Polytope of Type {4,246}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,246}*1968b
if this polytope has a name.
Group : SmallGroup(1968,193)
Rank : 3
Schlafli Type : {4,246}
Number of vertices, edges, etc : 4, 492, 246
Order of s₀s₁s₂ : 246
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,123}*984
   41-fold quotients : {4,6}*48c
   82-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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