Polytope of Type {248,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {248,4}*1984a
Also Known As : {248,4|2}. if this polytope has another name.
Group : SmallGroup(1984,685)
Rank : 3
Schlafli Type : {248,4}
Number of vertices, edges, etc : 248, 496, 4
Order of s₀s₁s₂ : 248
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
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 : {124,4}*992, {248,2}*992
   4-fold quotients : {124,2}*496, {62,4}*496
   8-fold quotients : {62,2}*248
   16-fold quotients : {31,2}*124
   31-fold quotients : {8,4}*64a
   62-fold quotients : {4,4}*32, {8,2}*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 := (  1,497)(  2,527)(  3,526)(  4,525)(  5,524)(  6,523)(  7,522)(  8,521)
(  9,520)( 10,519)( 11,518)( 12,517)( 13,516)( 14,515)( 15,514)( 16,513)
( 17,512)( 18,511)( 19,510)( 20,509)( 21,508)( 22,507)( 23,506)( 24,505)
( 25,504)( 26,503)( 27,502)( 28,501)( 29,500)( 30,499)( 31,498)( 32,528)
( 33,558)( 34,557)( 35,556)( 36,555)( 37,554)( 38,553)( 39,552)( 40,551)
( 41,550)( 42,549)( 43,548)( 44,547)( 45,546)( 46,545)( 47,544)( 48,543)
( 49,542)( 50,541)( 51,540)( 52,539)( 53,538)( 54,537)( 55,536)( 56,535)
( 57,534)( 58,533)( 59,532)( 60,531)( 61,530)( 62,529)( 63,559)( 64,589)
( 65,588)( 66,587)( 67,586)( 68,585)( 69,584)( 70,583)( 71,582)( 72,581)
( 73,580)( 74,579)( 75,578)( 76,577)( 77,576)( 78,575)( 79,574)( 80,573)
( 81,572)( 82,571)( 83,570)( 84,569)( 85,568)( 86,567)( 87,566)( 88,565)
( 89,564)( 90,563)( 91,562)( 92,561)( 93,560)( 94,590)( 95,620)( 96,619)
( 97,618)( 98,617)( 99,616)(100,615)(101,614)(102,613)(103,612)(104,611)
(105,610)(106,609)(107,608)(108,607)(109,606)(110,605)(111,604)(112,603)
(113,602)(114,601)(115,600)(116,599)(117,598)(118,597)(119,596)(120,595)
(121,594)(122,593)(123,592)(124,591)(125,652)(126,682)(127,681)(128,680)
(129,679)(130,678)(131,677)(132,676)(133,675)(134,674)(135,673)(136,672)
(137,671)(138,670)(139,669)(140,668)(141,667)(142,666)(143,665)(144,664)
(145,663)(146,662)(147,661)(148,660)(149,659)(150,658)(151,657)(152,656)
(153,655)(154,654)(155,653)(156,621)(157,651)(158,650)(159,649)(160,648)
(161,647)(162,646)(163,645)(164,644)(165,643)(166,642)(167,641)(168,640)
(169,639)(170,638)(171,637)(172,636)(173,635)(174,634)(175,633)(176,632)
(177,631)(178,630)(179,629)(180,628)(181,627)(182,626)(183,625)(184,624)
(185,623)(186,622)(187,714)(188,744)(189,743)(190,742)(191,741)(192,740)
(193,739)(194,738)(195,737)(196,736)(197,735)(198,734)(199,733)(200,732)
(201,731)(202,730)(203,729)(204,728)(205,727)(206,726)(207,725)(208,724)
(209,723)(210,722)(211,721)(212,720)(213,719)(214,718)(215,717)(216,716)
(217,715)(218,683)(219,713)(220,712)(221,711)(222,710)(223,709)(224,708)
(225,707)(226,706)(227,705)(228,704)(229,703)(230,702)(231,701)(232,700)
(233,699)(234,698)(235,697)(236,696)(237,695)(238,694)(239,693)(240,692)
(241,691)(242,690)(243,689)(244,688)(245,687)(246,686)(247,685)(248,684)
(249,745)(250,775)(251,774)(252,773)(253,772)(254,771)(255,770)(256,769)
(257,768)(258,767)(259,766)(260,765)(261,764)(262,763)(263,762)(264,761)
(265,760)(266,759)(267,758)(268,757)(269,756)(270,755)(271,754)(272,753)
(273,752)(274,751)(275,750)(276,749)(277,748)(278,747)(279,746)(280,776)
(281,806)(282,805)(283,804)(284,803)(285,802)(286,801)(287,800)(288,799)
(289,798)(290,797)(291,796)(292,795)(293,794)(294,793)(295,792)(296,791)
(297,790)(298,789)(299,788)(300,787)(301,786)(302,785)(303,784)(304,783)
(305,782)(306,781)(307,780)(308,779)(309,778)(310,777)(311,807)(312,837)
(313,836)(314,835)(315,834)(316,833)(317,832)(318,831)(319,830)(320,829)
(321,828)(322,827)(323,826)(324,825)(325,824)(326,823)(327,822)(328,821)
