Polytope of Type {40,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,24}*1920b
if this polytope has a name.
Group : SmallGroup(1920,14535)
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 : {20,24}*960a, {40,12}*960b
3-fold quotients : {40,8}*640d
4-fold quotients : {10,24}*480, {20,12}*480
5-fold quotients : {8,24}*384a
6-fold quotients : {40,4}*320b, {20,8}*320a
8-fold quotients : {10,12}*240, {20,6}*240a
10-fold quotients : {4,24}*192a, {8,12}*192b
12-fold quotients : {20,4}*160, {10,8}*160
15-fold quotients : {8,8}*128a
16-fold quotients : {10,6}*120
20-fold quotients : {4,12}*96a, {2,24}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {4,8}*64a, {8,4}*64b
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {2,8}*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 := ( 1,721)( 2,725)( 3,724)( 4,723)( 5,722)( 6,726)( 7,730)( 8,729)
( 9,728)( 10,727)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)( 16,736)
( 17,740)( 18,739)( 19,738)( 20,737)( 21,741)( 22,745)( 23,744)( 24,743)
( 25,742)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,751)( 32,755)
( 33,754)( 34,753)( 35,752)( 36,756)( 37,760)( 38,759)( 39,758)( 40,757)
( 41,761)( 42,765)( 43,764)( 44,763)( 45,762)( 46,766)( 47,770)( 48,769)
( 49,768)( 50,767)( 51,771)( 52,775)( 53,774)( 54,773)( 55,772)( 56,776)
( 57,780)( 58,779)( 59,778)( 60,777)( 61,781)( 62,785)( 63,784)( 64,783)
( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)( 72,795)
( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)( 80,797)
( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)( 88,809)
( 89,808)( 90,807)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)( 96,816)
( 97,820)( 98,819)( 99,818)(100,817)(101,821)(102,825)(103,824)(104,823)
(105,822)(106,826)(107,830)(108,829)(109,828)(110,827)(111,831)(112,835)
(113,834)(114,833)(115,832)(116,836)(117,840)(118,839)(119,838)(120,837)
(121,886)(122,890)(123,889)(124,888)(125,887)(126,891)(127,895)(128,894)
(129,893)(130,892)(131,896)(132,900)(133,899)(134,898)(135,897)(136,871)
(137,875)(138,874)(139,873)(140,872)(141,876)(142,880)(143,879)(144,878)
(145,877)(146,881)(147,885)(148,884)(149,883)(150,882)(151,856)(152,860)
(153,859)(154,858)(155,857)(156,861)(157,865)(158,864)(159,863)(160,862)
(161,866)(162,870)(163,869)(164,868)(165,867)(166,841)(167,845)(168,844)
(169,843)(170,842)(171,846)(172,850)(173,849)(174,848)(175,847)(176,851)
(177,855)(178,854)(179,853)(180,852)(181,946)(182,950)(183,949)(184,948)
(185,947)(186,951)(187,955)(188,954)(189,953)(190,952)(191,956)(192,960)
(193,959)(194,958)(195,957)(196,931)(197,935)(198,934)(199,933)(200,932)
(201,936)(202,940)(203,939)(204,938)(205,937)(206,941)(207,945)(208,944)
(209,943)(210,942)(211,916)(212,920)(213,919)(214,918)(215,917)(216,921)
(217,925)(218,924)(219,923)(220,922)(221,926)(222,930)(223,929)(224,928)
(225,927)(226,901)(227,905)(228,904)(229,903)(230,902)(231,906)(232,910)
(233,909)(234,908)(235,907)(236,911)(237,915)(238,914)(239,913)(240,912)
(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)(248,489)
(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)(256,496)
(257,500)(258,499)(259,498)(260,497)(261,501)(262,505)(263,504)(264,503)
(265,502)(266,506)(267,510)(268,509)(269,508)(270,507)(271,511)(272,515)
(273,514)(274,513)(275,512)(276,516)(277,520)(278,519)(279,518)(280,517)
(281,521)(282,525)(283,524)(284,523)(285,522)(286,526)(287,530)(288,529)
(289,528)(290,527)(291,531)(292,535)(293,534)(294,533)(295,532)(296,536)
(297,540)(298,539)(299,538)(300,537)(301,541)(302,545)(303,544)(304,543)
(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)(312,555)
(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)(320,557)
