Polytope of Type {60,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*1920i
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 240, 480, 16
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4}*960d
3-fold quotients : {20,4}*640d
4-fold quotients : {15,4}*480
6-fold quotients : {10,4}*320b
12-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)( 42,137)
( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)( 50,155)
( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)( 58,147)
( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)( 66, 98)
( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)( 74,105)
( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)( 82,123)
( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)( 90,115)
( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)(162,322)
(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)(170,329)
(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)(178,347)
(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)(186,339)
(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)(194,450)
(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)(202,457)
(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)(210,475)
(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)(218,467)
(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)(226,418)
(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)(234,425)
(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)(242,443)
(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)(250,435)
(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)(258,386)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)(266,393)
(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)(274,411)
(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)(282,403)
(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)(290,354)
(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)(298,361)
(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)(306,379)
(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)(314,371)
(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)(483,484)
(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)(500,506)
(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)(516,611)
(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)(524,620)
(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)(532,634)
(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)(540,626)
(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)(548,579)
(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)(556,588)
(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)(564,602)
(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)(572,594)
(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)(644,803)
(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)(652,812)
(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)(660,826)
(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)(668,818)
(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)(676,931)
(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)(684,940)
(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)(692,954)
(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)(700,946)
(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)(708,899)
(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)(716,908)
(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)(724,922)
(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)(732,914)
(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)(740,867)
(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)(748,876)
(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)(756,890)
