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