Questions?
See the FAQ
or other info.

Polytope of Type {60,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,8}*1920h
if this polytope has a name.
Group : SmallGroup(1920,239511)
Rank : 3
Schlafli Type : {60,8}
Number of vertices, edges, etc : 120, 480, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {60,4}*960c, {30,8}*960b
   4-fold quotients : {15,8}*480, {30,4}*480
   5-fold quotients : {12,8}*384h
   8-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192c, {6,8}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {3,8}*96, {6,4}*96
   32-fold quotients : {15,2}*60
   40-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   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 := (  1,481)(  2,482)(  3,484)(  4,483)(  5,487)(  6,488)(  7,485)(  8,486)
(  9,513)( 10,514)( 11,516)( 12,515)( 13,519)( 14,520)( 15,517)( 16,518)
( 17,505)( 18,506)( 19,508)( 20,507)( 21,511)( 22,512)( 23,509)( 24,510)
( 25,497)( 26,498)( 27,500)( 28,499)( 29,503)( 30,504)( 31,501)( 32,502)
( 33,489)( 34,490)( 35,492)( 36,491)( 37,495)( 38,496)( 39,493)( 40,494)
( 41,561)( 42,562)( 43,564)( 44,563)( 45,567)( 46,568)( 47,565)( 48,566)
( 49,593)( 50,594)( 51,596)( 52,595)( 53,599)( 54,600)( 55,597)( 56,598)
( 57,585)( 58,586)( 59,588)( 60,587)( 61,591)( 62,592)( 63,589)( 64,590)
( 65,577)( 66,578)( 67,580)( 68,579)( 69,583)( 70,584)( 71,581)( 72,582)
( 73,569)( 74,570)( 75,572)( 76,571)( 77,575)( 78,576)( 79,573)( 80,574)
( 81,521)( 82,522)( 83,524)( 84,523)( 85,527)( 86,528)( 87,525)( 88,526)
( 89,553)( 90,554)( 91,556)( 92,555)( 93,559)( 94,560)( 95,557)( 96,558)
( 97,545)( 98,546)( 99,548)(100,547)(101,551)(102,552)(103,549)(104,550)
(105,537)(106,538)(107,540)(108,539)(109,543)(110,544)(111,541)(112,542)
(113,529)(114,530)(115,532)(116,531)(117,535)(118,536)(119,533)(120,534)
(121,601)(122,602)(123,604)(124,603)(125,607)(126,608)(127,605)(128,606)
(129,633)(130,634)(131,636)(132,635)(133,639)(134,640)(135,637)(136,638)
(137,625)(138,626)(139,628)(140,627)(141,631)(142,632)(143,629)(144,630)
(145,617)(146,618)(147,620)(148,619)(149,623)(150,624)(151,621)(152,622)
(153,609)(154,610)(155,612)(156,611)(157,615)(158,616)(159,613)(160,614)
(161,681)(162,682)(163,684)(164,683)(165,687)(166,688)(167,685)(168,686)
(169,713)(170,714)(171,716)(172,715)(173,719)(174,720)(175,717)(176,718)
(177,705)(178,706)(179,708)(180,707)(181,711)(182,712)(183,709)(184,710)
(185,697)(186,698)(187,700)(188,699)(189,703)(190,704)(191,701)(192,702)
(193,689)(194,690)(195,692)(196,691)(197,695)(198,696)(199,693)(200,694)
(201,641)(202,642)(203,644)(204,643)(205,647)(206,648)(207,645)(208,646)
(209,673)(210,674)(211,676)(212,675)(213,679)(214,680)(215,677)(216,678)
(217,665)(218,666)(219,668)(220,667)(221,671)(222,672)(223,669)(224,670)
(225,657)(226,658)(227,660)(228,659)(229,663)(230,664)(231,661)(232,662)
(233,649)(234,650)(235,652)(236,651)(237,655)(238,656)(239,653)(240,654)
(241,842)(242,841)(243,843)(244,844)(245,848)(246,847)(247,846)(248,845)
(249,874)(250,873)(251,875)(252,876)(253,880)(254,879)(255,878)(256,877)
(257,866)(258,865)(259,867)(260,868)(261,872)(262,871)(263,870)(264,869)
(265,858)(266,857)(267,859)(268,860)(269,864)(270,863)(271,862)(272,861)
(273,850)(274,849)(275,851)(276,852)(277,856)(278,855)(279,854)(280,853)
(281,922)(282,921)(283,923)(284,924)(285,928)(286,927)(287,926)(288,925)
(289,954)(290,953)(291,955)(292,956)(293,960)(294,959)(295,958)(296,957)
(297,946)(298,945)(299,947)(300,948)(301,952)(302,951)(303,950)(304,949)
(305,938)(306,937)(307,939)(308,940)(309,944)(310,943)(311,942)(312,941)
(313,930)(314,929)(315,931)(316,932)(317,936)(318,935)(319,934)(320,933)
(321,882)(322,881)(323,883)(324,884)(325,888)(326,887)(327,886)(328,885)
(329,914)(330,913)(331,915)(332,916)(333,920)(334,919)(335,918)(336,917)