(329,820)(330,819)(331,818)(332,817)(333,816)(334,815)(335,814)(336,813)
(337,812)(338,811)(339,810)(340,809)(341,808)(342,838)(343,868)(344,867)
(345,866)(346,865)(347,864)(348,863)(349,862)(350,861)(351,860)(352,859)
(353,858)(354,857)(355,856)(356,855)(357,854)(358,853)(359,852)(360,851)
(361,850)(362,849)(363,848)(364,847)(365,846)(366,845)(367,844)(368,843)
(369,842)(370,841)(371,840)(372,839)(373,900)(374,930)(375,929)(376,928)
(377,927)(378,926)(379,925)(380,924)(381,923)(382,922)(383,921)(384,920)
(385,919)(386,918)(387,917)(388,916)(389,915)(390,914)(391,913)(392,912)
(393,911)(394,910)(395,909)(396,908)(397,907)(398,906)(399,905)(400,904)
(401,903)(402,902)(403,901)(404,869)(405,899)(406,898)(407,897)(408,896)
(409,895)(410,894)(411,893)(412,892)(413,891)(414,890)(415,889)(416,888)
(417,887)(418,886)(419,885)(420,884)(421,883)(422,882)(423,881)(424,880)
(425,879)(426,878)(427,877)(428,876)(429,875)(430,874)(431,873)(432,872)
(433,871)(434,870)(435,962)(436,992)(437,991)(438,990)(439,989)(440,988)
(441,987)(442,986)(443,985)(444,984)(445,983)(446,982)(447,981)(448,980)
(449,979)(450,978)(451,977)(452,976)(453,975)(454,974)(455,973)(456,972)
(457,971)(458,970)(459,969)(460,968)(461,967)(462,966)(463,965)(464,964)
(465,963)(466,931)(467,961)(468,960)(469,959)(470,958)(471,957)(472,956)
(473,955)(474,954)(475,953)(476,952)(477,951)(478,950)(479,949)(480,948)
(481,947)(482,946)(483,945)(484,944)(485,943)(486,942)(487,941)(488,940)
(489,939)(490,938)(491,937)(492,936)(493,935)(494,934)(495,933)(496,932);;
s1 := (  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)
( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)
( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)
( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)
( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)
( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)
( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)
(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)(127,186)(128,185)
(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)(136,177)
(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)(144,169)
(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)
(153,160)(154,159)(155,158)(187,219)(188,218)(189,248)(190,247)(191,246)
(192,245)(193,244)(194,243)(195,242)(196,241)(197,240)(198,239)(199,238)
(200,237)(201,236)(202,235)(203,234)(204,233)(205,232)(206,231)(207,230)
(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)(215,222)
(216,221)(217,220)(249,312)(250,311)(251,341)(252,340)(253,339)(254,338)
(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)
(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)(270,322)
(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)
(279,313)(280,343)(281,342)(282,372)(283,371)(284,370)(285,369)(286,368)
(287,367)(288,366)(289,365)(290,364)(291,363)(292,362)(293,361)(294,360)
(295,359)(296,358)(297,357)(298,356)(299,355)(300,354)(301,353)(302,352)
(303,351)(304,350)(305,349)(306,348)(307,347)(308,346)(309,345)(310,344)
(373,467)(374,466)(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)
(381,490)(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)
(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)
(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,436)
(405,435)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)
(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)
(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)
(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(497,622)(498,621)
(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)(506,644)
(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)(514,636)
(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)(522,628)
