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