(337,906)(338,905)(339,907)(340,908)(341,912)(342,911)(343,910)(344,909)
(345,898)(346,897)(347,899)(348,900)(349,904)(350,903)(351,902)(352,901)
(353,890)(354,889)(355,891)(356,892)(357,896)(358,895)(359,894)(360,893)
(361,722)(362,721)(363,723)(364,724)(365,728)(366,727)(367,726)(368,725)
(369,754)(370,753)(371,755)(372,756)(373,760)(374,759)(375,758)(376,757)
(377,746)(378,745)(379,747)(380,748)(381,752)(382,751)(383,750)(384,749)
(385,738)(386,737)(387,739)(388,740)(389,744)(390,743)(391,742)(392,741)
(393,730)(394,729)(395,731)(396,732)(397,736)(398,735)(399,734)(400,733)
(401,802)(402,801)(403,803)(404,804)(405,808)(406,807)(407,806)(408,805)
(409,834)(410,833)(411,835)(412,836)(413,840)(414,839)(415,838)(416,837)
(417,826)(418,825)(419,827)(420,828)(421,832)(422,831)(423,830)(424,829)
(425,818)(426,817)(427,819)(428,820)(429,824)(430,823)(431,822)(432,821)
(433,810)(434,809)(435,811)(436,812)(437,816)(438,815)(439,814)(440,813)
(441,762)(442,761)(443,763)(444,764)(445,768)(446,767)(447,766)(448,765)
(449,794)(450,793)(451,795)(452,796)(453,800)(454,799)(455,798)(456,797)
(457,786)(458,785)(459,787)(460,788)(461,792)(462,791)(463,790)(464,789)
(465,778)(466,777)(467,779)(468,780)(469,784)(470,783)(471,782)(472,781)
(473,770)(474,769)(475,771)(476,772)(477,776)(478,775)(479,774)(480,773);;
s1 := (  1,289)(  2,290)(  3,295)(  4,296)(  5,294)(  6,293)(  7,291)(  8,292)
(  9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)( 16,284)
( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)( 24,316)
( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)( 32,308)
( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)( 40,300)
( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)( 48,252)
( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)( 56,244)
( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)( 64,276)
( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)( 72,268)
( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)( 80,260)
( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)( 88,332)
( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)( 96,324)
( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)(104,356)
(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)(112,348)
(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)(120,340)
(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)(128,412)
(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)(136,404)
(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)(144,436)
(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)(152,428)
(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)(160,420)
(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)(168,372)
(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)(176,364)
(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)(184,396)
(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)(192,388)
(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)(200,380)
(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)(208,452)
(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)(216,444)
(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)(224,476)
(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)(232,468)
(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)(240,460)
(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)(488,771)
(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)(496,763)
(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)(504,795)
(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)(512,787)
(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)(520,779)
(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)(528,731)
(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)(536,723)
(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)(544,755)