(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)(328,569)
(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)(336,576)
(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)(344,583)
(345,582)(346,586)(347,590)(348,589)(349,588)(350,587)(351,591)(352,595)
(353,594)(354,593)(355,592)(356,596)(357,600)(358,599)(359,598)(360,597)
(361,646)(362,650)(363,649)(364,648)(365,647)(366,651)(367,655)(368,654)
(369,653)(370,652)(371,656)(372,660)(373,659)(374,658)(375,657)(376,631)
(377,635)(378,634)(379,633)(380,632)(381,636)(382,640)(383,639)(384,638)
(385,637)(386,641)(387,645)(388,644)(389,643)(390,642)(391,616)(392,620)
(393,619)(394,618)(395,617)(396,621)(397,625)(398,624)(399,623)(400,622)
(401,626)(402,630)(403,629)(404,628)(405,627)(406,601)(407,605)(408,604)
(409,603)(410,602)(411,606)(412,610)(413,609)(414,608)(415,607)(416,611)
(417,615)(418,614)(419,613)(420,612)(421,706)(422,710)(423,709)(424,708)
(425,707)(426,711)(427,715)(428,714)(429,713)(430,712)(431,716)(432,720)
(433,719)(434,718)(435,717)(436,691)(437,695)(438,694)(439,693)(440,692)
(441,696)(442,700)(443,699)(444,698)(445,697)(446,701)(447,705)(448,704)
(449,703)(450,702)(451,676)(452,680)(453,679)(454,678)(455,677)(456,681)
(457,685)(458,684)(459,683)(460,682)(461,686)(462,690)(463,689)(464,688)
(465,687)(466,661)(467,665)(468,664)(469,663)(470,662)(471,666)(472,670)
(473,669)(474,668)(475,667)(476,671)(477,675)(478,674)(479,673)(480,672);;
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 := ( 1,486)( 2,487)( 3,488)( 4,489)( 5,490)( 6,481)( 7,482)( 8,483)
( 9,484)( 10,485)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,501)
( 17,502)( 18,503)( 19,504)( 20,505)( 21,496)( 22,497)( 23,498)( 24,499)
( 25,500)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,516)( 32,517)
( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)( 40,515)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,531)( 47,532)( 48,533)
( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,561)( 62,562)( 63,563)( 64,564)
( 65,565)( 66,556)( 67,557)( 68,558)( 69,559)( 70,560)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,546)( 77,547)( 78,548)( 79,549)( 80,550)
( 81,541)( 82,542)( 83,543)( 84,544)( 85,545)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,591)( 92,592)( 93,593)( 94,594)( 95,595)( 96,586)
( 97,587)( 98,588)( 99,589)(100,590)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,576)(107,577)(108,578)(109,579)(110,580)(111,571)(112,572)
(113,573)(114,574)(115,575)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,636)(122,637)(123,638)(124,639)(125,640)(126,631)(127,632)(128,633)
(129,634)(130,635)(131,641)(132,642)(133,643)(134,644)(135,645)(136,651)
(137,652)(138,653)(139,654)(140,655)(141,646)(142,647)(143,648)(144,649)
(145,650)(146,656)(147,657)(148,658)(149,659)(150,660)(151,606)(152,607)
(153,608)(154,609)(155,610)(156,601)(157,602)(158,603)(159,604)(160,605)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,621)(167,622)(168,623)
(169,624)(170,625)(171,616)(172,617)(173,618)(174,619)(175,620)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,711)(182,712)(183,713)(184,714)
(185,715)(186,706)(187,707)(188,708)(189,709)(190,710)(191,716)(192,717)
(193,718)(194,719)(195,720)(196,696)(197,697)(198,698)(199,699)(200,700)
(201,691)(202,692)(203,693)(204,694)(205,695)(206,701)(207,702)(208,703)
(209,704)(210,705)(211,681)(212,682)(213,683)(214,684)(215,685)(216,676)
(217,677)(218,678)(219,679)(220,680)(221,686)(222,687)(223,688)(224,689)
(225,690)(226,666)(227,667)(228,668)(229,669)(230,670)(231,661)(232,662)
(233,663)(234,664)(235,665)(236,671)(237,672)(238,673)(239,674)(240,675)
(241,726)(242,727)(243,728)(244,729)(245,730)(246,721)(247,722)(248,723)