(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)(764,882)
(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)(772,835)
(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)(780,844)
(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)(788,858)
(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)(796,850)
(797,854)(798,853)(799,856)(800,855);;
s1 := ( 1,673)( 2,674)( 3,704)( 4,703)( 5,684)( 6,683)( 7,693)( 8,694)
( 9,700)( 10,699)( 11,678)( 12,677)( 13,690)( 14,689)( 15,688)( 16,687)
( 17,686)( 18,685)( 19,691)( 20,692)( 21,679)( 22,680)( 23,698)( 24,697)
( 25,696)( 26,695)( 27,682)( 28,681)( 29,702)( 30,701)( 31,676)( 32,675)
( 33,641)( 34,642)( 35,672)( 36,671)( 37,652)( 38,651)( 39,661)( 40,662)
( 41,668)( 42,667)( 43,646)( 44,645)( 45,658)( 46,657)( 47,656)( 48,655)
( 49,654)( 50,653)( 51,659)( 52,660)( 53,647)( 54,648)( 55,666)( 56,665)
( 57,664)( 58,663)( 59,650)( 60,649)( 61,670)( 62,669)( 63,644)( 64,643)
( 65,769)( 66,770)( 67,800)( 68,799)( 69,780)( 70,779)( 71,789)( 72,790)
( 73,796)( 74,795)( 75,774)( 76,773)( 77,786)( 78,785)( 79,784)( 80,783)
( 81,782)( 82,781)( 83,787)( 84,788)( 85,775)( 86,776)( 87,794)( 88,793)
( 89,792)( 90,791)( 91,778)( 92,777)( 93,798)( 94,797)( 95,772)( 96,771)
( 97,737)( 98,738)( 99,768)(100,767)(101,748)(102,747)(103,757)(104,758)
(105,764)(106,763)(107,742)(108,741)(109,754)(110,753)(111,752)(112,751)
(113,750)(114,749)(115,755)(116,756)(117,743)(118,744)(119,762)(120,761)
(121,760)(122,759)(123,746)(124,745)(125,766)(126,765)(127,740)(128,739)
(129,705)(130,706)(131,736)(132,735)(133,716)(134,715)(135,725)(136,726)
(137,732)(138,731)(139,710)(140,709)(141,722)(142,721)(143,720)(144,719)
(145,718)(146,717)(147,723)(148,724)(149,711)(150,712)(151,730)(152,729)
(153,728)(154,727)(155,714)(156,713)(157,734)(158,733)(159,708)(160,707)
(161,513)(162,514)(163,544)(164,543)(165,524)(166,523)(167,533)(168,534)
(169,540)(170,539)(171,518)(172,517)(173,530)(174,529)(175,528)(176,527)
(177,526)(178,525)(179,531)(180,532)(181,519)(182,520)(183,538)(184,537)
(185,536)(186,535)(187,522)(188,521)(189,542)(190,541)(191,516)(192,515)
(193,481)(194,482)(195,512)(196,511)(197,492)(198,491)(199,501)(200,502)
(201,508)(202,507)(203,486)(204,485)(205,498)(206,497)(207,496)(208,495)
(209,494)(210,493)(211,499)(212,500)(213,487)(214,488)(215,506)(216,505)
(217,504)(218,503)(219,490)(220,489)(221,510)(222,509)(223,484)(224,483)
(225,609)(226,610)(227,640)(228,639)(229,620)(230,619)(231,629)(232,630)
(233,636)(234,635)(235,614)(236,613)(237,626)(238,625)(239,624)(240,623)
(241,622)(242,621)(243,627)(244,628)(245,615)(246,616)(247,634)(248,633)
(249,632)(250,631)(251,618)(252,617)(253,638)(254,637)(255,612)(256,611)
(257,577)(258,578)(259,608)(260,607)(261,588)(262,587)(263,597)(264,598)
(265,604)(266,603)(267,582)(268,581)(269,594)(270,593)(271,592)(272,591)
(273,590)(274,589)(275,595)(276,596)(277,583)(278,584)(279,602)(280,601)
(281,600)(282,599)(283,586)(284,585)(285,606)(286,605)(287,580)(288,579)
(289,545)(290,546)(291,576)(292,575)(293,556)(294,555)(295,565)(296,566)
(297,572)(298,571)(299,550)(300,549)(301,562)(302,561)(303,560)(304,559)
(305,558)(306,557)(307,563)(308,564)(309,551)(310,552)(311,570)(312,569)
(313,568)(314,567)(315,554)(316,553)(317,574)(318,573)(319,548)(320,547)
(321,833)(322,834)(323,864)(324,863)(325,844)(326,843)(327,853)(328,854)
(329,860)(330,859)(331,838)(332,837)(333,850)(334,849)(335,848)(336,847)
(337,846)(338,845)(339,851)(340,852)(341,839)(342,840)(343,858)(344,857)
(345,856)(346,855)(347,842)(348,841)(349,862)(350,861)(351,836)(352,835)
(353,801)(354,802)(355,832)(356,831)(357,812)(358,811)(359,821)(360,822)