(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)(552,747)
(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)(560,739)
(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)(568,811)
(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)(576,803)
(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)(584,835)
(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)(592,827)
(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)(600,819)
(601,890)(602,889)(603,896)(604,895)(605,893)(606,894)(607,892)(608,891)
(609,882)(610,881)(611,888)(612,887)(613,885)(614,886)(615,884)(616,883)
(617,914)(618,913)(619,920)(620,919)(621,917)(622,918)(623,916)(624,915)
(625,906)(626,905)(627,912)(628,911)(629,909)(630,910)(631,908)(632,907)
(633,898)(634,897)(635,904)(636,903)(637,901)(638,902)(639,900)(640,899)
(641,850)(642,849)(643,856)(644,855)(645,853)(646,854)(647,852)(648,851)
(649,842)(650,841)(651,848)(652,847)(653,845)(654,846)(655,844)(656,843)
(657,874)(658,873)(659,880)(660,879)(661,877)(662,878)(663,876)(664,875)
(665,866)(666,865)(667,872)(668,871)(669,869)(670,870)(671,868)(672,867)
(673,858)(674,857)(675,864)(676,863)(677,861)(678,862)(679,860)(680,859)
(681,930)(682,929)(683,936)(684,935)(685,933)(686,934)(687,932)(688,931)
(689,922)(690,921)(691,928)(692,927)(693,925)(694,926)(695,924)(696,923)
(697,954)(698,953)(699,960)(700,959)(701,957)(702,958)(703,956)(704,955)
(705,946)(706,945)(707,952)(708,951)(709,949)(710,950)(711,948)(712,947)
(713,938)(714,937)(715,944)(716,943)(717,941)(718,942)(719,940)(720,939);;
s2 := (  1,483)(  2,484)(  3,482)(  4,481)(  5,487)(  6,488)(  7,486)(  8,485)
(  9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)( 16,493)
( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)( 24,501)
( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)( 32,509)
( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)( 40,517)
( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)( 48,525)
( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)( 56,533)
( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)( 64,541)
( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)( 72,549)
( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)( 80,557)
( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)( 88,565)
( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)( 96,573)
( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)(104,581)
(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)(112,589)
(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)(120,597)
(121,603)(122,604)(123,602)(124,601)(125,607)(126,608)(127,606)(128,605)
(129,611)(130,612)(131,610)(132,609)(133,615)(134,616)(135,614)(136,613)
(137,619)(138,620)(139,618)(140,617)(141,623)(142,624)(143,622)(144,621)
(145,627)(146,628)(147,626)(148,625)(149,631)(150,632)(151,630)(152,629)
(153,635)(154,636)(155,634)(156,633)(157,639)(158,640)(159,638)(160,637)
(161,643)(162,644)(163,642)(164,641)(165,647)(166,648)(167,646)(168,645)
(169,651)(170,652)(171,650)(172,649)(173,655)(174,656)(175,654)(176,653)
(177,659)(178,660)(179,658)(180,657)(181,663)(182,664)(183,662)(184,661)
(185,667)(186,668)(187,666)(188,665)(189,671)(190,672)(191,670)(192,669)
(193,675)(194,676)(195,674)(196,673)(197,679)(198,680)(199,678)(200,677)
(201,683)(202,684)(203,682)(204,681)(205,687)(206,688)(207,686)(208,685)
(209,691)(210,692)(211,690)(212,689)(213,695)(214,696)(215,694)(216,693)
(217,699)(218,700)(219,698)(220,697)(221,703)(222,704)(223,702)(224,701)
(225,707)(226,708)(227,706)(228,705)(229,711)(230,712)(231,710)(232,709)
(233,715)(234,716)(235,714)(236,713)(237,719)(238,720)(239,718)(240,717)
(241,843)(242,844)(243,842)(244,841)(245,847)(246,848)(247,846)(248,845)
(249,851)(250,852)(251,850)(252,849)(253,855)(254,856)(255,854)(256,853)
