Polytope of Type {8,124}

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

Permutation Representation (Magma) :

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

References : None.
to this polytope