(361,828)(362,827)(363,806)(364,805)(365,818)(366,817)(367,816)(368,815)
(369,814)(370,813)(371,819)(372,820)(373,807)(374,808)(375,826)(376,825)
(377,824)(378,823)(379,810)(380,809)(381,830)(382,829)(383,804)(384,803)
(385,929)(386,930)(387,960)(388,959)(389,940)(390,939)(391,949)(392,950)
(393,956)(394,955)(395,934)(396,933)(397,946)(398,945)(399,944)(400,943)
(401,942)(402,941)(403,947)(404,948)(405,935)(406,936)(407,954)(408,953)
(409,952)(410,951)(411,938)(412,937)(413,958)(414,957)(415,932)(416,931)
(417,897)(418,898)(419,928)(420,927)(421,908)(422,907)(423,917)(424,918)
(425,924)(426,923)(427,902)(428,901)(429,914)(430,913)(431,912)(432,911)
(433,910)(434,909)(435,915)(436,916)(437,903)(438,904)(439,922)(440,921)
(441,920)(442,919)(443,906)(444,905)(445,926)(446,925)(447,900)(448,899)
(449,865)(450,866)(451,896)(452,895)(453,876)(454,875)(455,885)(456,886)
(457,892)(458,891)(459,870)(460,869)(461,882)(462,881)(463,880)(464,879)
(465,878)(466,877)(467,883)(468,884)(469,871)(470,872)(471,890)(472,889)
(473,888)(474,887)(475,874)(476,873)(477,894)(478,893)(479,868)(480,867);;
s2 := ( 1,490)( 2,489)( 3,492)( 4,491)( 5,493)( 6,494)( 7,495)( 8,496)
( 9,481)( 10,482)( 11,483)( 12,484)( 13,486)( 14,485)( 15,488)( 16,487)
( 17,506)( 18,505)( 19,508)( 20,507)( 21,509)( 22,510)( 23,511)( 24,512)
( 25,497)( 26,498)( 27,499)( 28,500)( 29,502)( 30,501)( 31,504)( 32,503)
( 33,522)( 34,521)( 35,524)( 36,523)( 37,525)( 38,526)( 39,527)( 40,528)
( 41,513)( 42,514)( 43,515)( 44,516)( 45,518)( 46,517)( 47,520)( 48,519)
( 49,538)( 50,537)( 51,540)( 52,539)( 53,541)( 54,542)( 55,543)( 56,544)
( 57,529)( 58,530)( 59,531)( 60,532)( 61,534)( 62,533)( 63,536)( 64,535)
( 65,554)( 66,553)( 67,556)( 68,555)( 69,557)( 70,558)( 71,559)( 72,560)
( 73,545)( 74,546)( 75,547)( 76,548)( 77,550)( 78,549)( 79,552)( 80,551)
( 81,570)( 82,569)( 83,572)( 84,571)( 85,573)( 86,574)( 87,575)( 88,576)
( 89,561)( 90,562)( 91,563)( 92,564)( 93,566)( 94,565)( 95,568)( 96,567)
( 97,586)( 98,585)( 99,588)(100,587)(101,589)(102,590)(103,591)(104,592)
(105,577)(106,578)(107,579)(108,580)(109,582)(110,581)(111,584)(112,583)
(113,602)(114,601)(115,604)(116,603)(117,605)(118,606)(119,607)(120,608)
(121,593)(122,594)(123,595)(124,596)(125,598)(126,597)(127,600)(128,599)
(129,618)(130,617)(131,620)(132,619)(133,621)(134,622)(135,623)(136,624)
(137,609)(138,610)(139,611)(140,612)(141,614)(142,613)(143,616)(144,615)
(145,634)(146,633)(147,636)(148,635)(149,637)(150,638)(151,639)(152,640)
(153,625)(154,626)(155,627)(156,628)(157,630)(158,629)(159,632)(160,631)
(161,650)(162,649)(163,652)(164,651)(165,653)(166,654)(167,655)(168,656)
(169,641)(170,642)(171,643)(172,644)(173,646)(174,645)(175,648)(176,647)
(177,666)(178,665)(179,668)(180,667)(181,669)(182,670)(183,671)(184,672)
(185,657)(186,658)(187,659)(188,660)(189,662)(190,661)(191,664)(192,663)
(193,682)(194,681)(195,684)(196,683)(197,685)(198,686)(199,687)(200,688)
(201,673)(202,674)(203,675)(204,676)(205,678)(206,677)(207,680)(208,679)
(209,698)(210,697)(211,700)(212,699)(213,701)(214,702)(215,703)(216,704)
(217,689)(218,690)(219,691)(220,692)(221,694)(222,693)(223,696)(224,695)
(225,714)(226,713)(227,716)(228,715)(229,717)(230,718)(231,719)(232,720)
(233,705)(234,706)(235,707)(236,708)(237,710)(238,709)(239,712)(240,711)
(241,730)(242,729)(243,732)(244,731)(245,733)(246,734)(247,735)(248,736)
(249,721)(250,722)(251,723)(252,724)(253,726)(254,725)(255,728)(256,727)
(257,746)(258,745)(259,748)(260,747)(261,749)(262,750)(263,751)(264,752)
(265,737)(266,738)(267,739)(268,740)(269,742)(270,741)(271,744)(272,743)
(273,762)(274,761)(275,764)(276,763)(277,765)(278,766)(279,767)(280,768)