(257,859)(258,860)(259,858)(260,857)(261,863)(262,864)(263,862)(264,861)
(265,867)(266,868)(267,866)(268,865)(269,871)(270,872)(271,870)(272,869)
(273,875)(274,876)(275,874)(276,873)(277,879)(278,880)(279,878)(280,877)
(281,883)(282,884)(283,882)(284,881)(285,887)(286,888)(287,886)(288,885)
(289,891)(290,892)(291,890)(292,889)(293,895)(294,896)(295,894)(296,893)
(297,899)(298,900)(299,898)(300,897)(301,903)(302,904)(303,902)(304,901)
(305,907)(306,908)(307,906)(308,905)(309,911)(310,912)(311,910)(312,909)
(313,915)(314,916)(315,914)(316,913)(317,919)(318,920)(319,918)(320,917)
(321,923)(322,924)(323,922)(324,921)(325,927)(326,928)(327,926)(328,925)
(329,931)(330,932)(331,930)(332,929)(333,935)(334,936)(335,934)(336,933)
(337,939)(338,940)(339,938)(340,937)(341,943)(342,944)(343,942)(344,941)
(345,947)(346,948)(347,946)(348,945)(349,951)(350,952)(351,950)(352,949)
(353,955)(354,956)(355,954)(356,953)(357,959)(358,960)(359,958)(360,957)
(361,723)(362,724)(363,722)(364,721)(365,727)(366,728)(367,726)(368,725)
(369,731)(370,732)(371,730)(372,729)(373,735)(374,736)(375,734)(376,733)
(377,739)(378,740)(379,738)(380,737)(381,743)(382,744)(383,742)(384,741)
(385,747)(386,748)(387,746)(388,745)(389,751)(390,752)(391,750)(392,749)
(393,755)(394,756)(395,754)(396,753)(397,759)(398,760)(399,758)(400,757)
(401,763)(402,764)(403,762)(404,761)(405,767)(406,768)(407,766)(408,765)
(409,771)(410,772)(411,770)(412,769)(413,775)(414,776)(415,774)(416,773)
(417,779)(418,780)(419,778)(420,777)(421,783)(422,784)(423,782)(424,781)
(425,787)(426,788)(427,786)(428,785)(429,791)(430,792)(431,790)(432,789)
(433,795)(434,796)(435,794)(436,793)(437,799)(438,800)(439,798)(440,797)
(441,803)(442,804)(443,802)(444,801)(445,807)(446,808)(447,806)(448,805)
(449,811)(450,812)(451,810)(452,809)(453,815)(454,816)(455,814)(456,813)
(457,819)(458,820)(459,818)(460,817)(461,823)(462,824)(463,822)(464,821)
(465,827)(466,828)(467,826)(468,825)(469,831)(470,832)(471,830)(472,829)
(473,835)(474,836)(475,834)(476,833)(477,839)(478,840)(479,838)(480,837);;
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2, 
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*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*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)(  2,482)(  3,484)(  4,483)(  5,487)(  6,488)(  7,485)
(  8,486)(  9,513)( 10,514)( 11,516)( 12,515)( 13,519)( 14,520)( 15,517)
( 16,518)( 17,505)( 18,506)( 19,508)( 20,507)( 21,511)( 22,512)( 23,509)
( 24,510)( 25,497)( 26,498)( 27,500)( 28,499)( 29,503)( 30,504)( 31,501)
( 32,502)( 33,489)( 34,490)( 35,492)( 36,491)( 37,495)( 38,496)( 39,493)
( 40,494)( 41,561)( 42,562)( 43,564)( 44,563)( 45,567)( 46,568)( 47,565)
( 48,566)( 49,593)( 50,594)( 51,596)( 52,595)( 53,599)( 54,600)( 55,597)
( 56,598)( 57,585)( 58,586)( 59,588)( 60,587)( 61,591)( 62,592)( 63,589)
( 64,590)( 65,577)( 66,578)( 67,580)( 68,579)( 69,583)( 70,584)( 71,581)
( 72,582)( 73,569)( 74,570)( 75,572)( 76,571)( 77,575)( 78,576)( 79,573)
( 80,574)( 81,521)( 82,522)( 83,524)( 84,523)( 85,527)( 86,528)( 87,525)
( 88,526)( 89,553)( 90,554)( 91,556)( 92,555)( 93,559)( 94,560)( 95,557)
( 96,558)( 97,545)( 98,546)( 99,548)(100,547)(101,551)(102,552)(103,549)
(104,550)(105,537)(106,538)(107,540)(108,539)(109,543)(110,544)(111,541)
(112,542)(113,529)(114,530)(115,532)(116,531)(117,535)(118,536)(119,533)
(120,534)(121,601)(122,602)(123,604)(124,603)(125,607)(126,608)(127,605)
(128,606)(129,633)(130,634)(131,636)(132,635)(133,639)(134,640)(135,637)
(136,638)(137,625)(138,626)(139,628)(140,627)(141,631)(142,632)(143,629)
(144,630)(145,617)(146,618)(147,620)(148,619)(149,623)(150,624)(151,621)
(152,622)(153,609)(154,610)(155,612)(156,611)(157,615)(158,616)(159,613)
(160,614)(161,681)(162,682)(163,684)(164,683)(165,687)(166,688)(167,685)