(249,724)(250,725)(251,731)(252,732)(253,733)(254,734)(255,735)(256,741)
(257,742)(258,743)(259,744)(260,745)(261,736)(262,737)(263,738)(264,739)
(265,740)(266,746)(267,747)(268,748)(269,749)(270,750)(271,756)(272,757)
(273,758)(274,759)(275,760)(276,751)(277,752)(278,753)(279,754)(280,755)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,771)(287,772)(288,773)
(289,774)(290,775)(291,766)(292,767)(293,768)(294,769)(295,770)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,801)(302,802)(303,803)(304,804)
(305,805)(306,796)(307,797)(308,798)(309,799)(310,800)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,786)(317,787)(318,788)(319,789)(320,790)
(321,781)(322,782)(323,783)(324,784)(325,785)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,831)(332,832)(333,833)(334,834)(335,835)(336,826)
(337,827)(338,828)(339,829)(340,830)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,816)(347,817)(348,818)(349,819)(350,820)(351,811)(352,812)
(353,813)(354,814)(355,815)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,876)(362,877)(363,878)(364,879)(365,880)(366,871)(367,872)(368,873)
(369,874)(370,875)(371,881)(372,882)(373,883)(374,884)(375,885)(376,891)
(377,892)(378,893)(379,894)(380,895)(381,886)(382,887)(383,888)(384,889)
(385,890)(386,896)(387,897)(388,898)(389,899)(390,900)(391,846)(392,847)
(393,848)(394,849)(395,850)(396,841)(397,842)(398,843)(399,844)(400,845)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,861)(407,862)(408,863)
(409,864)(410,865)(411,856)(412,857)(413,858)(414,859)(415,860)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,951)(422,952)(423,953)(424,954)
(425,955)(426,946)(427,947)(428,948)(429,949)(430,950)(431,956)(432,957)
(433,958)(434,959)(435,960)(436,936)(437,937)(438,938)(439,939)(440,940)
(441,931)(442,932)(443,933)(444,934)(445,935)(446,941)(447,942)(448,943)
(449,944)(450,945)(451,921)(452,922)(453,923)(454,924)(455,925)(456,916)
(457,917)(458,918)(459,919)(460,920)(461,926)(462,927)(463,928)(464,929)
(465,930)(466,906)(467,907)(468,908)(469,909)(470,910)(471,901)(472,902)
(473,903)(474,904)(475,905)(476,911)(477,912)(478,913)(479,914)(480,915);;
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,
s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,721)( 2,725)( 3,724)( 4,723)( 5,722)( 6,726)( 7,730)
( 8,729)( 9,728)( 10,727)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)
( 16,736)( 17,740)( 18,739)( 19,738)( 20,737)( 21,741)( 22,745)( 23,744)
( 24,743)( 25,742)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,751)
( 32,755)( 33,754)( 34,753)( 35,752)( 36,756)( 37,760)( 38,759)( 39,758)
( 40,757)( 41,761)( 42,765)( 43,764)( 44,763)( 45,762)( 46,766)( 47,770)
( 48,769)( 49,768)( 50,767)( 51,771)( 52,775)( 53,774)( 54,773)( 55,772)
( 56,776)( 57,780)( 58,779)( 59,778)( 60,777)( 61,781)( 62,785)( 63,784)
( 64,783)( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)
( 72,795)( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)
( 80,797)( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)
( 88,809)( 89,808)( 90,807)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)
( 96,816)( 97,820)( 98,819)( 99,818)(100,817)(101,821)(102,825)(103,824)
(104,823)(105,822)(106,826)(107,830)(108,829)(109,828)(110,827)(111,831)
(112,835)(113,834)(114,833)(115,832)(116,836)(117,840)(118,839)(119,838)
(120,837)(121,886)(122,890)(123,889)(124,888)(125,887)(126,891)(127,895)
(128,894)(129,893)(130,892)(131,896)(132,900)(133,899)(134,898)(135,897)
(136,871)(137,875)(138,874)(139,873)(140,872)(141,876)(142,880)(143,879)
(144,878)(145,877)(146,881)(147,885)(148,884)(149,883)(150,882)(151,856)
(152,860)(153,859)(154,858)(155,857)(156,861)(157,865)(158,864)(159,863)
