Polytope of Type {24,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,40}*1920c
if this polytope has a name.
Group : SmallGroup(1920,14538)
Rank : 3
Schlafli Type : {24,40}
Number of vertices, edges, etc : 24, 480, 40
Order of s0s1s2 : 120
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 : {12,40}*960a, {24,20}*960b
3-fold quotients : {8,40}*640a
4-fold quotients : {6,40}*480, {12,20}*480
5-fold quotients : {24,8}*384d
6-fold quotients : {4,40}*320a, {8,20}*320b
8-fold quotients : {12,10}*240, {6,20}*240a
10-fold quotients : {24,4}*192b, {12,8}*192a
12-fold quotients : {4,20}*160, {2,40}*160
15-fold quotients : {8,8}*128a
16-fold quotients : {6,10}*120
20-fold quotients : {12,4}*96a, {6,8}*96
24-fold quotients : {2,20}*80, {4,10}*80
30-fold quotients : {4,8}*64a, {8,4}*64b
40-fold quotients : {12,2}*48, {6,4}*48a
48-fold quotients : {2,10}*40
60-fold quotients : {4,4}*32, {2,8}*32
80-fold quotients : {6,2}*24
96-fold quotients : {2,5}*20
120-fold quotients : {2,4}*16, {4,2}*16
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,721)( 2,722)( 3,723)( 4,724)( 5,725)( 6,731)( 7,732)( 8,733)
( 9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)( 16,736)
( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)( 24,749)
( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,751)( 32,752)
( 33,753)( 34,754)( 35,755)( 36,761)( 37,762)( 38,763)( 39,764)( 40,765)
( 41,756)( 42,757)( 43,758)( 44,759)( 45,760)( 46,766)( 47,767)( 48,768)
( 49,769)( 50,770)( 51,776)( 52,777)( 53,778)( 54,779)( 55,780)( 56,771)
( 57,772)( 58,773)( 59,774)( 60,775)( 61,781)( 62,782)( 63,783)( 64,784)
( 65,785)( 66,791)( 67,792)( 68,793)( 69,794)( 70,795)( 71,786)( 72,787)
( 73,788)( 74,789)( 75,790)( 76,796)( 77,797)( 78,798)( 79,799)( 80,800)
( 81,806)( 82,807)( 83,808)( 84,809)( 85,810)( 86,801)( 87,802)( 88,803)
( 89,804)( 90,805)( 91,811)( 92,812)( 93,813)( 94,814)( 95,815)( 96,821)
( 97,822)( 98,823)( 99,824)(100,825)(101,816)(102,817)(103,818)(104,819)
(105,820)(106,826)(107,827)(108,828)(109,829)(110,830)(111,836)(112,837)
(113,838)(114,839)(115,840)(116,831)(117,832)(118,833)(119,834)(120,835)
(121,886)(122,887)(123,888)(124,889)(125,890)(126,896)(127,897)(128,898)
(129,899)(130,900)(131,891)(132,892)(133,893)(134,894)(135,895)(136,871)
(137,872)(138,873)(139,874)(140,875)(141,881)(142,882)(143,883)(144,884)
(145,885)(146,876)(147,877)(148,878)(149,879)(150,880)(151,856)(152,857)
(153,858)(154,859)(155,860)(156,866)(157,867)(158,868)(159,869)(160,870)
(161,861)(162,862)(163,863)(164,864)(165,865)(166,841)(167,842)(168,843)
(169,844)(170,845)(171,851)(172,852)(173,853)(174,854)(175,855)(176,846)
(177,847)(178,848)(179,849)(180,850)(181,946)(182,947)(183,948)(184,949)
(185,950)(186,956)(187,957)(188,958)(189,959)(190,960)(191,951)(192,952)
(193,953)(194,954)(195,955)(196,931)(197,932)(198,933)(199,934)(200,935)
(201,941)(202,942)(203,943)(204,944)(205,945)(206,936)(207,937)(208,938)
(209,939)(210,940)(211,916)(212,917)(213,918)(214,919)(215,920)(216,926)
(217,927)(218,928)(219,929)(220,930)(221,921)(222,922)(223,923)(224,924)
(225,925)(226,901)(227,902)(228,903)(229,904)(230,905)(231,911)(232,912)
(233,913)(234,914)(235,915)(236,906)(237,907)(238,908)(239,909)(240,910)
(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)(248,493)
(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)(256,496)
(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)(264,509)
(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,511)(272,512)
(273,513)(274,514)(275,515)(276,521)(277,522)(278,523)(279,524)(280,525)
(281,516)(282,517)(283,518)(284,519)(285,520)(286,526)(287,527)(288,528)
(289,529)(290,530)(291,536)(292,537)(293,538)(294,539)(295,540)(296,531)
(297,532)(298,533)(299,534)(300,535)(301,541)(302,542)(303,543)(304,544)