(168,686)(169,713)(170,714)(171,716)(172,715)(173,719)(174,720)(175,717)
(176,718)(177,705)(178,706)(179,708)(180,707)(181,711)(182,712)(183,709)
(184,710)(185,697)(186,698)(187,700)(188,699)(189,703)(190,704)(191,701)
(192,702)(193,689)(194,690)(195,692)(196,691)(197,695)(198,696)(199,693)
(200,694)(201,641)(202,642)(203,644)(204,643)(205,647)(206,648)(207,645)
(208,646)(209,673)(210,674)(211,676)(212,675)(213,679)(214,680)(215,677)
(216,678)(217,665)(218,666)(219,668)(220,667)(221,671)(222,672)(223,669)
(224,670)(225,657)(226,658)(227,660)(228,659)(229,663)(230,664)(231,661)
(232,662)(233,649)(234,650)(235,652)(236,651)(237,655)(238,656)(239,653)
(240,654)(241,842)(242,841)(243,843)(244,844)(245,848)(246,847)(247,846)
(248,845)(249,874)(250,873)(251,875)(252,876)(253,880)(254,879)(255,878)
(256,877)(257,866)(258,865)(259,867)(260,868)(261,872)(262,871)(263,870)
(264,869)(265,858)(266,857)(267,859)(268,860)(269,864)(270,863)(271,862)
(272,861)(273,850)(274,849)(275,851)(276,852)(277,856)(278,855)(279,854)
(280,853)(281,922)(282,921)(283,923)(284,924)(285,928)(286,927)(287,926)
(288,925)(289,954)(290,953)(291,955)(292,956)(293,960)(294,959)(295,958)
(296,957)(297,946)(298,945)(299,947)(300,948)(301,952)(302,951)(303,950)
(304,949)(305,938)(306,937)(307,939)(308,940)(309,944)(310,943)(311,942)
(312,941)(313,930)(314,929)(315,931)(316,932)(317,936)(318,935)(319,934)
(320,933)(321,882)(322,881)(323,883)(324,884)(325,888)(326,887)(327,886)
(328,885)(329,914)(330,913)(331,915)(332,916)(333,920)(334,919)(335,918)
(336,917)(337,906)(338,905)(339,907)(340,908)(341,912)(342,911)(343,910)
(344,909)(345,898)(346,897)(347,899)(348,900)(349,904)(350,903)(351,902)
(352,901)(353,890)(354,889)(355,891)(356,892)(357,896)(358,895)(359,894)
(360,893)(361,722)(362,721)(363,723)(364,724)(365,728)(366,727)(367,726)
(368,725)(369,754)(370,753)(371,755)(372,756)(373,760)(374,759)(375,758)
(376,757)(377,746)(378,745)(379,747)(380,748)(381,752)(382,751)(383,750)
(384,749)(385,738)(386,737)(387,739)(388,740)(389,744)(390,743)(391,742)
(392,741)(393,730)(394,729)(395,731)(396,732)(397,736)(398,735)(399,734)
(400,733)(401,802)(402,801)(403,803)(404,804)(405,808)(406,807)(407,806)
(408,805)(409,834)(410,833)(411,835)(412,836)(413,840)(414,839)(415,838)
(416,837)(417,826)(418,825)(419,827)(420,828)(421,832)(422,831)(423,830)
(424,829)(425,818)(426,817)(427,819)(428,820)(429,824)(430,823)(431,822)
(432,821)(433,810)(434,809)(435,811)(436,812)(437,816)(438,815)(439,814)
(440,813)(441,762)(442,761)(443,763)(444,764)(445,768)(446,767)(447,766)
(448,765)(449,794)(450,793)(451,795)(452,796)(453,800)(454,799)(455,798)
(456,797)(457,786)(458,785)(459,787)(460,788)(461,792)(462,791)(463,790)
(464,789)(465,778)(466,777)(467,779)(468,780)(469,784)(470,783)(471,782)
(472,781)(473,770)(474,769)(475,771)(476,772)(477,776)(478,775)(479,774)
(480,773);
s1 := Sym(960)!(  1,289)(  2,290)(  3,295)(  4,296)(  5,294)(  6,293)(  7,291)
(  8,292)(  9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)
( 16,284)( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)
( 24,316)( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)
( 32,308)( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)
( 40,300)( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)
( 48,252)( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)
( 56,244)( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)
( 64,276)( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)
( 72,268)( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)
( 80,260)( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)
( 88,332)( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)
( 96,324)( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)
(104,356)(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)
(112,348)(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)
(120,340)(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)
(128,412)(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)
(136,404)(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)
(144,436)(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)
(152,428)(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)
(160,420)(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)
(168,372)(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)
(176,364)(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)
(184,396)(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)
(192,388)(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)
(200,380)(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)
(208,452)(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)
(216,444)(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)
(224,476)(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)
(232,468)(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)
(240,460)(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)
(488,771)(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)
(496,763)(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)
(504,795)(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)
(512,787)(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)
(520,779)(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)
(528,731)(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)
(536,723)(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)
(544,755)(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)
(552,747)(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)
(560,739)(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)
(568,811)(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)
(576,803)(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)
(584,835)(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)
(592,827)(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)
(600,819)(601,890)(602,889)(603,896)(604,895)(605,893)(606,894)(607,892)
(608,891)(609,882)(610,881)(611,888)(612,887)(613,885)(614,886)(615,884)
(616,883)(617,914)(618,913)(619,920)(620,919)(621,917)(622,918)(623,916)
(624,915)(625,906)(626,905)(627,912)(628,911)(629,909)(630,910)(631,908)
(632,907)(633,898)(634,897)(635,904)(636,903)(637,901)(638,902)(639,900)
(640,899)(641,850)(642,849)(643,856)(644,855)(645,853)(646,854)(647,852)
(648,851)(649,842)(650,841)(651,848)(652,847)(653,845)(654,846)(655,844)
(656,843)(657,874)(658,873)(659,880)(660,879)(661,877)(662,878)(663,876)
(664,875)(665,866)(666,865)(667,872)(668,871)(669,869)(670,870)(671,868)
(672,867)(673,858)(674,857)(675,864)(676,863)(677,861)(678,862)(679,860)
(680,859)(681,930)(682,929)(683,936)(684,935)(685,933)(686,934)(687,932)
(688,931)(689,922)(690,921)(691,928)(692,927)(693,925)(694,926)(695,924)
(696,923)(697,954)(698,953)(699,960)(700,959)(701,957)(702,958)(703,956)
(704,955)(705,946)(706,945)(707,952)(708,951)(709,949)(710,950)(711,948)
(712,947)(713,938)(714,937)(715,944)(716,943)(717,941)(718,942)(719,940)
(720,939);
s2 := Sym(960)!(  1,483)(  2,484)(  3,482)(  4,481)(  5,487)(  6,488)(  7,486)
(  8,485)(  9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)
( 16,493)( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)
( 24,501)( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)
( 32,509)( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)
( 40,517)( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)
( 48,525)( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)
( 56,533)( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)
( 64,541)( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)
( 72,549)( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)
( 80,557)( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)
