Polytope of Type {4,248}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,248}*1984a
Also Known As : {4,248|2}. if this polytope has another name.
Group : SmallGroup(1984,685)
Rank : 3
Schlafli Type : {4,248}
Number of vertices, edges, etc : 4, 496, 248
Order of s₀s₁s₂ : 248
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,124}*992, {2,248}*992
   4-fold quotients : {2,124}*496, {4,62}*496
   8-fold quotients : {2,62}*248
   16-fold quotients : {2,31}*124
   31-fold quotients : {4,8}*64a
   62-fold quotients : {4,4}*32, {2,8}*32
   124-fold quotients : {2,4}*16, {4,2}*16
   248-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)(  8,256)
(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)( 16,264)
( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)
( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)( 32,280)
( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)
( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)( 64,312)
( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)( 80,328)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)
( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)
(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)(112,360)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)(128,376)
(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)
(137,385)(138,386)(139,387)(140,388)(141,389)(142,390)(143,391)(144,392)
(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)
(153,401)(154,402)(155,403)(156,404)(157,405)(158,406)(159,407)(160,408)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)(176,424)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)(192,440)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,465)(218,466)(219,467)(220,468)(221,469)(222,470)(223,471)(224,472)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)(240,488)
(241,489)(242,490)(243,491)(244,492)(245,493)(246,494)(247,495)(248,496)
(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)(504,752)
(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)(512,760)
(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)(520,768)
(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)(528,776)
(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)(536,784)
(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)(544,792)
(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)(552,800)
(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)(560,808)
(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)(568,816)
(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)(576,824)
(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)(584,832)
(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)(592,840)
(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)(600,848)
(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)(608,856)
(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)(616,864)
(617,865)(618,866)(619,867)(620,868)(621,869)(622,870)(623,871)(624,872)
(625,873)(626,874)(627,875)(628,876)(629,877)(630,878)(631,879)(632,880)
(633,881)(634,882)(635,883)(636,884)(637,885)(638,886)(639,887)(640,888)
(641,889)(642,890)(643,891)(644,892)(645,893)(646,894)(647,895)(648,896)
(649,897)(650,898)(651,899)(652,900)(653,901)(654,902)(655,903)(656,904)
(657,905)(658,906)(659,907)(660,908)(661,909)(662,910)(663,911)(664,912)
(665,913)(666,914)(667,915)(668,916)(669,917)(670,918)(671,919)(672,920)
(673,921)(674,922)(675,923)(676,924)(677,925)(678,926)(679,927)(680,928)
(681,929)(682,930)(683,931)(684,932)(685,933)(686,934)(687,935)(688,936)
(689,937)(690,938)(691,939)(692,940)(693,941)(694,942)(695,943)(696,944)
(697,945)(698,946)(699,947)(700,948)(701,949)(702,950)(703,951)(704,952)