(281,753)(282,754)(283,755)(284,756)(285,758)(286,757)(287,760)(288,759)
(289,778)(290,777)(291,780)(292,779)(293,781)(294,782)(295,783)(296,784)
(297,769)(298,770)(299,771)(300,772)(301,774)(302,773)(303,776)(304,775)
(305,794)(306,793)(307,796)(308,795)(309,797)(310,798)(311,799)(312,800)
(313,785)(314,786)(315,787)(316,788)(317,790)(318,789)(319,792)(320,791)
(321,810)(322,809)(323,812)(324,811)(325,813)(326,814)(327,815)(328,816)
(329,801)(330,802)(331,803)(332,804)(333,806)(334,805)(335,808)(336,807)
(337,826)(338,825)(339,828)(340,827)(341,829)(342,830)(343,831)(344,832)
(345,817)(346,818)(347,819)(348,820)(349,822)(350,821)(351,824)(352,823)
(353,842)(354,841)(355,844)(356,843)(357,845)(358,846)(359,847)(360,848)
(361,833)(362,834)(363,835)(364,836)(365,838)(366,837)(367,840)(368,839)
(369,858)(370,857)(371,860)(372,859)(373,861)(374,862)(375,863)(376,864)
(377,849)(378,850)(379,851)(380,852)(381,854)(382,853)(383,856)(384,855)
(385,874)(386,873)(387,876)(388,875)(389,877)(390,878)(391,879)(392,880)
(393,865)(394,866)(395,867)(396,868)(397,870)(398,869)(399,872)(400,871)
(401,890)(402,889)(403,892)(404,891)(405,893)(406,894)(407,895)(408,896)
(409,881)(410,882)(411,883)(412,884)(413,886)(414,885)(415,888)(416,887)
(417,906)(418,905)(419,908)(420,907)(421,909)(422,910)(423,911)(424,912)
(425,897)(426,898)(427,899)(428,900)(429,902)(430,901)(431,904)(432,903)
(433,922)(434,921)(435,924)(436,923)(437,925)(438,926)(439,927)(440,928)
(441,913)(442,914)(443,915)(444,916)(445,918)(446,917)(447,920)(448,919)
(449,938)(450,937)(451,940)(452,939)(453,941)(454,942)(455,943)(456,944)
(457,929)(458,930)(459,931)(460,932)(461,934)(462,933)(463,936)(464,935)
(465,954)(466,953)(467,956)(468,955)(469,957)(470,958)(471,959)(472,960)
(473,945)(474,946)(475,947)(476,948)(477,950)(478,949)(479,952)(480,951);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*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*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)
( 42,137)( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)
( 50,155)( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)
( 58,147)( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)
( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)
( 74,105)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)
( 82,123)( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)
( 90,115)( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)
(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)
(170,329)(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)
(178,347)(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)
(186,339)(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)
(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)
(202,457)(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)
(210,475)(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)
(218,467)(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)
(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)
(234,425)(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)
(242,443)(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)
(250,435)(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)
(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)
(266,393)(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)
(274,411)(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)
(282,403)(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)
(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)
(298,361)(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)
(306,379)(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)