(160,862)(161,866)(162,870)(163,869)(164,868)(165,867)(166,841)(167,845)
(168,844)(169,843)(170,842)(171,846)(172,850)(173,849)(174,848)(175,847)
(176,851)(177,855)(178,854)(179,853)(180,852)(181,946)(182,950)(183,949)
(184,948)(185,947)(186,951)(187,955)(188,954)(189,953)(190,952)(191,956)
(192,960)(193,959)(194,958)(195,957)(196,931)(197,935)(198,934)(199,933)
(200,932)(201,936)(202,940)(203,939)(204,938)(205,937)(206,941)(207,945)
(208,944)(209,943)(210,942)(211,916)(212,920)(213,919)(214,918)(215,917)
(216,921)(217,925)(218,924)(219,923)(220,922)(221,926)(222,930)(223,929)
(224,928)(225,927)(226,901)(227,905)(228,904)(229,903)(230,902)(231,906)
(232,910)(233,909)(234,908)(235,907)(236,911)(237,915)(238,914)(239,913)
(240,912)(241,481)(242,485)(243,484)(244,483)(245,482)(246,486)(247,490)
(248,489)(249,488)(250,487)(251,491)(252,495)(253,494)(254,493)(255,492)
(256,496)(257,500)(258,499)(259,498)(260,497)(261,501)(262,505)(263,504)
(264,503)(265,502)(266,506)(267,510)(268,509)(269,508)(270,507)(271,511)
(272,515)(273,514)(274,513)(275,512)(276,516)(277,520)(278,519)(279,518)
(280,517)(281,521)(282,525)(283,524)(284,523)(285,522)(286,526)(287,530)
(288,529)(289,528)(290,527)(291,531)(292,535)(293,534)(294,533)(295,532)
(296,536)(297,540)(298,539)(299,538)(300,537)(301,541)(302,545)(303,544)
(304,543)(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)
(312,555)(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)
(320,557)(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)
(328,569)(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)
(336,576)(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)
(344,583)(345,582)(346,586)(347,590)(348,589)(349,588)(350,587)(351,591)
(352,595)(353,594)(354,593)(355,592)(356,596)(357,600)(358,599)(359,598)
(360,597)(361,646)(362,650)(363,649)(364,648)(365,647)(366,651)(367,655)
(368,654)(369,653)(370,652)(371,656)(372,660)(373,659)(374,658)(375,657)
(376,631)(377,635)(378,634)(379,633)(380,632)(381,636)(382,640)(383,639)
(384,638)(385,637)(386,641)(387,645)(388,644)(389,643)(390,642)(391,616)
(392,620)(393,619)(394,618)(395,617)(396,621)(397,625)(398,624)(399,623)
(400,622)(401,626)(402,630)(403,629)(404,628)(405,627)(406,601)(407,605)
(408,604)(409,603)(410,602)(411,606)(412,610)(413,609)(414,608)(415,607)
(416,611)(417,615)(418,614)(419,613)(420,612)(421,706)(422,710)(423,709)
(424,708)(425,707)(426,711)(427,715)(428,714)(429,713)(430,712)(431,716)
(432,720)(433,719)(434,718)(435,717)(436,691)(437,695)(438,694)(439,693)
(440,692)(441,696)(442,700)(443,699)(444,698)(445,697)(446,701)(447,705)
(448,704)(449,703)(450,702)(451,676)(452,680)(453,679)(454,678)(455,677)
(456,681)(457,685)(458,684)(459,683)(460,682)(461,686)(462,690)(463,689)
(464,688)(465,687)(466,661)(467,665)(468,664)(469,663)(470,662)(471,666)
(472,670)(473,669)(474,668)(475,667)(476,671)(477,675)(478,674)(479,673)
(480,672);
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)!( 1,486)( 2,487)( 3,488)( 4,489)( 5,490)( 6,481)( 7,482)
( 8,483)( 9,484)( 10,485)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,501)( 17,502)( 18,503)( 19,504)( 20,505)( 21,496)( 22,497)( 23,498)
( 24,499)( 25,500)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,516)
( 32,517)( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)
( 40,515)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,531)( 47,532)
( 48,533)( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,561)( 62,562)( 63,563)
( 64,564)( 65,565)( 66,556)( 67,557)( 68,558)( 69,559)( 70,560)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,546)( 77,547)( 78,548)( 79,549)
( 80,550)( 81,541)( 82,542)( 83,543)( 84,544)( 85,545)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,591)( 92,592)( 93,593)( 94,594)( 95,595)
