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