(705,953)(706,954)(707,955)(708,956)(709,957)(710,958)(711,959)(712,960)
(713,961)(714,962)(715,963)(716,964)(717,965)(718,966)(719,967)(720,968)
(721,969)(722,970)(723,971)(724,972)(725,973)(726,974)(727,975)(728,976)
(729,977)(730,978)(731,979)(732,980)(733,981)(734,982)(735,983)(736,984)
(737,985)(738,986)(739,987)(740,988)(741,989)(742,990)(743,991)(744,992);;
s1 := (  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 33, 62)
( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)
( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)( 65, 92)
( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)( 97,122)
( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)
(106,113)(107,112)(108,111)(109,110)(125,156)(126,186)(127,185)(128,184)
(129,183)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)(136,176)
(137,175)(138,174)(139,173)(140,172)(141,171)(142,170)(143,169)(144,168)
(145,167)(146,166)(147,165)(148,164)(149,163)(150,162)(151,161)(152,160)
(153,159)(154,158)(155,157)(187,218)(188,248)(189,247)(190,246)(191,245)
(192,244)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,237)
(200,236)(201,235)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)
(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)(215,221)
(216,220)(217,219)(249,311)(250,341)(251,340)(252,339)(253,338)(254,337)
(255,336)(256,335)(257,334)(258,333)(259,332)(260,331)(261,330)(262,329)
(263,328)(264,327)(265,326)(266,325)(267,324)(268,323)(269,322)(270,321)
(271,320)(272,319)(273,318)(274,317)(275,316)(276,315)(277,314)(278,313)
(279,312)(280,342)(281,372)(282,371)(283,370)(284,369)(285,368)(286,367)
(287,366)(288,365)(289,364)(290,363)(291,362)(292,361)(293,360)(294,359)
(295,358)(296,357)(297,356)(298,355)(299,354)(300,353)(301,352)(302,351)
(303,350)(304,349)(305,348)(306,347)(307,346)(308,345)(309,344)(310,343)
(373,466)(374,496)(375,495)(376,494)(377,493)(378,492)(379,491)(380,490)
(381,489)(382,488)(383,487)(384,486)(385,485)(386,484)(387,483)(388,482)
(389,481)(390,480)(391,479)(392,478)(393,477)(394,476)(395,475)(396,474)
(397,473)(398,472)(399,471)(400,470)(401,469)(402,468)(403,467)(404,435)
(405,465)(406,464)(407,463)(408,462)(409,461)(410,460)(411,459)(412,458)
(413,457)(414,456)(415,455)(416,454)(417,453)(418,452)(419,451)(420,450)
(421,449)(422,448)(423,447)(424,446)(425,445)(426,444)(427,443)(428,442)
(429,441)(430,440)(431,439)(432,438)(433,437)(434,436)(497,621)(498,651)
(499,650)(500,649)(501,648)(502,647)(503,646)(504,645)(505,644)(506,643)
(507,642)(508,641)(509,640)(510,639)(511,638)(512,637)(513,636)(514,635)
(515,634)(516,633)(517,632)(518,631)(519,630)(520,629)(521,628)(522,627)
(523,626)(524,625)(525,624)(526,623)(527,622)(528,652)(529,682)(530,681)
(531,680)(532,679)(533,678)(534,677)(535,676)(536,675)(537,674)(538,673)
(539,672)(540,671)(541,670)(542,669)(543,668)(544,667)(545,666)(546,665)
(547,664)(548,663)(549,662)(550,661)(551,660)(552,659)(553,658)(554,657)
(555,656)(556,655)(557,654)(558,653)(559,683)(560,713)(561,712)(562,711)
(563,710)(564,709)(565,708)(566,707)(567,706)(568,705)(569,704)(570,703)
(571,702)(572,701)(573,700)(574,699)(575,698)(576,697)(577,696)(578,695)
(579,694)(580,693)(581,692)(582,691)(583,690)(584,689)(585,688)(586,687)
(587,686)(588,685)(589,684)(590,714)(591,744)(592,743)(593,742)(594,741)
(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)(601,734)(602,733)
(603,732)(604,731)(605,730)(606,729)(607,728)(608,727)(609,726)(610,725)
(611,724)(612,723)(613,722)(614,721)(615,720)(616,719)(617,718)(618,717)
(619,716)(620,715)(745,931)(746,961)(747,960)(748,959)(749,958)(750,957)
(751,956)(752,955)(753,954)(754,953)(755,952)(756,951)(757,950)(758,949)
(759,948)(760,947)(761,946)(762,945)(763,944)(764,943)(765,942)(766,941)