(305,545)(306,551)(307,552)(308,553)(309,554)(310,555)(311,546)(312,547)
(313,548)(314,549)(315,550)(316,556)(317,557)(318,558)(319,559)(320,560)
(321,566)(322,567)(323,568)(324,569)(325,570)(326,561)(327,562)(328,563)
(329,564)(330,565)(331,571)(332,572)(333,573)(334,574)(335,575)(336,581)
(337,582)(338,583)(339,584)(340,585)(341,576)(342,577)(343,578)(344,579)
(345,580)(346,586)(347,587)(348,588)(349,589)(350,590)(351,596)(352,597)
(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)(360,595)
(361,646)(362,647)(363,648)(364,649)(365,650)(366,656)(367,657)(368,658)
(369,659)(370,660)(371,651)(372,652)(373,653)(374,654)(375,655)(376,631)
(377,632)(378,633)(379,634)(380,635)(381,641)(382,642)(383,643)(384,644)
(385,645)(386,636)(387,637)(388,638)(389,639)(390,640)(391,616)(392,617)
(393,618)(394,619)(395,620)(396,626)(397,627)(398,628)(399,629)(400,630)
(401,621)(402,622)(403,623)(404,624)(405,625)(406,601)(407,602)(408,603)
(409,604)(410,605)(411,611)(412,612)(413,613)(414,614)(415,615)(416,606)
(417,607)(418,608)(419,609)(420,610)(421,706)(422,707)(423,708)(424,709)
(425,710)(426,716)(427,717)(428,718)(429,719)(430,720)(431,711)(432,712)
(433,713)(434,714)(435,715)(436,691)(437,692)(438,693)(439,694)(440,695)
(441,701)(442,702)(443,703)(444,704)(445,705)(446,696)(447,697)(448,698)
(449,699)(450,700)(451,676)(452,677)(453,678)(454,679)(455,680)(456,686)
(457,687)(458,688)(459,689)(460,690)(461,681)(462,682)(463,683)(464,684)
(465,685)(466,661)(467,662)(468,663)(469,664)(470,665)(471,671)(472,672)
(473,673)(474,674)(475,675)(476,666)(477,667)(478,668)(479,669)(480,670);;
s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61, 81)( 62, 85)( 63, 84)( 64, 83)
( 65, 82)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 86)( 72, 90)
( 73, 89)( 74, 88)( 75, 87)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)
( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)
(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)(134,163)
(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)
(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)(150,177)
(181,231)(182,235)(183,234)(184,233)(185,232)(186,226)(187,230)(188,229)
(189,228)(190,227)(191,236)(192,240)(193,239)(194,238)(195,237)(196,216)
(197,220)(198,219)(199,218)(200,217)(201,211)(202,215)(203,214)(204,213)
(205,212)(206,221)(207,225)(208,224)(209,223)(210,222)(241,306)(242,310)
(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)
(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)(258,324)
(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)(266,326)
(267,330)(268,329)(269,328)(270,327)(271,336)(272,340)(273,339)(274,338)
(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)(281,341)(282,345)
(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)(289,353)(290,352)
(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)(297,360)(298,359)
(299,358)(300,357)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)
(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)(374,463)
(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)(382,470)
(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)(390,477)
(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)(398,424)
(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)(406,441)
(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)(414,438)
(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)(482,610)
(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)(490,602)
(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)(498,624)
(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)(506,626)
(507,630)(508,629)(509,628)(510,627)(511,636)(512,640)(513,639)(514,638)
(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)(521,641)(522,645)
(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)(529,653)(530,652)
