(397,921)(398,924)(399,923)(400,922)
(401,917)(402,920)(403,919)(404,918)(405,913)(406,916)(407,915)(408,914)
(409,909)(410,912)(411,911)(412,910)(413,905)(414,908)(415,907)(416,906)
(417,901)(418,904)(419,903)(420,902)(421,897)(422,900)(423,899)(424,898)
(425,893)(426,896)(427,895)(428,894)(429,889)(430,892)(431,891)(432,890)
(433,885)(434,888)(435,887)(436,886)(437,881)(438,884)(439,883)(440,882)
(441,877)(442,880)(443,879)(444,878)(445,873)(446,876)(447,875)(448,874)
(449,869)(450,872)(451,871)(452,870)(453,865)(454,868)(455,867)(456,866)
(457,861)(458,864)(459,863)(460,862)(461,857)(462,860)(463,859)(464,858)
(465,853)(466,856)(467,855)(468,854)(469,849)(470,852)(471,851)(472,850)
(473,845)(474,848)(475,847)(476,846)(477,841)(478,844)(479,843)(480,842)
(481,837)(482,840)(483,839)(484,838)(485,833)(486,836)(487,835)(488,834)
(489,829)(490,832)(491,831)(492,830);;
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*s2*s1*s0*s2*s1*s0*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 ];;
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)!(  1,661)(  2,664)(  3,663)(  4,662)(  5,657)(  6,660)(  7,659)
(  8,658)(  9,817)( 10,820)( 11,819)( 12,818)( 13,813)( 14,816)( 15,815)
( 16,814)( 17,809)( 18,812)( 19,811)( 20,810)( 21,805)( 22,808)( 23,807)
( 24,806)( 25,801)( 26,804)( 27,803)( 28,802)( 29,797)( 30,800)( 31,799)
( 32,798)( 33,793)( 34,796)( 35,795)( 36,794)( 37,789)( 38,792)( 39,791)
( 40,790)( 41,785)( 42,788)( 43,787)( 44,786)( 45,781)( 46,784)( 47,783)
( 48,782)( 49,777)( 50,780)( 51,779)( 52,778)( 53,773)( 54,776)( 55,775)
( 56,774)( 57,769)( 58,772)( 59,771)( 60,770)( 61,765)( 62,768)( 63,767)
( 64,766)( 65,761)( 66,764)( 67,763)( 68,762)( 69,757)( 70,760)( 71,759)
( 72,758)( 73,753)( 74,756)( 75,755)( 76,754)( 77,749)( 78,752)( 79,751)
( 80,750)( 81,745)( 82,748)( 83,747)( 84,746)( 85,741)( 86,744)( 87,743)
( 88,742)( 89,737)( 90,740)( 91,739)( 92,738)( 93,733)( 94,736)( 95,735)
( 96,734)( 97,729)( 98,732)( 99,731)(100,730)(101,725)(102,728)(103,727)
(104,726)(105,721)(106,724)(107,723)(108,722)(109,717)(110,720)(111,719)
(112,718)(113,713)(114,716)(115,715)(116,714)(117,709)(118,712)(119,711)
(120,710)(121,705)(122,708)(123,707)(124,706)(125,701)(126,704)(127,703)
(128,702)(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)
(136,694)(137,689)(138,692)(139,691)(140,690)(141,685)(142,688)(143,687)
(144,686)(145,681)(146,684)(147,683)(148,682)(149,677)(150,680)(151,679)
(152,678)(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)
(160,670)(161,665)(162,668)(163,667)(164,666)(165,497)(166,500)(167,499)
(168,498)(169,493)(170,496)(171,495)(172,494)(173,653)(174,656)(175,655)
(176,654)(177,649)(178,652)(179,651)(180,650)(181,645)(182,648)(183,647)
(184,646)(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)
(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)
(200,630)(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)
(208,622)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)
(216,614)(217,609)(218,612)(219,611)(220,610)(221,605)(222,608)(223,607)
(224,606)(225,601)(226,604)(227,603)(228,602)(229,597)(230,600)(231,599)
(232,598)(233,593)(234,596)(235,595)(236,594)(237,589)(238,592)(239,591)
(240,590)(241,585)(242,588)(243,587)(244,586)(245,581)(246,584)(247,583)
(248,582)(249,577)(250,580)(251,579)(252,578)(253,573)(254,576)(255,575)
(256,574)(257,569)(258,572)(259,571)(260,570)(261,565)(262,568)(263,567)
(264,566)(265,561)(266,564)(267,563)(268,562)(269,557)(270,560)(271,559)
(272,558)(273,553)(274,556)(275,555)(276,554)(277,549)(278,552)(279,551)
(280,550)(281,545)(282,548)(283,547)(284,546)(285,541)(286,544)(287,543)
(288,542)(289,537)(290,540)(291,539)(292,538)(293,533)(294,536)(295,535)
(296,534)(297,529)(298,532)(299,531)(300,530)(301,525)(302,528)(303,527)
(304,526)(305,521)(306,524)(307,523)(308,522)(309,517)(310,520)(311,519)
(312,518)(313,513)(314,516)(315,515)(316,514)(317,509)(318,512)(319,511)
(320,510)(321,505)(322,508)(323,507)(324,506)(325,501)(326,504)(327,503)
(328,502)(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)
(336,822)(337,981)(338,984)(339,983)(340,982)(341,977)(342,980)(343,979)
(344,978)(345,973)(346,976)(347,975)(348,974)(349,969)(350,972)(351,971)
(352,970)(353,965)(354,968)(355,967)(356,966)(357,961)(358,964)(359,963)
(360,962)(361,957)(362,960)(363,959)(364,958)(365,953)(366,956)(367,955)
(368,954)(369,949)(370,952)(371,951)(372,950)(373,945)(374,948)(375,947)
(376,946)(377,941)(378,944)(379,943)(380,942)(381,937)(382,940)(383,939)
(384,938)(385,933)(386,936)(387,935)(388,934)(389,929)(390,932)(391,931)
(392,930)(393,925)(394,928)(395,927)(396,926)(397,921)(398,924)(399,923)
(400,922)(401,917)(402,920)(403,919)(404,918)(405,913)(406,916)(407,915)
(408,914)(409,909)(410,912)(411,911)(412,910)(413,905)(414,908)(415,907)
(416,906)(417,901)(418,904)(419,903)(420,902)(421,897)(422,900)(423,899)
(424,898)(425,893)(426,896)(427,895)(428,894)(429,889)(430,892)(431,891)
(432,890)(433,885)(434,888)(435,887)(436,886)(437,881)(438,884)(439,883)
(440,882)(441,877)(442,880)(443,879)(444,878)(445,873)(446,876)(447,875)
(448,874)(449,869)(450,872)(451,871)(452,870)(453,865)(454,868)(455,867)
(456,866)(457,861)(458,864)(459,863)(460,862)(461,857)(462,860)(463,859)
(464,858)(465,853)(466,856)(467,855)(468,854)(469,849)(470,852)(471,851)
(472,850)(473,845)(474,848)(475,847)(476,846)(477,841)(478,844)(479,843)
(480,842)(481,837)(482,840)(483,839)(484,838)(485,833)(486,836)(487,835)
(488,834)(489,829)(490,832)(491,831)(492,830);
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*s2*s1*s0*s2*s1*s0*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 >;

References : None.
to this polytope