( 96,586)( 97,587)( 98,588)( 99,589)(100,590)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,576)(107,577)(108,578)(109,579)(110,580)(111,571)
(112,572)(113,573)(114,574)(115,575)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,636)(122,637)(123,638)(124,639)(125,640)(126,631)(127,632)
(128,633)(129,634)(130,635)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,651)(137,652)(138,653)(139,654)(140,655)(141,646)(142,647)(143,648)
(144,649)(145,650)(146,656)(147,657)(148,658)(149,659)(150,660)(151,606)
(152,607)(153,608)(154,609)(155,610)(156,601)(157,602)(158,603)(159,604)
(160,605)(161,611)(162,612)(163,613)(164,614)(165,615)(166,621)(167,622)
(168,623)(169,624)(170,625)(171,616)(172,617)(173,618)(174,619)(175,620)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,711)(182,712)(183,713)
(184,714)(185,715)(186,706)(187,707)(188,708)(189,709)(190,710)(191,716)
(192,717)(193,718)(194,719)(195,720)(196,696)(197,697)(198,698)(199,699)
(200,700)(201,691)(202,692)(203,693)(204,694)(205,695)(206,701)(207,702)
(208,703)(209,704)(210,705)(211,681)(212,682)(213,683)(214,684)(215,685)
(216,676)(217,677)(218,678)(219,679)(220,680)(221,686)(222,687)(223,688)
(224,689)(225,690)(226,666)(227,667)(228,668)(229,669)(230,670)(231,661)
(232,662)(233,663)(234,664)(235,665)(236,671)(237,672)(238,673)(239,674)
(240,675)(241,726)(242,727)(243,728)(244,729)(245,730)(246,721)(247,722)
(248,723)(249,724)(250,725)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,741)(257,742)(258,743)(259,744)(260,745)(261,736)(262,737)(263,738)
(264,739)(265,740)(266,746)(267,747)(268,748)(269,749)(270,750)(271,756)
(272,757)(273,758)(274,759)(275,760)(276,751)(277,752)(278,753)(279,754)
(280,755)(281,761)(282,762)(283,763)(284,764)(285,765)(286,771)(287,772)
(288,773)(289,774)(290,775)(291,766)(292,767)(293,768)(294,769)(295,770)
(296,776)(297,777)(298,778)(299,779)(300,780)(301,801)(302,802)(303,803)
(304,804)(305,805)(306,796)(307,797)(308,798)(309,799)(310,800)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,786)(317,787)(318,788)(319,789)
(320,790)(321,781)(322,782)(323,783)(324,784)(325,785)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,831)(332,832)(333,833)(334,834)(335,835)
(336,826)(337,827)(338,828)(339,829)(340,830)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,816)(347,817)(348,818)(349,819)(350,820)(351,811)
(352,812)(353,813)(354,814)(355,815)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,876)(362,877)(363,878)(364,879)(365,880)(366,871)(367,872)
(368,873)(369,874)(370,875)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,891)(377,892)(378,893)(379,894)(380,895)(381,886)(382,887)(383,888)
(384,889)(385,890)(386,896)(387,897)(388,898)(389,899)(390,900)(391,846)
(392,847)(393,848)(394,849)(395,850)(396,841)(397,842)(398,843)(399,844)
(400,845)(401,851)(402,852)(403,853)(404,854)(405,855)(406,861)(407,862)
(408,863)(409,864)(410,865)(411,856)(412,857)(413,858)(414,859)(415,860)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,951)(422,952)(423,953)
(424,954)(425,955)(426,946)(427,947)(428,948)(429,949)(430,950)(431,956)
(432,957)(433,958)(434,959)(435,960)(436,936)(437,937)(438,938)(439,939)
(440,940)(441,931)(442,932)(443,933)(444,934)(445,935)(446,941)(447,942)
(448,943)(449,944)(450,945)(451,921)(452,922)(453,923)(454,924)(455,925)
(456,916)(457,917)(458,918)(459,919)(460,920)(461,926)(462,927)(463,928)
(464,929)(465,930)(466,906)(467,907)(468,908)(469,909)(470,910)(471,901)
(472,902)(473,903)(474,904)(475,905)(476,911)(477,912)(478,913)(479,914)
(480,915);
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,
s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope