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