(523,627)(524,626)(525,625)(526,624)(527,623)(528,653)(529,652)(530,682)
(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)
(539,673)(540,672)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)
(547,665)(548,664)(549,663)(550,662)(551,661)(552,660)(553,659)(554,658)
(555,657)(556,656)(557,655)(558,654)(559,684)(560,683)(561,713)(562,712)
(563,711)(564,710)(565,709)(566,708)(567,707)(568,706)(569,705)(570,704)
(571,703)(572,702)(573,701)(574,700)(575,699)(576,698)(577,697)(578,696)
(579,695)(580,694)(581,693)(582,692)(583,691)(584,690)(585,689)(586,688)
(587,687)(588,686)(589,685)(590,715)(591,714)(592,744)(593,743)(594,742)
(595,741)(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)(602,734)
(603,733)(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)(610,726)
(611,725)(612,724)(613,723)(614,722)(615,721)(616,720)(617,719)(618,718)
(619,717)(620,716)(745,932)(746,931)(747,961)(748,960)(749,959)(750,958)
(751,957)(752,956)(753,955)(754,954)(755,953)(756,952)(757,951)(758,950)
(759,949)(760,948)(761,947)(762,946)(763,945)(764,944)(765,943)(766,942)
(767,941)(768,940)(769,939)(770,938)(771,937)(772,936)(773,935)(774,934)
(775,933)(776,963)(777,962)(778,992)(779,991)(780,990)(781,989)(782,988)
(783,987)(784,986)(785,985)(786,984)(787,983)(788,982)(789,981)(790,980)
(791,979)(792,978)(793,977)(794,976)(795,975)(796,974)(797,973)(798,972)
(799,971)(800,970)(801,969)(802,968)(803,967)(804,966)(805,965)(806,964)
(807,870)(808,869)(809,899)(810,898)(811,897)(812,896)(813,895)(814,894)
(815,893)(816,892)(817,891)(818,890)(819,889)(820,888)(821,887)(822,886)
(823,885)(824,884)(825,883)(826,882)(827,881)(828,880)(829,879)(830,878)
(831,877)(832,876)(833,875)(834,874)(835,873)(836,872)(837,871)(838,901)
(839,900)(840,930)(841,929)(842,928)(843,927)(844,926)(845,925)(846,924)
(847,923)(848,922)(849,921)(850,920)(851,919)(852,918)(853,917)(854,916)
(855,915)(856,914)(857,913)(858,912)(859,911)(860,910)(861,909)(862,908)
(863,907)(864,906)(865,905)(866,904)(867,903)(868,902);;
s2 := (  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);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(992)!(  1,497)(  2,527)(  3,526)(  4,525)(  5,524)(  6,523)(  7,522)
(  8,521)(  9,520)( 10,519)( 11,518)( 12,517)( 13,516)( 14,515)( 15,514)
( 16,513)( 17,512)( 18,511)( 19,510)( 20,509)( 21,508)( 22,507)( 23,506)
( 24,505)( 25,504)( 26,503)( 27,502)( 28,501)( 29,500)( 30,499)( 31,498)
( 32,528)( 33,558)( 34,557)( 35,556)( 36,555)( 37,554)( 38,553)( 39,552)
( 40,551)( 41,550)( 42,549)( 43,548)( 44,547)( 45,546)( 46,545)( 47,544)
( 48,543)( 49,542)( 50,541)( 51,540)( 52,539)( 53,538)( 54,537)( 55,536)
( 56,535)( 57,534)( 58,533)( 59,532)( 60,531)( 61,530)( 62,529)( 63,559)
( 64,589)( 65,588)( 66,587)( 67,586)( 68,585)( 69,584)( 70,583)( 71,582)
( 72,581)( 73,580)( 74,579)( 75,578)( 76,577)( 77,576)( 78,575)( 79,574)
( 80,573)( 81,572)( 82,571)( 83,570)( 84,569)( 85,568)( 86,567)( 87,566)
( 88,565)( 89,564)( 90,563)( 91,562)( 92,561)( 93,560)( 94,590)( 95,620)
( 96,619)( 97,618)( 98,617)( 99,616)(100,615)(101,614)(102,613)(103,612)
(104,611)(105,610)(106,609)(107,608)(108,607)(109,606)(110,605)(111,604)
(112,603)(113,602)(114,601)(115,600)(116,599)(117,598)(118,597)(119,596)
(120,595)(121,594)(122,593)(123,592)(124,591)(125,652)(126,682)(127,681)
(128,680)(129,679)(130,678)(131,677)(132,676)(133,675)(134,674)(135,673)
(136,672)(137,671)(138,670)(139,669)(140,668)(141,667)(142,666)(143,665)
(144,664)(145,663)(146,662)(147,661)(148,660)(149,659)(150,658)(151,657)
(152,656)(153,655)(154,654)(155,653)(156,621)(157,651)(158,650)(159,649)
(160,648)(161,647)(162,646)(163,645)(164,644)(165,643)(166,642)(167,641)
(168,640)(169,639)(170,638)(171,637)(172,636)(173,635)(174,634)(175,633)
(176,632)(177,631)(178,630)(179,629)(180,628)(181,627)(182,626)(183,625)
(184,624)(185,623)(186,622)(187,714)(188,744)(189,743)(190,742)(191,741)
(192,740)(193,739)(194,738)(195,737)(196,736)(197,735)(198,734)(199,733)
(200,732)(201,731)(202,730)(203,729)(204,728)(205,727)(206,726)(207,725)
(208,724)(209,723)(210,722)(211,721)(212,720)(213,719)(214,718)(215,717)
(216,716)(217,715)(218,683)(219,713)(220,712)(221,711)(222,710)(223,709)
(224,708)(225,707)(226,706)(227,705)(228,704)(229,703)(230,702)(231,701)
(232,700)(233,699)(234,698)(235,697)(236,696)(237,695)(238,694)(239,693)
(240,692)(241,691)(242,690)(243,689)(244,688)(245,687)(246,686)(247,685)
(248,684)(249,745)(250,775)(251,774)(252,773)(253,772)(254,771)(255,770)
(256,769)(257,768)(258,767)(259,766)(260,765)(261,764)(262,763)(263,762)
(264,761)(265,760)(266,759)(267,758)(268,757)(269,756)(270,755)(271,754)
(272,753)(273,752)(274,751)(275,750)(276,749)(277,748)(278,747)(279,746)
(280,776)(281,806)(282,805)(283,804)(284,803)(285,802)(286,801)(287,800)
(288,799)(289,798)(290,797)(291,796)(292,795)(293,794)(294,793)(295,792)
(296,791)(297,790)(298,789)(299,788)(300,787)(301,786)(302,785)(303,784)
(304,783)(305,782)(306,781)(307,780)(308,779)(309,778)(310,777)(311,807)
(312,837)(313,836)(314,835)(315,834)(316,833)(317,832)(318,831)(319,830)
(320,829)(321,828)(322,827)(323,826)(324,825)(325,824)(326,823)(327,822)
(328,821)(329,820)(330,819)(331,818)(332,817)(333,816)(334,815)(335,814)
(336,813)(337,812)(338,811)(339,810)(340,809)(341,808)(342,838)(343,868)
(344,867)(345,866)(346,865)(347,864)(348,863)(349,862)(350,861)(351,860)
(352,859)(353,858)(354,857)(355,856)(356,855)(357,854)(358,853)(359,852)
(360,851)(361,850)(362,849)(363,848)(364,847)(365,846)(366,845)(367,844)
(368,843)(369,842)(370,841)(371,840)(372,839)(373,900)(374,930)(375,929)
(376,928)(377,927)(378,926)(379,925)(380,924)(381,923)(382,922)(383,921)
(384,920)(385,919)(386,918)(387,917)(388,916)(389,915)(390,914)(391,913)
(392,912)(393,911)(394,910)(395,909)(396,908)(397,907)(398,906)(399,905)
(400,904)(401,903)(402,902)(403,901)(404,869)(405,899)(406,898)(407,897)
(408,896)(409,895)(410,894)(411,893)(412,892)(413,891)(414,890)(415,889)
(416,888)(417,887)(418,886)(419,885)(420,884)(421,883)(422,882)(423,881)
(424,880)(425,879)(426,878)(427,877)(428,876)(429,875)(430,874)(431,873)
(432,872)(433,871)(434,870)(435,962)(436,992)(437,991)(438,990)(439,989)
(440,988)(441,987)(442,986)(443,985)(444,984)(445,983)(446,982)(447,981)
(448,980)(449,979)(450,978)(451,977)(452,976)(453,975)(454,974)(455,973)
(456,972)(457,971)(458,970)(459,969)(460,968)(461,967)(462,966)(463,965)
(464,964)(465,963)(466,931)(467,961)(468,960)(469,959)(470,958)(471,957)
(472,956)(473,955)(474,954)(475,953)(476,952)(477,951)(478,950)(479,949)
(480,948)(481,947)(482,946)(483,945)(484,944)(485,943)(486,942)(487,941)
(488,940)(489,939)(490,938)(491,937)(492,936)(493,935)(494,934)(495,933)
(496,932);
s1 := Sym(992)!(  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)
(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)
( 32, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)
( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)
( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)
( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)
( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)
(105,115)(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)(127,186)
(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)
(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)
(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)
(152,161)(153,160)(154,159)(155,158)(187,219)(188,218)(189,248)(190,247)
(191,246)(192,245)(193,244)(194,243)(195,242)(196,241)(197,240)(198,239)
(199,238)(200,237)(201,236)(202,235)(203,234)(204,233)(205,232)(206,231)
(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)
(215,222)(216,221)(217,220)(249,312)(250,311)(251,341)(252,340)(253,339)
(254,338)(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)
(262,330)(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)
(270,322)(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)
(278,314)(279,313)(280,343)(281,342)(282,372)(283,371)(284,370)(285,369)
(286,368)(287,367)(288,366)(289,365)(290,364)(291,363)(292,362)(293,361)
(294,360)(295,359)(296,358)(297,357)(298,356)(299,355)(300,354)(301,353)
(302,352)(303,351)(304,350)(305,349)(306,348)(307,347)(308,346)(309,345)
(310,344)(373,467)(374,466)(375,496)(376,495)(377,494)(378,493)(379,492)
(380,491)(381,490)(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)
(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)
(396,475)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)
(404,436)(405,435)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)
(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)
(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)
(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(497,622)
(498,621)(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)
(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)
(514,636)(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)
(522,628)(523,627)(524,626)(525,625)(526,624)(527,623)(528,653)(529,652)
(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)
(538,674)(539,673)(540,672)(541,671)(542,670)(543,669)(544,668)(545,667)
(546,666)(547,665)(548,664)(549,663)(550,662)(551,661)(552,660)(553,659)
(554,658)(555,657)(556,656)(557,655)(558,654)(559,684)(560,683)(561,713)
(562,712)(563,711)(564,710)(565,709)(566,708)(567,707)(568,706)(569,705)
(570,704)(571,703)(572,702)(573,701)(574,700)(575,699)(576,698)(577,697)
(578,696)(579,695)(580,694)(581,693)(582,692)(583,691)(584,690)(585,689)
(586,688)(587,687)(588,686)(589,685)(590,715)(591,714)(592,744)(593,743)
(594,742)(595,741)(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)
(602,734)(603,733)(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)
(610,726)(611,725)(612,724)(613,723)(614,722)(615,721)(616,720)(617,719)
(618,718)(619,717)(620,716)(745,932)(746,931)(747,961)(748,960)(749,959)
(750,958)(751,957)(752,956)(753,955)(754,954)(755,953)(756,952)(757,951)
(758,950)(759,949)(760,948)(761,947)(762,946)(763,945)(764,944)(765,943)
(766,942)(767,941)(768,940)(769,939)(770,938)(771,937)(772,936)(773,935)
(774,934)(775,933)(776,963)(777,962)(778,992)(779,991)(780,990)(781,989)
(782,988)(783,987)(784,986)(785,985)(786,984)(787,983)(788,982)(789,981)
(790,980)(791,979)(792,978)(793,977)(794,976)(795,975)(796,974)(797,973)
(798,972)(799,971)(800,970)(801,969)(802,968)(803,967)(804,966)(805,965)
(806,964)(807,870)(808,869)(809,899)(810,898)(811,897)(812,896)(813,895)
(814,894)(815,893)(816,892)(817,891)(818,890)(819,889)(820,888)(821,887)
(822,886)(823,885)(824,884)(825,883)(826,882)(827,881)(828,880)(829,879)
(830,878)(831,877)(832,876)(833,875)(834,874)(835,873)(836,872)(837,871)
(838,901)(839,900)(840,930)(841,929)(842,928)(843,927)(844,926)(845,925)
(846,924)(847,923)(848,922)(849,921)(850,920)(851,919)(852,918)(853,917)
(854,916)(855,915)(856,914)(857,913)(858,912)(859,911)(860,910)(861,909)
(862,908)(863,907)(864,906)(865,905)(866,904)(867,903)(868,902);
s2 := 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);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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