( 88,565)( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)
( 96,573)( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)
(104,581)(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)
(112,589)(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)
(120,597)(121,603)(122,604)(123,602)(124,601)(125,607)(126,608)(127,606)
(128,605)(129,611)(130,612)(131,610)(132,609)(133,615)(134,616)(135,614)
(136,613)(137,619)(138,620)(139,618)(140,617)(141,623)(142,624)(143,622)
(144,621)(145,627)(146,628)(147,626)(148,625)(149,631)(150,632)(151,630)
(152,629)(153,635)(154,636)(155,634)(156,633)(157,639)(158,640)(159,638)
(160,637)(161,643)(162,644)(163,642)(164,641)(165,647)(166,648)(167,646)
(168,645)(169,651)(170,652)(171,650)(172,649)(173,655)(174,656)(175,654)
(176,653)(177,659)(178,660)(179,658)(180,657)(181,663)(182,664)(183,662)
(184,661)(185,667)(186,668)(187,666)(188,665)(189,671)(190,672)(191,670)
(192,669)(193,675)(194,676)(195,674)(196,673)(197,679)(198,680)(199,678)
(200,677)(201,683)(202,684)(203,682)(204,681)(205,687)(206,688)(207,686)
(208,685)(209,691)(210,692)(211,690)(212,689)(213,695)(214,696)(215,694)
(216,693)(217,699)(218,700)(219,698)(220,697)(221,703)(222,704)(223,702)
(224,701)(225,707)(226,708)(227,706)(228,705)(229,711)(230,712)(231,710)
(232,709)(233,715)(234,716)(235,714)(236,713)(237,719)(238,720)(239,718)
(240,717)(241,843)(242,844)(243,842)(244,841)(245,847)(246,848)(247,846)
(248,845)(249,851)(250,852)(251,850)(252,849)(253,855)(254,856)(255,854)
(256,853)(257,859)(258,860)(259,858)(260,857)(261,863)(262,864)(263,862)
(264,861)(265,867)(266,868)(267,866)(268,865)(269,871)(270,872)(271,870)
(272,869)(273,875)(274,876)(275,874)(276,873)(277,879)(278,880)(279,878)
(280,877)(281,883)(282,884)(283,882)(284,881)(285,887)(286,888)(287,886)
(288,885)(289,891)(290,892)(291,890)(292,889)(293,895)(294,896)(295,894)
(296,893)(297,899)(298,900)(299,898)(300,897)(301,903)(302,904)(303,902)
(304,901)(305,907)(306,908)(307,906)(308,905)(309,911)(310,912)(311,910)
(312,909)(313,915)(314,916)(315,914)(316,913)(317,919)(318,920)(319,918)
(320,917)(321,923)(322,924)(323,922)(324,921)(325,927)(326,928)(327,926)
(328,925)(329,931)(330,932)(331,930)(332,929)(333,935)(334,936)(335,934)
(336,933)(337,939)(338,940)(339,938)(340,937)(341,943)(342,944)(343,942)
(344,941)(345,947)(346,948)(347,946)(348,945)(349,951)(350,952)(351,950)
(352,949)(353,955)(354,956)(355,954)(356,953)(357,959)(358,960)(359,958)
(360,957)(361,723)(362,724)(363,722)(364,721)(365,727)(366,728)(367,726)
(368,725)(369,731)(370,732)(371,730)(372,729)(373,735)(374,736)(375,734)
(376,733)(377,739)(378,740)(379,738)(380,737)(381,743)(382,744)(383,742)
(384,741)(385,747)(386,748)(387,746)(388,745)(389,751)(390,752)(391,750)
(392,749)(393,755)(394,756)(395,754)(396,753)(397,759)(398,760)(399,758)
(400,757)(401,763)(402,764)(403,762)(404,761)(405,767)(406,768)(407,766)
(408,765)(409,771)(410,772)(411,770)(412,769)(413,775)(414,776)(415,774)
(416,773)(417,779)(418,780)(419,778)(420,777)(421,783)(422,784)(423,782)
(424,781)(425,787)(426,788)(427,786)(428,785)(429,791)(430,792)(431,790)
(432,789)(433,795)(434,796)(435,794)(436,793)(437,799)(438,800)(439,798)
(440,797)(441,803)(442,804)(443,802)(444,801)(445,807)(446,808)(447,806)
(448,805)(449,811)(450,812)(451,810)(452,809)(453,815)(454,816)(455,814)
(456,813)(457,819)(458,820)(459,818)(460,817)(461,823)(462,824)(463,822)
(464,821)(465,827)(466,828)(467,826)(468,825)(469,831)(470,832)(471,830)
(472,829)(473,835)(474,836)(475,834)(476,833)(477,839)(478,840)(479,838)
(480,837);
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2, 
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*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*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