(767,940)(768,939)(769,938)(770,937)(771,936)(772,935)(773,934)(774,933)
(775,932)(776,962)(777,992)(778,991)(779,990)(780,989)(781,988)(782,987)
(783,986)(784,985)(785,984)(786,983)(787,982)(788,981)(789,980)(790,979)
(791,978)(792,977)(793,976)(794,975)(795,974)(796,973)(797,972)(798,971)
(799,970)(800,969)(801,968)(802,967)(803,966)(804,965)(805,964)(806,963)
(807,869)(808,899)(809,898)(810,897)(811,896)(812,895)(813,894)(814,893)
(815,892)(816,891)(817,890)(818,889)(819,888)(820,887)(821,886)(822,885)
(823,884)(824,883)(825,882)(826,881)(827,880)(828,879)(829,878)(830,877)
(831,876)(832,875)(833,874)(834,873)(835,872)(836,871)(837,870)(838,900)
(839,930)(840,929)(841,928)(842,927)(843,926)(844,925)(845,924)(846,923)
(847,922)(848,921)(849,920)(850,919)(851,918)(852,917)(853,916)(854,915)
(855,914)(856,913)(857,912)(858,911)(859,910)(860,909)(861,908)(862,907)
(863,906)(864,905)(865,904)(866,903)(867,902)(868,901);;
s2 := (  1,498)(  2,497)(  3,527)(  4,526)(  5,525)(  6,524)(  7,523)(  8,522)
(  9,521)( 10,520)( 11,519)( 12,518)( 13,517)( 14,516)( 15,515)( 16,514)
( 17,513)( 18,512)( 19,511)( 20,510)( 21,509)( 22,508)( 23,507)( 24,506)
( 25,505)( 26,504)( 27,503)( 28,502)( 29,501)( 30,500)( 31,499)( 32,529)
( 33,528)( 34,558)( 35,557)( 36,556)( 37,555)( 38,554)( 39,553)( 40,552)
( 41,551)( 42,550)( 43,549)( 44,548)( 45,547)( 46,546)( 47,545)( 48,544)
( 49,543)( 50,542)( 51,541)( 52,540)( 53,539)( 54,538)( 55,537)( 56,536)
( 57,535)( 58,534)( 59,533)( 60,532)( 61,531)( 62,530)( 63,560)( 64,559)
( 65,589)( 66,588)( 67,587)( 68,586)( 69,585)( 70,584)( 71,583)( 72,582)
( 73,581)( 74,580)( 75,579)( 76,578)( 77,577)( 78,576)( 79,575)( 80,574)
( 81,573)( 82,572)( 83,571)( 84,570)( 85,569)( 86,568)( 87,567)( 88,566)
( 89,565)( 90,564)( 91,563)( 92,562)( 93,561)( 94,591)( 95,590)( 96,620)
( 97,619)( 98,618)( 99,617)(100,616)(101,615)(102,614)(103,613)(104,612)
(105,611)(106,610)(107,609)(108,608)(109,607)(110,606)(111,605)(112,604)
(113,603)(114,602)(115,601)(116,600)(117,599)(118,598)(119,597)(120,596)
(121,595)(122,594)(123,593)(124,592)(125,653)(126,652)(127,682)(128,681)
(129,680)(130,679)(131,678)(132,677)(133,676)(134,675)(135,674)(136,673)
(137,672)(138,671)(139,670)(140,669)(141,668)(142,667)(143,666)(144,665)
(145,664)(146,663)(147,662)(148,661)(149,660)(150,659)(151,658)(152,657)
(153,656)(154,655)(155,654)(156,622)(157,621)(158,651)(159,650)(160,649)
(161,648)(162,647)(163,646)(164,645)(165,644)(166,643)(167,642)(168,641)
(169,640)(170,639)(171,638)(172,637)(173,636)(174,635)(175,634)(176,633)
(177,632)(178,631)(179,630)(180,629)(181,628)(182,627)(183,626)(184,625)
(185,624)(186,623)(187,715)(188,714)(189,744)(190,743)(191,742)(192,741)
(193,740)(194,739)(195,738)(196,737)(197,736)(198,735)(199,734)(200,733)
(201,732)(202,731)(203,730)(204,729)(205,728)(206,727)(207,726)(208,725)
(209,724)(210,723)(211,722)(212,721)(213,720)(214,719)(215,718)(216,717)
(217,716)(218,684)(219,683)(220,713)(221,712)(222,711)(223,710)(224,709)
(225,708)(226,707)(227,706)(228,705)(229,704)(230,703)(231,702)(232,701)
(233,700)(234,699)(235,698)(236,697)(237,696)(238,695)(239,694)(240,693)
(241,692)(242,691)(243,690)(244,689)(245,688)(246,687)(247,686)(248,685)
(249,746)(250,745)(251,775)(252,774)(253,773)(254,772)(255,771)(256,770)
(257,769)(258,768)(259,767)(260,766)(261,765)(262,764)(263,763)(264,762)
(265,761)(266,760)(267,759)(268,758)(269,757)(270,756)(271,755)(272,754)
(273,753)(274,752)(275,751)(276,750)(277,749)(278,748)(279,747)(280,777)
(281,776)(282,806)(283,805)(284,804)(285,803)(286,802)(287,801)(288,800)
(289,799)(290,798)(291,797)(292,796)(293,795)(294,794)(295,793)(296,792)
(297,791)(298,790)(299,789)(300,788)(301,787)(302,786)(303,785)(304,784)
(305,783)(306,782)(307,781)(308,780)(309,779)(310,778)(311,808)(312,807)
(313,837)(314,836)(315,835)(316,834)(317,833)(318,832)(319,831)(320,830)
(321,829)(322,828)(323,827)(324,826)(325,825)(326,824)(327,823)(328,822)
(329,821)(330,820)(331,819)(332,818)(333,817)(334,816)(335,815)(336,814)
(337,813)(338,812)(339,811)(340,810)(341,809)(342,839)(343,838)(344,868)
(345,867)(346,866)(347,865)(348,864)(349,863)(350,862)(351,861)(352,860)
(353,859)(354,858)(355,857)(356,856)(357,855)(358,854)(359,853)(360,852)
(361,851)(362,850)(363,849)(364,848)(365,847)(366,846)(367,845)(368,844)
(369,843)(370,842)(371,841)(372,840)(373,901)(374,900)(375,930)(376,929)
(377,928)(378,927)(379,926)(380,925)(381,924)(382,923)(383,922)(384,921)
(385,920)(386,919)(387,918)(388,917)(389,916)(390,915)(391,914)(392,913)
(393,912)(394,911)(395,910)(396,909)(397,908)(398,907)(399,906)(400,905)
(401,904)(402,903)(403,902)(404,870)(405,869)(406,899)(407,898)(408,897)
(409,896)(410,895)(411,894)(412,893)(413,892)(414,891)(415,890)(416,889)
(417,888)(418,887)(419,886)(420,885)(421,884)(422,883)(423,882)(424,881)
(425,880)(426,879)(427,878)(428,877)(429,876)(430,875)(431,874)(432,873)
(433,872)(434,871)(435,963)(436,962)(437,992)(438,991)(439,990)(440,989)
(441,988)(442,987)(443,986)(444,985)(445,984)(446,983)(447,982)(448,981)
(449,980)(450,979)(451,978)(452,977)(453,976)(454,975)(455,974)(456,973)
(457,972)(458,971)(459,970)(460,969)(461,968)(462,967)(463,966)(464,965)
(465,964)(466,932)(467,931)(468,961)(469,960)(470,959)(471,958)(472,957)
(473,956)(474,955)(475,954)(476,953)(477,952)(478,951)(479,950)(480,949)
(481,948)(482,947)(483,946)(484,945)(485,944)(486,943)(487,942)(488,941)
(489,940)(490,939)(491,938)(492,937)(493,936)(494,935)(495,934)(496,933);;
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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(992)!(  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)
(  8,256)(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)
( 16,264)( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)
( 24,272)( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)
( 32,280)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)
( 40,288)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)
( 48,296)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)
( 56,304)( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)
( 64,312)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)
( 80,328)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)
( 96,344)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)
(104,352)(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)
(112,360)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)
(128,376)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)
(136,384)(137,385)(138,386)(139,387)(140,388)(141,389)(142,390)(143,391)
(144,392)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)
(152,400)(153,401)(154,402)(155,403)(156,404)(157,405)(158,406)(159,407)
(160,408)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,417)(170,418)(171,419)(172,420)(173,421)(174,422)(175,423)
(176,424)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)
(184,432)(185,433)(186,434)(187,435)(188,436)(189,437)(190,438)(191,439)
(192,440)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)
(200,448)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)
(208,456)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,465)(218,466)(219,467)(220,468)(221,469)(222,470)(223,471)
(224,472)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)
(232,480)(233,481)(234,482)(235,483)(236,484)(237,485)(238,486)(239,487)
(240,488)(241,489)(242,490)(243,491)(244,492)(245,493)(246,494)(247,495)
(248,496)(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)
(504,752)(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)
(512,760)(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)
(520,768)(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)
(528,776)(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)
(536,784)(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)
(544,792)(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)
(552,800)(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)
(560,808)(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)
(568,816)(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)
(576,824)(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)
(584,832)(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)
(592,840)(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)
(600,848)(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)
(608,856)(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)
(616,864)(617,865)(618,866)(619,867)(620,868)(621,869)(622,870)(623,871)
(624,872)(625,873)(626,874)(627,875)(628,876)(629,877)(630,878)(631,879)
(632,880)(633,881)(634,882)(635,883)(636,884)(637,885)(638,886)(639,887)
(640,888)(641,889)(642,890)(643,891)(644,892)(645,893)(646,894)(647,895)
(648,896)(649,897)(650,898)(651,899)(652,900)(653,901)(654,902)(655,903)
(656,904)(657,905)(658,906)(659,907)(660,908)(661,909)(662,910)(663,911)
(664,912)(665,913)(666,914)(667,915)(668,916)(669,917)(670,918)(671,919)
(672,920)(673,921)(674,922)(675,923)(676,924)(677,925)(678,926)(679,927)
(680,928)(681,929)(682,930)(683,931)(684,932)(685,933)(686,934)(687,935)
(688,936)(689,937)(690,938)(691,939)(692,940)(693,941)(694,942)(695,943)
(696,944)(697,945)(698,946)(699,947)(700,948)(701,949)(702,950)(703,951)
(704,952)(705,953)(706,954)(707,955)(708,956)(709,957)(710,958)(711,959)
(712,960)(713,961)(714,962)(715,963)(716,964)(717,965)(718,966)(719,967)
(720,968)(721,969)(722,970)(723,971)(724,972)(725,973)(726,974)(727,975)
(728,976)(729,977)(730,978)(731,979)(732,980)(733,981)(734,982)(735,983)
(736,984)(737,985)(738,986)(739,987)(740,988)(741,989)(742,990)(743,991)
(744,992);
s1 := Sym(992)!(  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)
(  9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 33, 62)( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)
( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 64, 93)
( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)
( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)
(105,114)(106,113)(107,112)(108,111)(109,110)(125,156)(126,186)(127,185)
(128,184)(129,183)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)
(136,176)(137,175)(138,174)(139,173)(140,172)(141,171)(142,170)(143,169)
(144,168)(145,167)(146,166)(147,165)(148,164)(149,163)(150,162)(151,161)
(152,160)(153,159)(154,158)(155,157)(187,218)(188,248)(189,247)(190,246)
(191,245)(192,244)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)
(199,237)(200,236)(201,235)(202,234)(203,233)(204,232)(205,231)(206,230)
(207,229)(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)
(215,221)(216,220)(217,219)(249,311)(250,341)(251,340)(252,339)(253,338)
(254,337)(255,336)(256,335)(257,334)(258,333)(259,332)(260,331)(261,330)
(262,329)(263,328)(264,327)(265,326)(266,325)(267,324)(268,323)(269,322)
(270,321)(271,320)(272,319)(273,318)(274,317)(275,316)(276,315)(277,314)
(278,313)(279,312)(280,342)(281,372)(282,371)(283,370)(284,369)(285,368)
(286,367)(287,366)(288,365)(289,364)(290,363)(291,362)(292,361)(293,360)
(294,359)(295,358)(296,357)(297,356)(298,355)(299,354)(300,353)(301,352)
(302,351)(303,350)(304,349)(305,348)(306,347)(307,346)(308,345)(309,344)
(310,343)(373,466)(374,496)(375,495)(376,494)(377,493)(378,492)(379,491)
(380,490)(381,489)(382,488)(383,487)(384,486)(385,485)(386,484)(387,483)
(388,482)(389,481)(390,480)(391,479)(392,478)(393,477)(394,476)(395,475)
(396,474)(397,473)(398,472)(399,471)(400,470)(401,469)(402,468)(403,467)
(404,435)(405,465)(406,464)(407,463)(408,462)(409,461)(410,460)(411,459)
(412,458)(413,457)(414,456)(415,455)(416,454)(417,453)(418,452)(419,451)
(420,450)(421,449)(422,448)(423,447)(424,446)(425,445)(426,444)(427,443)
(428,442)(429,441)(430,440)(431,439)(432,438)(433,437)(434,436)(497,621)
(498,651)(499,650)(500,649)(501,648)(502,647)(503,646)(504,645)(505,644)
(506,643)(507,642)(508,641)(509,640)(510,639)(511,638)(512,637)(513,636)
(514,635)(515,634)(516,633)(517,632)(518,631)(519,630)(520,629)(521,628)
(522,627)(523,626)(524,625)(525,624)(526,623)(527,622)(528,652)(529,682)
(530,681)(531,680)(532,679)(533,678)(534,677)(535,676)(536,675)(537,674)
(538,673)(539,672)(540,671)(541,670)(542,669)(543,668)(544,667)(545,666)
(546,665)(547,664)(548,663)(549,662)(550,661)(551,660)(552,659)(553,658)
(554,657)(555,656)(556,655)(557,654)(558,653)(559,683)(560,713)(561,712)
(562,711)(563,710)(564,709)(565,708)(566,707)(567,706)(568,705)(569,704)
(570,703)(571,702)(572,701)(573,700)(574,699)(575,698)(576,697)(577,696)
(578,695)(579,694)(580,693)(581,692)(582,691)(583,690)(584,689)(585,688)
(586,687)(587,686)(588,685)(589,684)(590,714)(591,744)(592,743)(593,742)
(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)(601,734)
(602,733)(603,732)(604,731)(605,730)(606,729)(607,728)(608,727)(609,726)
(610,725)(611,724)(612,723)(613,722)(614,721)(615,720)(616,719)(617,718)
(618,717)(619,716)(620,715)(745,931)(746,961)(747,960)(748,959)(749,958)
(750,957)(751,956)(752,955)(753,954)(754,953)(755,952)(756,951)(757,950)
(758,949)(759,948)(760,947)(761,946)(762,945)(763,944)(764,943)(765,942)
(766,941)(767,940)(768,939)(769,938)(770,937)(771,936)(772,935)(773,934)
(774,933)(775,932)(776,962)(777,992)(778,991)(779,990)(780,989)(781,988)
(782,987)(783,986)(784,985)(785,984)(786,983)(787,982)(788,981)(789,980)
(790,979)(791,978)(792,977)(793,976)(794,975)(795,974)(796,973)(797,972)
(798,971)(799,970)(800,969)(801,968)(802,967)(803,966)(804,965)(805,964)
(806,963)(807,869)(808,899)(809,898)(810,897)(811,896)(812,895)(813,894)
(814,893)(815,892)(816,891)(817,890)(818,889)(819,888)(820,887)(821,886)
(822,885)(823,884)(824,883)(825,882)(826,881)(827,880)(828,879)(829,878)
(830,877)(831,876)(832,875)(833,874)(834,873)(835,872)(836,871)(837,870)
(838,900)(839,930)(840,929)(841,928)(842,927)(843,926)(844,925)(845,924)
(846,923)(847,922)(848,921)(849,920)(850,919)(851,918)(852,917)(853,916)
(854,915)(855,914)(856,913)(857,912)(858,911)(859,910)(860,909)(861,908)
(862,907)(863,906)(864,905)(865,904)(866,903)(867,902)(868,901);
s2 := Sym(992)!(  1,498)(  2,497)(  3,527)(  4,526)(  5,525)(  6,524)(  7,523)
(  8,522)(  9,521)( 10,520)( 11,519)( 12,518)( 13,517)( 14,516)( 15,515)
( 16,514)( 17,513)( 18,512)( 19,511)( 20,510)( 21,509)( 22,508)( 23,507)
( 24,506)( 25,505)( 26,504)( 27,503)( 28,502)( 29,501)( 30,500)( 31,499)
( 32,529)( 33,528)( 34,558)( 35,557)( 36,556)( 37,555)( 38,554)( 39,553)
( 40,552)( 41,551)( 42,550)( 43,549)( 44,548)( 45,547)( 46,546)( 47,545)
( 48,544)( 49,543)( 50,542)( 51,541)( 52,540)( 53,539)( 54,538)( 55,537)
( 56,536)( 57,535)( 58,534)( 59,533)( 60,532)( 61,531)( 62,530)( 63,560)
( 64,559)( 65,589)( 66,588)( 67,587)( 68,586)( 69,585)( 70,584)( 71,583)
( 72,582)( 73,581)( 74,580)( 75,579)( 76,578)( 77,577)( 78,576)( 79,575)
( 80,574)( 81,573)( 82,572)( 83,571)( 84,570)( 85,569)( 86,568)( 87,567)
( 88,566)( 89,565)( 90,564)( 91,563)( 92,562)( 93,561)( 94,591)( 95,590)
( 96,620)( 97,619)( 98,618)( 99,617)(100,616)(101,615)(102,614)(103,613)
(104,612)(105,611)(106,610)(107,609)(108,608)(109,607)(110,606)(111,605)
(112,604)(113,603)(114,602)(115,601)(116,600)(117,599)(118,598)(119,597)
(120,596)(121,595)(122,594)(123,593)(124,592)(125,653)(126,652)(127,682)
(128,681)(129,680)(130,679)(131,678)(132,677)(133,676)(134,675)(135,674)
(136,673)(137,672)(138,671)(139,670)(140,669)(141,668)(142,667)(143,666)
(144,665)(145,664)(146,663)(147,662)(148,661)(149,660)(150,659)(151,658)
(152,657)(153,656)(154,655)(155,654)(156,622)(157,621)(158,651)(159,650)
(160,649)(161,648)(162,647)(163,646)(164,645)(165,644)(166,643)(167,642)
(168,641)(169,640)(170,639)(171,638)(172,637)(173,636)(174,635)(175,634)
(176,633)(177,632)(178,631)(179,630)(180,629)(181,628)(182,627)(183,626)
(184,625)(185,624)(186,623)(187,715)(188,714)(189,744)(190,743)(191,742)
(192,741)(193,740)(194,739)(195,738)(196,737)(197,736)(198,735)(199,734)
(200,733)(201,732)(202,731)(203,730)(204,729)(205,728)(206,727)(207,726)
(208,725)(209,724)(210,723)(211,722)(212,721)(213,720)(214,719)(215,718)
(216,717)(217,716)(218,684)(219,683)(220,713)(221,712)(222,711)(223,710)
(224,709)(225,708)(226,707)(227,706)(228,705)(229,704)(230,703)(231,702)
(232,701)(233,700)(234,699)(235,698)(236,697)(237,696)(238,695)(239,694)
(240,693)(241,692)(242,691)(243,690)(244,689)(245,688)(246,687)(247,686)
(248,685)(249,746)(250,745)(251,775)(252,774)(253,773)(254,772)(255,771)
(256,770)(257,769)(258,768)(259,767)(260,766)(261,765)(262,764)(263,763)
(264,762)(265,761)(266,760)(267,759)(268,758)(269,757)(270,756)(271,755)
(272,754)(273,753)(274,752)(275,751)(276,750)(277,749)(278,748)(279,747)
(280,777)(281,776)(282,806)(283,805)(284,804)(285,803)(286,802)(287,801)
(288,800)(289,799)(290,798)(291,797)(292,796)(293,795)(294,794)(295,793)
(296,792)(297,791)(298,790)(299,789)(300,788)(301,787)(302,786)(303,785)
(304,784)(305,783)(306,782)(307,781)(308,780)(309,779)(310,778)(311,808)
(312,807)(313,837)(314,836)(315,835)(316,834)(317,833)(318,832)(319,831)
(320,830)(321,829)(322,828)(323,827)(324,826)(325,825)(326,824)(327,823)
(328,822)(329,821)(330,820)(331,819)(332,818)(333,817)(334,816)(335,815)
(336,814)(337,813)(338,812)(339,811)(340,810)(341,809)(342,839)(343,838)
(344,868)(345,867)(346,866)(347,865)(348,864)(349,863)(350,862)(351,861)
(352,860)(353,859)(354,858)(355,857)(356,856)(357,855)(358,854)(359,853)
(360,852)(361,851)(362,850)(363,849)(364,848)(365,847)(366,846)(367,845)
(368,844)(369,843)(370,842)(371,841)(372,840)(373,901)(374,900)(375,930)
(376,929)(377,928)(378,927)(379,926)(380,925)(381,924)(382,923)(383,922)
(384,921)(385,920)(386,919)(387,918)(388,917)(389,916)(390,915)(391,914)
(392,913)(393,912)(394,911)(395,910)(396,909)(397,908)(398,907)(399,906)
(400,905)(401,904)(402,903)(403,902)(404,870)(405,869)(406,899)(407,898)
(408,897)(409,896)(410,895)(411,894)(412,893)(413,892)(414,891)(415,890)
(416,889)(417,888)(418,887)(419,886)(420,885)(421,884)(422,883)(423,882)
(424,881)(425,880)(426,879)(427,878)(428,877)(429,876)(430,875)(431,874)
(432,873)(433,872)(434,871)(435,963)(436,962)(437,992)(438,991)(439,990)
(440,989)(441,988)(442,987)(443,986)(444,985)(445,984)(446,983)(447,982)
(448,981)(449,980)(450,979)(451,978)(452,977)(453,976)(454,975)(455,974)
(456,973)(457,972)(458,971)(459,970)(460,969)(461,968)(462,967)(463,966)
(464,965)(465,964)(466,932)(467,931)(468,961)(469,960)(470,959)(471,958)
(472,957)(473,956)(474,955)(475,954)(476,953)(477,952)(478,951)(479,950)
(480,949)(481,948)(482,947)(483,946)(484,945)(485,944)(486,943)(487,942)
(488,941)(489,940)(490,939)(491,938)(492,937)(493,936)(494,935)(495,934)
(496,933);
poly := sub<Sym(992)|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*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*s1*s2*s1*s2 >;

References : None.
to this polytope