(314,371)(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)
(483,484)(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)
(500,506)(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)
(516,611)(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)
(524,620)(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)
(532,634)(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)
(540,626)(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)
(548,579)(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)
(556,588)(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)
(564,602)(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)
(572,594)(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)
(644,803)(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)
(652,812)(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)
(660,826)(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)
(668,818)(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)
(676,931)(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)
(684,940)(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)
(692,954)(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)
(700,946)(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)
(708,899)(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)
(716,908)(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)
(724,922)(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)
(732,914)(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)
(740,867)(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)
(748,876)(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)
(756,890)(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)
(764,882)(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)
(772,835)(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)
(780,844)(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)
(788,858)(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)
(796,850)(797,854)(798,853)(799,856)(800,855);
s1 := Sym(960)!( 1,673)( 2,674)( 3,704)( 4,703)( 5,684)( 6,683)( 7,693)
( 8,694)( 9,700)( 10,699)( 11,678)( 12,677)( 13,690)( 14,689)( 15,688)
( 16,687)( 17,686)( 18,685)( 19,691)( 20,692)( 21,679)( 22,680)( 23,698)
( 24,697)( 25,696)( 26,695)( 27,682)( 28,681)( 29,702)( 30,701)( 31,676)
( 32,675)( 33,641)( 34,642)( 35,672)( 36,671)( 37,652)( 38,651)( 39,661)
( 40,662)( 41,668)( 42,667)( 43,646)( 44,645)( 45,658)( 46,657)( 47,656)
( 48,655)( 49,654)( 50,653)( 51,659)( 52,660)( 53,647)( 54,648)( 55,666)
( 56,665)( 57,664)( 58,663)( 59,650)( 60,649)( 61,670)( 62,669)( 63,644)
( 64,643)( 65,769)( 66,770)( 67,800)( 68,799)( 69,780)( 70,779)( 71,789)
( 72,790)( 73,796)( 74,795)( 75,774)( 76,773)( 77,786)( 78,785)( 79,784)
( 80,783)( 81,782)( 82,781)( 83,787)( 84,788)( 85,775)( 86,776)( 87,794)
( 88,793)( 89,792)( 90,791)( 91,778)( 92,777)( 93,798)( 94,797)( 95,772)
( 96,771)( 97,737)( 98,738)( 99,768)(100,767)(101,748)(102,747)(103,757)
(104,758)(105,764)(106,763)(107,742)(108,741)(109,754)(110,753)(111,752)
(112,751)(113,750)(114,749)(115,755)(116,756)(117,743)(118,744)(119,762)
(120,761)(121,760)(122,759)(123,746)(124,745)(125,766)(126,765)(127,740)
(128,739)(129,705)(130,706)(131,736)(132,735)(133,716)(134,715)(135,725)
(136,726)(137,732)(138,731)(139,710)(140,709)(141,722)(142,721)(143,720)
(144,719)(145,718)(146,717)(147,723)(148,724)(149,711)(150,712)(151,730)
(152,729)(153,728)(154,727)(155,714)(156,713)(157,734)(158,733)(159,708)
(160,707)(161,513)(162,514)(163,544)(164,543)(165,524)(166,523)(167,533)
(168,534)(169,540)(170,539)(171,518)(172,517)(173,530)(174,529)(175,528)
(176,527)(177,526)(178,525)(179,531)(180,532)(181,519)(182,520)(183,538)
