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