(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)(537,660)(538,659)
(539,658)(540,657)(541,681)(542,685)(543,684)(544,683)(545,682)(546,676)
(547,680)(548,679)(549,678)(550,677)(551,686)(552,690)(553,689)(554,688)
(555,687)(556,666)(557,670)(558,669)(559,668)(560,667)(561,661)(562,665)
(563,664)(564,663)(565,662)(566,671)(567,675)(568,674)(569,673)(570,672)
(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)(578,709)
(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)(586,696)
(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)(594,693)
(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,921)(722,925)
(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)(730,917)
(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)(738,909)
(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)(746,911)
(747,915)(748,914)(749,913)(750,912)(751,951)(752,955)(753,954)(754,953)
(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)(762,960)
(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)(770,937)
(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)(778,944)
(779,943)(780,942)(781,861)(782,865)(783,864)(784,863)(785,862)(786,856)
(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)(794,868)
(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)(802,845)
(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)(810,852)
(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)(818,889)
(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)(826,876)
(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)(834,873)
(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);;
s2 := ( 1,482)( 2,481)( 3,485)( 4,484)( 5,483)( 6,487)( 7,486)( 8,490)
( 9,489)( 10,488)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)( 16,497)
( 17,496)( 18,500)( 19,499)( 20,498)( 21,502)( 22,501)( 23,505)( 24,504)
( 25,503)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,512)( 32,511)
( 33,515)( 34,514)( 35,513)( 36,517)( 37,516)( 38,520)( 39,519)( 40,518)
( 41,522)( 42,521)( 43,525)( 44,524)( 45,523)( 46,527)( 47,526)( 48,530)
( 49,529)( 50,528)( 51,532)( 52,531)( 53,535)( 54,534)( 55,533)( 56,537)
( 57,536)( 58,540)( 59,539)( 60,538)( 61,557)( 62,556)( 63,560)( 64,559)
( 65,558)( 66,562)( 67,561)( 68,565)( 69,564)( 70,563)( 71,567)( 72,566)
( 73,570)( 74,569)( 75,568)( 76,542)( 77,541)( 78,545)( 79,544)( 80,543)
( 81,547)( 82,546)( 83,550)( 84,549)( 85,548)( 86,552)( 87,551)( 88,555)
( 89,554)( 90,553)( 91,587)( 92,586)( 93,590)( 94,589)( 95,588)( 96,592)
( 97,591)( 98,595)( 99,594)(100,593)(101,597)(102,596)(103,600)(104,599)
(105,598)(106,572)(107,571)(108,575)(109,574)(110,573)(111,577)(112,576)
(113,580)(114,579)(115,578)(116,582)(117,581)(118,585)(119,584)(120,583)
(121,632)(122,631)(123,635)(124,634)(125,633)(126,637)(127,636)(128,640)
(129,639)(130,638)(131,642)(132,641)(133,645)(134,644)(135,643)(136,647)
(137,646)(138,650)(139,649)(140,648)(141,652)(142,651)(143,655)(144,654)
(145,653)(146,657)(147,656)(148,660)(149,659)(150,658)(151,602)(152,601)
(153,605)(154,604)(155,603)(156,607)(157,606)(158,610)(159,609)(160,608)
(161,612)(162,611)(163,615)(164,614)(165,613)(166,617)(167,616)(168,620)
(169,619)(170,618)(171,622)(172,621)(173,625)(174,624)(175,623)(176,627)
(177,626)(178,630)(179,629)(180,628)(181,707)(182,706)(183,710)(184,709)
(185,708)(186,712)(187,711)(188,715)(189,714)(190,713)(191,717)(192,716)
(193,720)(194,719)(195,718)(196,692)(197,691)(198,695)(199,694)(200,693)
(201,697)(202,696)(203,700)(204,699)(205,698)(206,702)(207,701)(208,705)
(209,704)(210,703)(211,677)(212,676)(213,680)(214,679)(215,678)(216,682)
(217,681)(218,685)(219,684)(220,683)(221,687)(222,686)(223,690)(224,689)
(225,688)(226,662)(227,661)(228,665)(229,664)(230,663)(231,667)(232,666)
(233,670)(234,669)(235,668)(236,672)(237,671)(238,675)(239,674)(240,673)
(241,722)(242,721)(243,725)(244,724)(245,723)(246,727)(247,726)(248,730)
(249,729)(250,728)(251,732)(252,731)(253,735)(254,734)(255,733)(256,737)
(257,736)(258,740)(259,739)(260,738)(261,742)(262,741)(263,745)(264,744)
(265,743)(266,747)(267,746)(268,750)(269,749)(270,748)(271,752)(272,751)
(273,755)(274,754)(275,753)(276,757)(277,756)(278,760)(279,759)(280,758)
(281,762)(282,761)(283,765)(284,764)(285,763)(286,767)(287,766)(288,770)
(289,769)(290,768)(291,772)(292,771)(293,775)(294,774)(295,773)(296,777)
(297,776)(298,780)(299,779)(300,778)(301,797)(302,796)(303,800)(304,799)
(305,798)(306,802)(307,801)(308,805)(309,804)(310,803)(311,807)(312,806)
(313,810)(314,809)(315,808)(316,782)(317,781)(318,785)(319,784)(320,783)
(321,787)(322,786)(323,790)(324,789)(325,788)(326,792)(327,791)(328,795)
(329,794)(330,793)(331,827)(332,826)(333,830)(334,829)(335,828)(336,832)
(337,831)(338,835)(339,834)(340,833)(341,837)(342,836)(343,840)(344,839)
(345,838)(346,812)(347,811)(348,815)(349,814)(350,813)(351,817)(352,816)
(353,820)(354,819)(355,818)(356,822)(357,821)(358,825)(359,824)(360,823)
(361,872)(362,871)(363,875)(364,874)(365,873)(366,877)(367,876)(368,880)
(369,879)(370,878)(371,882)(372,881)(373,885)(374,884)(375,883)(376,887)
(377,886)(378,890)(379,889)(380,888)(381,892)(382,891)(383,895)(384,894)
(385,893)(386,897)(387,896)(388,900)(389,899)(390,898)(391,842)(392,841)
(393,845)(394,844)(395,843)(396,847)(397,846)(398,850)(399,849)(400,848)
(401,852)(402,851)(403,855)(404,854)(405,853)(406,857)(407,856)(408,860)
(409,859)(410,858)(411,862)(412,861)(413,865)(414,864)(415,863)(416,867)
(417,866)(418,870)(419,869)(420,868)(421,947)(422,946)(423,950)(424,949)
(425,948)(426,952)(427,951)(428,955)(429,954)(430,953)(431,957)(432,956)
(433,960)(434,959)(435,958)(436,932)(437,931)(438,935)(439,934)(440,933)
(441,937)(442,936)(443,940)(444,939)(445,938)(446,942)(447,941)(448,945)
(449,944)(450,943)(451,917)(452,916)(453,920)(454,919)(455,918)(456,922)
(457,921)(458,925)(459,924)(460,923)(461,927)(462,926)(463,930)(464,929)
(465,928)(466,902)(467,901)(468,905)(469,904)(470,903)(471,907)(472,906)
(473,910)(474,909)(475,908)(476,912)(477,911)(478,915)(479,914)(480,913);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(960)!( 1,721)( 2,722)( 3,723)( 4,724)( 5,725)( 6,731)( 7,732)
( 8,733)( 9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)
( 16,736)( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)
( 24,749)( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,751)
( 32,752)( 33,753)( 34,754)( 35,755)( 36,761)( 37,762)( 38,763)( 39,764)
( 40,765)( 41,756)( 42,757)( 43,758)( 44,759)( 45,760)( 46,766)( 47,767)
( 48,768)( 49,769)( 50,770)( 51,776)( 52,777)( 53,778)( 54,779)( 55,780)
( 56,771)( 57,772)( 58,773)( 59,774)( 60,775)( 61,781)( 62,782)( 63,783)
( 64,784)( 65,785)( 66,791)( 67,792)( 68,793)( 69,794)( 70,795)( 71,786)
( 72,787)( 73,788)( 74,789)( 75,790)( 76,796)( 77,797)( 78,798)( 79,799)
( 80,800)( 81,806)( 82,807)( 83,808)( 84,809)( 85,810)( 86,801)( 87,802)
( 88,803)( 89,804)( 90,805)( 91,811)( 92,812)( 93,813)( 94,814)( 95,815)
( 96,821)( 97,822)( 98,823)( 99,824)(100,825)(101,816)(102,817)(103,818)
(104,819)(105,820)(106,826)(107,827)(108,828)(109,829)(110,830)(111,836)
(112,837)(113,838)(114,839)(115,840)(116,831)(117,832)(118,833)(119,834)
(120,835)(121,886)(122,887)(123,888)(124,889)(125,890)(126,896)(127,897)
(128,898)(129,899)(130,900)(131,891)(132,892)(133,893)(134,894)(135,895)
(136,871)(137,872)(138,873)(139,874)(140,875)(141,881)(142,882)(143,883)
(144,884)(145,885)(146,876)(147,877)(148,878)(149,879)(150,880)(151,856)
(152,857)(153,858)(154,859)(155,860)(156,866)(157,867)(158,868)(159,869)
(160,870)(161,861)(162,862)(163,863)(164,864)(165,865)(166,841)(167,842)
(168,843)(169,844)(170,845)(171,851)(172,852)(173,853)(174,854)(175,855)
(176,846)(177,847)(178,848)(179,849)(180,850)(181,946)(182,947)(183,948)
(184,949)(185,950)(186,956)(187,957)(188,958)(189,959)(190,960)(191,951)
(192,952)(193,953)(194,954)(195,955)(196,931)(197,932)(198,933)(199,934)
(200,935)(201,941)(202,942)(203,943)(204,944)(205,945)(206,936)(207,937)
(208,938)(209,939)(210,940)(211,916)(212,917)(213,918)(214,919)(215,920)
(216,926)(217,927)(218,928)(219,929)(220,930)(221,921)(222,922)(223,923)
(224,924)(225,925)(226,901)(227,902)(228,903)(229,904)(230,905)(231,911)
(232,912)(233,913)(234,914)(235,915)(236,906)(237,907)(238,908)(239,909)
(240,910)(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)
(248,493)(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)
(256,496)(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)
(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,511)
(272,512)(273,513)(274,514)(275,515)(276,521)(277,522)(278,523)(279,524)
(280,525)(281,516)(282,517)(283,518)(284,519)(285,520)(286,526)(287,527)
(288,528)(289,529)(290,530)(291,536)(292,537)(293,538)(294,539)(295,540)
(296,531)(297,532)(298,533)(299,534)(300,535)(301,541)(302,542)(303,543)
(304,544)(305,545)(306,551)(307,552)(308,553)(309,554)(310,555)(311,546)
(312,547)(313,548)(314,549)(315,550)(316,556)(317,557)(318,558)(319,559)
(320,560)(321,566)(322,567)(323,568)(324,569)(325,570)(326,561)(327,562)
(328,563)(329,564)(330,565)(331,571)(332,572)(333,573)(334,574)(335,575)
(336,581)(337,582)(338,583)(339,584)(340,585)(341,576)(342,577)(343,578)
(344,579)(345,580)(346,586)(347,587)(348,588)(349,589)(350,590)(351,596)
(352,597)(353,598)(354,599)(355,600)(356,591)(357,592)(358,593)(359,594)
(360,595)(361,646)(362,647)(363,648)(364,649)(365,650)(366,656)(367,657)
(368,658)(369,659)(370,660)(371,651)(372,652)(373,653)(374,654)(375,655)
(376,631)(377,632)(378,633)(379,634)(380,635)(381,641)(382,642)(383,643)
(384,644)(385,645)(386,636)(387,637)(388,638)(389,639)(390,640)(391,616)
(392,617)(393,618)(394,619)(395,620)(396,626)(397,627)(398,628)(399,629)
(400,630)(401,621)(402,622)(403,623)(404,624)(405,625)(406,601)(407,602)
(408,603)(409,604)(410,605)(411,611)(412,612)(413,613)(414,614)(415,615)
(416,606)(417,607)(418,608)(419,609)(420,610)(421,706)(422,707)(423,708)
(424,709)(425,710)(426,716)(427,717)(428,718)(429,719)(430,720)(431,711)
(432,712)(433,713)(434,714)(435,715)(436,691)(437,692)(438,693)(439,694)
(440,695)(441,701)(442,702)(443,703)(444,704)(445,705)(446,696)(447,697)
(448,698)(449,699)(450,700)(451,676)(452,677)(453,678)(454,679)(455,680)
(456,686)(457,687)(458,688)(459,689)(460,690)(461,681)(462,682)(463,683)
(464,684)(465,685)(466,661)(467,662)(468,663)(469,664)(470,665)(471,671)
(472,672)(473,673)(474,674)(475,675)(476,666)(477,667)(478,668)(479,669)
(480,670);
s1 := Sym(960)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)
( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 36)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61, 81)( 62, 85)( 63, 84)
( 64, 83)( 65, 82)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 86)
( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 91,111)( 92,115)( 93,114)( 94,113)
( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)
(103,119)(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)
(126,151)(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)
(134,163)(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)
(142,170)(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)
(150,177)(181,231)(182,235)(183,234)(184,233)(185,232)(186,226)(187,230)
(188,229)(189,228)(190,227)(191,236)(192,240)(193,239)(194,238)(195,237)
(196,216)(197,220)(198,219)(199,218)(200,217)(201,211)(202,215)(203,214)
(204,213)(205,212)(206,221)(207,225)(208,224)(209,223)(210,222)(241,306)
(242,310)(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)
(250,302)(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)
(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)
(266,326)(267,330)(268,329)(269,328)(270,327)(271,336)(272,340)(273,339)
(274,338)(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)(281,341)
(282,345)(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)(289,353)
(290,352)(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)(297,360)
(298,359)(299,358)(300,357)(361,456)(362,460)(363,459)(364,458)(365,457)
(366,451)(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)
(374,463)(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)
(382,470)(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)
(390,477)(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)
(398,424)(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)
(406,441)(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)
(414,438)(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)
(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)
(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)
(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)
(506,626)(507,630)(508,629)(509,628)(510,627)(511,636)(512,640)(513,639)
(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)(521,641)
(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)(529,653)
(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)(537,660)
(538,659)(539,658)(540,657)(541,681)(542,685)(543,684)(544,683)(545,682)
(546,676)(547,680)(548,679)(549,678)(550,677)(551,686)(552,690)(553,689)
(554,688)(555,687)(556,666)(557,670)(558,669)(559,668)(560,667)(561,661)
(562,665)(563,664)(564,663)(565,662)(566,671)(567,675)(568,674)(569,673)
(570,672)(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)
(578,709)(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)
(586,696)(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)
(594,693)(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,921)
(722,925)(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)
(730,917)(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)
(738,909)(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)
(746,911)(747,915)(748,914)(749,913)(750,912)(751,951)(752,955)(753,954)
(754,953)(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)
(762,960)(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)
(770,937)(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)
(778,944)(779,943)(780,942)(781,861)(782,865)(783,864)(784,863)(785,862)
(786,856)(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)
(794,868)(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)
(802,845)(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)
(810,852)(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)
(818,889)(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)
(826,876)(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)
(834,873)(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);
s2 := Sym(960)!( 1,482)( 2,481)( 3,485)( 4,484)( 5,483)( 6,487)( 7,486)
( 8,490)( 9,489)( 10,488)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)
( 16,497)( 17,496)( 18,500)( 19,499)( 20,498)( 21,502)( 22,501)( 23,505)
( 24,504)( 25,503)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,512)
( 32,511)( 33,515)( 34,514)( 35,513)( 36,517)( 37,516)( 38,520)( 39,519)
( 40,518)( 41,522)( 42,521)( 43,525)( 44,524)( 45,523)( 46,527)( 47,526)
( 48,530)( 49,529)( 50,528)( 51,532)( 52,531)( 53,535)( 54,534)( 55,533)
( 56,537)( 57,536)( 58,540)( 59,539)( 60,538)( 61,557)( 62,556)( 63,560)
( 64,559)( 65,558)( 66,562)( 67,561)( 68,565)( 69,564)( 70,563)( 71,567)
( 72,566)( 73,570)( 74,569)( 75,568)( 76,542)( 77,541)( 78,545)( 79,544)
( 80,543)( 81,547)( 82,546)( 83,550)( 84,549)( 85,548)( 86,552)( 87,551)
( 88,555)( 89,554)( 90,553)( 91,587)( 92,586)( 93,590)( 94,589)( 95,588)
( 96,592)( 97,591)( 98,595)( 99,594)(100,593)(101,597)(102,596)(103,600)
(104,599)(105,598)(106,572)(107,571)(108,575)(109,574)(110,573)(111,577)
(112,576)(113,580)(114,579)(115,578)(116,582)(117,581)(118,585)(119,584)
(120,583)(121,632)(122,631)(123,635)(124,634)(125,633)(126,637)(127,636)
(128,640)(129,639)(130,638)(131,642)(132,641)(133,645)(134,644)(135,643)
(136,647)(137,646)(138,650)(139,649)(140,648)(141,652)(142,651)(143,655)
(144,654)(145,653)(146,657)(147,656)(148,660)(149,659)(150,658)(151,602)
(152,601)(153,605)(154,604)(155,603)(156,607)(157,606)(158,610)(159,609)
(160,608)(161,612)(162,611)(163,615)(164,614)(165,613)(166,617)(167,616)
(168,620)(169,619)(170,618)(171,622)(172,621)(173,625)(174,624)(175,623)
(176,627)(177,626)(178,630)(179,629)(180,628)(181,707)(182,706)(183,710)
(184,709)(185,708)(186,712)(187,711)(188,715)(189,714)(190,713)(191,717)
(192,716)(193,720)(194,719)(195,718)(196,692)(197,691)(198,695)(199,694)
(200,693)(201,697)(202,696)(203,700)(204,699)(205,698)(206,702)(207,701)
(208,705)(209,704)(210,703)(211,677)(212,676)(213,680)(214,679)(215,678)
(216,682)(217,681)(218,685)(219,684)(220,683)(221,687)(222,686)(223,690)
(224,689)(225,688)(226,662)(227,661)(228,665)(229,664)(230,663)(231,667)
(232,666)(233,670)(234,669)(235,668)(236,672)(237,671)(238,675)(239,674)
(240,673)(241,722)(242,721)(243,725)(244,724)(245,723)(246,727)(247,726)
(248,730)(249,729)(250,728)(251,732)(252,731)(253,735)(254,734)(255,733)
(256,737)(257,736)(258,740)(259,739)(260,738)(261,742)(262,741)(263,745)
(264,744)(265,743)(266,747)(267,746)(268,750)(269,749)(270,748)(271,752)
(272,751)(273,755)(274,754)(275,753)(276,757)(277,756)(278,760)(279,759)
(280,758)(281,762)(282,761)(283,765)(284,764)(285,763)(286,767)(287,766)
(288,770)(289,769)(290,768)(291,772)(292,771)(293,775)(294,774)(295,773)
(296,777)(297,776)(298,780)(299,779)(300,778)(301,797)(302,796)(303,800)
(304,799)(305,798)(306,802)(307,801)(308,805)(309,804)(310,803)(311,807)
(312,806)(313,810)(314,809)(315,808)(316,782)(317,781)(318,785)(319,784)
(320,783)(321,787)(322,786)(323,790)(324,789)(325,788)(326,792)(327,791)
(328,795)(329,794)(330,793)(331,827)(332,826)(333,830)(334,829)(335,828)
(336,832)(337,831)(338,835)(339,834)(340,833)(341,837)(342,836)(343,840)
(344,839)(345,838)(346,812)(347,811)(348,815)(349,814)(350,813)(351,817)
(352,816)(353,820)(354,819)(355,818)(356,822)(357,821)(358,825)(359,824)
(360,823)(361,872)(362,871)(363,875)(364,874)(365,873)(366,877)(367,876)
(368,880)(369,879)(370,878)(371,882)(372,881)(373,885)(374,884)(375,883)
(376,887)(377,886)(378,890)(379,889)(380,888)(381,892)(382,891)(383,895)
(384,894)(385,893)(386,897)(387,896)(388,900)(389,899)(390,898)(391,842)
(392,841)(393,845)(394,844)(395,843)(396,847)(397,846)(398,850)(399,849)
(400,848)(401,852)(402,851)(403,855)(404,854)(405,853)(406,857)(407,856)
(408,860)(409,859)(410,858)(411,862)(412,861)(413,865)(414,864)(415,863)
(416,867)(417,866)(418,870)(419,869)(420,868)(421,947)(422,946)(423,950)
(424,949)(425,948)(426,952)(427,951)(428,955)(429,954)(430,953)(431,957)
(432,956)(433,960)(434,959)(435,958)(436,932)(437,931)(438,935)(439,934)
(440,933)(441,937)(442,936)(443,940)(444,939)(445,938)(446,942)(447,941)
(448,945)(449,944)(450,943)(451,917)(452,916)(453,920)(454,919)(455,918)
(456,922)(457,921)(458,925)(459,924)(460,923)(461,927)(462,926)(463,930)
(464,929)(465,928)(466,902)(467,901)(468,905)(469,904)(470,903)(471,907)
(472,906)(473,910)(474,909)(475,908)(476,912)(477,911)(478,915)(479,914)
(480,913);
poly := sub<Sym(960)|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*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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