(184,537)(185,536)(186,535)(187,522)(188,521)(189,542)(190,541)(191,516)
(192,515)(193,481)(194,482)(195,512)(196,511)(197,492)(198,491)(199,501)
(200,502)(201,508)(202,507)(203,486)(204,485)(205,498)(206,497)(207,496)
(208,495)(209,494)(210,493)(211,499)(212,500)(213,487)(214,488)(215,506)
(216,505)(217,504)(218,503)(219,490)(220,489)(221,510)(222,509)(223,484)
(224,483)(225,609)(226,610)(227,640)(228,639)(229,620)(230,619)(231,629)
(232,630)(233,636)(234,635)(235,614)(236,613)(237,626)(238,625)(239,624)
(240,623)(241,622)(242,621)(243,627)(244,628)(245,615)(246,616)(247,634)
(248,633)(249,632)(250,631)(251,618)(252,617)(253,638)(254,637)(255,612)
(256,611)(257,577)(258,578)(259,608)(260,607)(261,588)(262,587)(263,597)
(264,598)(265,604)(266,603)(267,582)(268,581)(269,594)(270,593)(271,592)
(272,591)(273,590)(274,589)(275,595)(276,596)(277,583)(278,584)(279,602)
(280,601)(281,600)(282,599)(283,586)(284,585)(285,606)(286,605)(287,580)
(288,579)(289,545)(290,546)(291,576)(292,575)(293,556)(294,555)(295,565)
(296,566)(297,572)(298,571)(299,550)(300,549)(301,562)(302,561)(303,560)
(304,559)(305,558)(306,557)(307,563)(308,564)(309,551)(310,552)(311,570)
(312,569)(313,568)(314,567)(315,554)(316,553)(317,574)(318,573)(319,548)
(320,547)(321,833)(322,834)(323,864)(324,863)(325,844)(326,843)(327,853)
(328,854)(329,860)(330,859)(331,838)(332,837)(333,850)(334,849)(335,848)
(336,847)(337,846)(338,845)(339,851)(340,852)(341,839)(342,840)(343,858)
(344,857)(345,856)(346,855)(347,842)(348,841)(349,862)(350,861)(351,836)
(352,835)(353,801)(354,802)(355,832)(356,831)(357,812)(358,811)(359,821)
(360,822)(361,828)(362,827)(363,806)(364,805)(365,818)(366,817)(367,816)
(368,815)(369,814)(370,813)(371,819)(372,820)(373,807)(374,808)(375,826)
(376,825)(377,824)(378,823)(379,810)(380,809)(381,830)(382,829)(383,804)
(384,803)(385,929)(386,930)(387,960)(388,959)(389,940)(390,939)(391,949)
(392,950)(393,956)(394,955)(395,934)(396,933)(397,946)(398,945)(399,944)
(400,943)(401,942)(402,941)(403,947)(404,948)(405,935)(406,936)(407,954)
(408,953)(409,952)(410,951)(411,938)(412,937)(413,958)(414,957)(415,932)
(416,931)(417,897)(418,898)(419,928)(420,927)(421,908)(422,907)(423,917)
(424,918)(425,924)(426,923)(427,902)(428,901)(429,914)(430,913)(431,912)
(432,911)(433,910)(434,909)(435,915)(436,916)(437,903)(438,904)(439,922)
(440,921)(441,920)(442,919)(443,906)(444,905)(445,926)(446,925)(447,900)
(448,899)(449,865)(450,866)(451,896)(452,895)(453,876)(454,875)(455,885)
(456,886)(457,892)(458,891)(459,870)(460,869)(461,882)(462,881)(463,880)
(464,879)(465,878)(466,877)(467,883)(468,884)(469,871)(470,872)(471,890)
(472,889)(473,888)(474,887)(475,874)(476,873)(477,894)(478,893)(479,868)
(480,867);
s2 := Sym(960)!( 1,490)( 2,489)( 3,492)( 4,491)( 5,493)( 6,494)( 7,495)
( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,486)( 14,485)( 15,488)
( 16,487)( 17,506)( 18,505)( 19,508)( 20,507)( 21,509)( 22,510)( 23,511)
( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,502)( 30,501)( 31,504)
( 32,503)( 33,522)( 34,521)( 35,524)( 36,523)( 37,525)( 38,526)( 39,527)
( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,518)( 46,517)( 47,520)
( 48,519)( 49,538)( 50,537)( 51,540)( 52,539)( 53,541)( 54,542)( 55,543)
( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,534)( 62,533)( 63,536)
( 64,535)( 65,554)( 66,553)( 67,556)( 68,555)( 69,557)( 70,558)( 71,559)
( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,550)( 78,549)( 79,552)
( 80,551)( 81,570)( 82,569)( 83,572)( 84,571)( 85,573)( 86,574)( 87,575)
( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,566)( 94,565)( 95,568)
( 96,567)( 97,586)( 98,585)( 99,588)(100,587)(101,589)(102,590)(103,591)
(104,592)(105,577)(106,578)(107,579)(108,580)(109,582)(110,581)(111,584)
(112,583)(113,602)(114,601)(115,604)(116,603)(117,605)(118,606)(119,607)
(120,608)(121,593)(122,594)(123,595)(124,596)(125,598)(126,597)(127,600)
(128,599)(129,618)(130,617)(131,620)(132,619)(133,621)(134,622)(135,623)
(136,624)(137,609)(138,610)(139,611)(140,612)(141,614)(142,613)(143,616)
(144,615)(145,634)(146,633)(147,636)(148,635)(149,637)(150,638)(151,639)
(152,640)(153,625)(154,626)(155,627)(156,628)(157,630)(158,629)(159,632)
(160,631)(161,650)(162,649)(163,652)(164,651)(165,653)(166,654)(167,655)
(168,656)(169,641)(170,642)(171,643)(172,644)(173,646)(174,645)(175,648)
(176,647)(177,666)(178,665)(179,668)(180,667)(181,669)(182,670)(183,671)
(184,672)(185,657)(186,658)(187,659)(188,660)(189,662)(190,661)(191,664)
(192,663)(193,682)(194,681)(195,684)(196,683)(197,685)(198,686)(199,687)
(200,688)(201,673)(202,674)(203,675)(204,676)(205,678)(206,677)(207,680)
(208,679)(209,698)(210,697)(211,700)(212,699)(213,701)(214,702)(215,703)
(216,704)(217,689)(218,690)(219,691)(220,692)(221,694)(222,693)(223,696)
(224,695)(225,714)(226,713)(227,716)(228,715)(229,717)(230,718)(231,719)
(232,720)(233,705)(234,706)(235,707)(236,708)(237,710)(238,709)(239,712)
(240,711)(241,730)(242,729)(243,732)(244,731)(245,733)(246,734)(247,735)
(248,736)(249,721)(250,722)(251,723)(252,724)(253,726)(254,725)(255,728)
(256,727)(257,746)(258,745)(259,748)(260,747)(261,749)(262,750)(263,751)
(264,752)(265,737)(266,738)(267,739)(268,740)(269,742)(270,741)(271,744)
(272,743)(273,762)(274,761)(275,764)(276,763)(277,765)(278,766)(279,767)
(280,768)(281,753)(282,754)(283,755)(284,756)(285,758)(286,757)(287,760)
(288,759)(289,778)(290,777)(291,780)(292,779)(293,781)(294,782)(295,783)
(296,784)(297,769)(298,770)(299,771)(300,772)(301,774)(302,773)(303,776)
(304,775)(305,794)(306,793)(307,796)(308,795)(309,797)(310,798)(311,799)
(312,800)(313,785)(314,786)(315,787)(316,788)(317,790)(318,789)(319,792)
(320,791)(321,810)(322,809)(323,812)(324,811)(325,813)(326,814)(327,815)
(328,816)(329,801)(330,802)(331,803)(332,804)(333,806)(334,805)(335,808)
(336,807)(337,826)(338,825)(339,828)(340,827)(341,829)(342,830)(343,831)
(344,832)(345,817)(346,818)(347,819)(348,820)(349,822)(350,821)(351,824)
(352,823)(353,842)(354,841)(355,844)(356,843)(357,845)(358,846)(359,847)
(360,848)(361,833)(362,834)(363,835)(364,836)(365,838)(366,837)(367,840)
(368,839)(369,858)(370,857)(371,860)(372,859)(373,861)(374,862)(375,863)
(376,864)(377,849)(378,850)(379,851)(380,852)(381,854)(382,853)(383,856)
(384,855)(385,874)(386,873)(387,876)(388,875)(389,877)(390,878)(391,879)
(392,880)(393,865)(394,866)(395,867)(396,868)(397,870)(398,869)(399,872)
(400,871)(401,890)(402,889)(403,892)(404,891)(405,893)(406,894)(407,895)
(408,896)(409,881)(410,882)(411,883)(412,884)(413,886)(414,885)(415,888)
(416,887)(417,906)(418,905)(419,908)(420,907)(421,909)(422,910)(423,911)
(424,912)(425,897)(426,898)(427,899)(428,900)(429,902)(430,901)(431,904)
(432,903)(433,922)(434,921)(435,924)(436,923)(437,925)(438,926)(439,927)
(440,928)(441,913)(442,914)(443,915)(444,916)(445,918)(446,917)(447,920)
(448,919)(449,938)(450,937)(451,940)(452,939)(453,941)(454,942)(455,943)
(456,944)(457,929)(458,930)(459,931)(460,932)(461,934)(462,933)(463,936)
(464,935)(465,954)(466,953)(467,956)(468,955)(469,957)(470,958)(471,959)
(472,960)(473,945)(474,946)(475,947)(476,948)(477,950)(478,949)(479,952)
(480,951);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*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*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope