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Polytope of Type {60,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,8}*1920f
if this polytope has a name.
Group : SmallGroup(1920,239469)
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
   Self-Petrie
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 : {60,4}*960b, {30,8}*960c
   4-fold quotients : {60,4}*480b, {60,4}*480c, {30,4}*480
   5-fold quotients : {12,8}*384f
   8-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192b, {6,8}*192c
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   24-fold quotients : {20,2}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {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
   120-fold quotients : {4,2}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,481)(  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, 49)(  2, 50)(  3, 55)(  4, 56)(  5, 54)(  6, 53)(  7, 51)(  8, 52)
(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)( 24, 76)
( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)
( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)( 40, 60)
( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)( 88, 92)
( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)(104,116)
(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)(125,174)
(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)(133,166)
(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)(141,198)
(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)(149,190)
(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)(157,182)
(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)(205,214)
(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)(221,238)
(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,409)(242,410)
(243,415)(244,416)(245,414)(246,413)(247,411)(248,412)(249,401)(250,402)
(251,407)(252,408)(253,406)(254,405)(255,403)(256,404)(257,433)(258,434)
(259,439)(260,440)(261,438)(262,437)(263,435)(264,436)(265,425)(266,426)
(267,431)(268,432)(269,430)(270,429)(271,427)(272,428)(273,417)(274,418)
(275,423)(276,424)(277,422)(278,421)(279,419)(280,420)(281,369)(282,370)
(283,375)(284,376)(285,374)(286,373)(287,371)(288,372)(289,361)(290,362)
(291,367)(292,368)(293,366)(294,365)(295,363)(296,364)(297,393)(298,394)
(299,399)(300,400)(301,398)(302,397)(303,395)(304,396)(305,385)(306,386)
(307,391)(308,392)(309,390)(310,389)(311,387)(312,388)(313,377)(314,378)
(315,383)(316,384)(317,382)(318,381)(319,379)(320,380)(321,449)(322,450)
(323,455)(324,456)(325,454)(326,453)(327,451)(328,452)(329,441)(330,442)
(331,447)(332,448)(333,446)(334,445)(335,443)(336,444)(337,473)(338,474)
(339,479)(340,480)(341,478)(342,477)(343,475)(344,476)(345,465)(346,466)
(347,471)(348,472)(349,470)(350,469)(351,467)(352,468)(353,457)(354,458)
(355,463)(356,464)(357,462)(358,461)(359,459)(360,460)(481,649)(482,650)
(483,655)(484,656)(485,654)(486,653)(487,651)(488,652)(489,641)(490,642)
(491,647)(492,648)(493,646)(494,645)(495,643)(496,644)(497,673)(498,674)
(499,679)(500,680)(501,678)(502,677)(503,675)(504,676)(505,665)(506,666)
(507,671)(508,672)(509,670)(510,669)(511,667)(512,668)(513,657)(514,658)
(515,663)(516,664)(517,662)(518,661)(519,659)(520,660)(521,609)(522,610)
(523,615)(524,616)(525,614)(526,613)(527,611)(528,612)(529,601)(530,602)
(531,607)(532,608)(533,606)(534,605)(535,603)(536,604)(537,633)(538,634)
(539,639)(540,640)(541,638)(542,637)(543,635)(544,636)(545,625)(546,626)
(547,631)(548,632)(549,630)(550,629)(551,627)(552,628)(553,617)(554,618)
(555,623)(556,624)(557,622)(558,621)(559,619)(560,620)(561,689)(562,690)
(563,695)(564,696)(565,694)(566,693)(567,691)(568,692)(569,681)(570,682)
(571,687)(572,688)(573,686)(574,685)(575,683)(576,684)(577,713)(578,714)
(579,719)(580,720)(581,718)(582,717)(583,715)(584,716)(585,705)(586,706)
(587,711)(588,712)(589,710)(590,709)(591,707)(592,708)(593,697)(594,698)
(595,703)(596,704)(597,702)(598,701)(599,699)(600,700)(721,769)(722,770)
(723,775)(724,776)(725,774)(726,773)(727,771)(728,772)(729,761)(730,762)
(731,767)(732,768)(733,766)(734,765)(735,763)(736,764)(737,793)(738,794)
(739,799)(740,800)(741,798)(742,797)(743,795)(744,796)(745,785)(746,786)
(747,791)(748,792)(749,790)(750,789)(751,787)(752,788)(753,777)(754,778)
(755,783)(756,784)(757,782)(758,781)(759,779)(760,780)(801,809)(802,810)
(803,815)(804,816)(805,814)(806,813)(807,811)(808,812)(817,833)(818,834)
(819,839)(820,840)(821,838)(822,837)(823,835)(824,836)(827,831)(828,832)
(829,830)(841,889)(842,890)(843,895)(844,896)(845,894)(846,893)(847,891)
(848,892)(849,881)(850,882)(851,887)(852,888)(853,886)(854,885)(855,883)
(856,884)(857,913)(858,914)(859,919)(860,920)(861,918)(862,917)(863,915)
(864,916)(865,905)(866,906)(867,911)(868,912)(869,910)(870,909)(871,907)
(872,908)(873,897)(874,898)(875,903)(876,904)(877,902)(878,901)(879,899)
(880,900)(921,929)(922,930)(923,935)(924,936)(925,934)(926,933)(927,931)
(928,932)(937,953)(938,954)(939,959)(940,960)(941,958)(942,957)(943,955)
(944,956)(947,951)(948,952)(949,950);;
s2 := (  1,723)(  2,724)(  3,722)(  4,721)(  5,727)(  6,728)(  7,726)(  8,725)
(  9,731)( 10,732)( 11,730)( 12,729)( 13,735)( 14,736)( 15,734)( 16,733)
( 17,739)( 18,740)( 19,738)( 20,737)( 21,743)( 22,744)( 23,742)( 24,741)
( 25,747)( 26,748)( 27,746)( 28,745)( 29,751)( 30,752)( 31,750)( 32,749)
( 33,755)( 34,756)( 35,754)( 36,753)( 37,759)( 38,760)( 39,758)( 40,757)
( 41,763)( 42,764)( 43,762)( 44,761)( 45,767)( 46,768)( 47,766)( 48,765)
( 49,771)( 50,772)( 51,770)( 52,769)( 53,775)( 54,776)( 55,774)( 56,773)
( 57,779)( 58,780)( 59,778)( 60,777)( 61,783)( 62,784)( 63,782)( 64,781)
( 65,787)( 66,788)( 67,786)( 68,785)( 69,791)( 70,792)( 71,790)( 72,789)
( 73,795)( 74,796)( 75,794)( 76,793)( 77,799)( 78,800)( 79,798)( 80,797)
( 81,803)( 82,804)( 83,802)( 84,801)( 85,807)( 86,808)( 87,806)( 88,805)
( 89,811)( 90,812)( 91,810)( 92,809)( 93,815)( 94,816)( 95,814)( 96,813)
( 97,819)( 98,820)( 99,818)(100,817)(101,823)(102,824)(103,822)(104,821)
(105,827)(106,828)(107,826)(108,825)(109,831)(110,832)(111,830)(112,829)
(113,835)(114,836)(115,834)(116,833)(117,839)(118,840)(119,838)(120,837)
(121,843)(122,844)(123,842)(124,841)(125,847)(126,848)(127,846)(128,845)
(129,851)(130,852)(131,850)(132,849)(133,855)(134,856)(135,854)(136,853)
(137,859)(138,860)(139,858)(140,857)(141,863)(142,864)(143,862)(144,861)
(145,867)(146,868)(147,866)(148,865)(149,871)(150,872)(151,870)(152,869)
(153,875)(154,876)(155,874)(156,873)(157,879)(158,880)(159,878)(160,877)
(161,883)(162,884)(163,882)(164,881)(165,887)(166,888)(167,886)(168,885)
(169,891)(170,892)(171,890)(172,889)(173,895)(174,896)(175,894)(176,893)
(177,899)(178,900)(179,898)(180,897)(181,903)(182,904)(183,902)(184,901)
(185,907)(186,908)(187,906)(188,905)(189,911)(190,912)(191,910)(192,909)
(193,915)(194,916)(195,914)(196,913)(197,919)(198,920)(199,918)(200,917)
(201,923)(202,924)(203,922)(204,921)(205,927)(206,928)(207,926)(208,925)
(209,931)(210,932)(211,930)(212,929)(213,935)(214,936)(215,934)(216,933)
(217,939)(218,940)(219,938)(220,937)(221,943)(222,944)(223,942)(224,941)
(225,947)(226,948)(227,946)(228,945)(229,951)(230,952)(231,950)(232,949)
(233,955)(234,956)(235,954)(236,953)(237,959)(238,960)(239,958)(240,957)
(241,604)(242,603)(243,601)(244,602)(245,608)(246,607)(247,605)(248,606)
(249,612)(250,611)(251,609)(252,610)(253,616)(254,615)(255,613)(256,614)
(257,620)(258,619)(259,617)(260,618)(261,624)(262,623)(263,621)(264,622)
(265,628)(266,627)(267,625)(268,626)(269,632)(270,631)(271,629)(272,630)
(273,636)(274,635)(275,633)(276,634)(277,640)(278,639)(279,637)(280,638)
(281,644)(282,643)(283,641)(284,642)(285,648)(286,647)(287,645)(288,646)
(289,652)(290,651)(291,649)(292,650)(293,656)(294,655)(295,653)(296,654)
(297,660)(298,659)(299,657)(300,658)(301,664)(302,663)(303,661)(304,662)
(305,668)(306,667)(307,665)(308,666)(309,672)(310,671)(311,669)(312,670)
(313,676)(314,675)(315,673)(316,674)(317,680)(318,679)(319,677)(320,678)
(321,684)(322,683)(323,681)(324,682)(325,688)(326,687)(327,685)(328,686)
(329,692)(330,691)(331,689)(332,690)(333,696)(334,695)(335,693)(336,694)
(337,700)(338,699)(339,697)(340,698)(341,704)(342,703)(343,701)(344,702)
(345,708)(346,707)(347,705)(348,706)(349,712)(350,711)(351,709)(352,710)
(353,716)(354,715)(355,713)(356,714)(357,720)(358,719)(359,717)(360,718)
(361,484)(362,483)(363,481)(364,482)(365,488)(366,487)(367,485)(368,486)
(369,492)(370,491)(371,489)(372,490)(373,496)(374,495)(375,493)(376,494)
(377,500)(378,499)(379,497)(380,498)(381,504)(382,503)(383,501)(384,502)
(385,508)(386,507)(387,505)(388,506)(389,512)(390,511)(391,509)(392,510)
(393,516)(394,515)(395,513)(396,514)(397,520)(398,519)(399,517)(400,518)
(401,524)(402,523)(403,521)(404,522)(405,528)(406,527)(407,525)(408,526)
(409,532)(410,531)(411,529)(412,530)(413,536)(414,535)(415,533)(416,534)
(417,540)(418,539)(419,537)(420,538)(421,544)(422,543)(423,541)(424,542)
(425,548)(426,547)(427,545)(428,546)(429,552)(430,551)(431,549)(432,550)
(433,556)(434,555)(435,553)(436,554)(437,560)(438,559)(439,557)(440,558)
(441,564)(442,563)(443,561)(444,562)(445,568)(446,567)(447,565)(448,566)
(449,572)(450,571)(451,569)(452,570)(453,576)(454,575)(455,573)(456,574)
(457,580)(458,579)(459,577)(460,578)(461,584)(462,583)(463,581)(464,582)
(465,588)(466,587)(467,585)(468,586)(469,592)(470,591)(471,589)(472,590)
(473,596)(474,595)(475,593)(476,594)(477,600)(478,599)(479,597)(480,598);;
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*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*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*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, 49)(  2, 50)(  3, 55)(  4, 56)(  5, 54)(  6, 53)(  7, 51)
(  8, 52)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)
( 24, 76)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)
( 32, 68)( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)
( 40, 60)( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)
( 88, 92)( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)
(104,116)(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)
(125,174)(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)
(133,166)(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)
(141,198)(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)
(149,190)(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)
(157,182)(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)
(205,214)(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)
(221,238)(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,409)
(242,410)(243,415)(244,416)(245,414)(246,413)(247,411)(248,412)(249,401)
(250,402)(251,407)(252,408)(253,406)(254,405)(255,403)(256,404)(257,433)
(258,434)(259,439)(260,440)(261,438)(262,437)(263,435)(264,436)(265,425)
(266,426)(267,431)(268,432)(269,430)(270,429)(271,427)(272,428)(273,417)
(274,418)(275,423)(276,424)(277,422)(278,421)(279,419)(280,420)(281,369)
(282,370)(283,375)(284,376)(285,374)(286,373)(287,371)(288,372)(289,361)
(290,362)(291,367)(292,368)(293,366)(294,365)(295,363)(296,364)(297,393)
(298,394)(299,399)(300,400)(301,398)(302,397)(303,395)(304,396)(305,385)
(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)(312,388)(313,377)
(314,378)(315,383)(316,384)(317,382)(318,381)(319,379)(320,380)(321,449)
(322,450)(323,455)(324,456)(325,454)(326,453)(327,451)(328,452)(329,441)
(330,442)(331,447)(332,448)(333,446)(334,445)(335,443)(336,444)(337,473)
(338,474)(339,479)(340,480)(341,478)(342,477)(343,475)(344,476)(345,465)
(346,466)(347,471)(348,472)(349,470)(350,469)(351,467)(352,468)(353,457)
(354,458)(355,463)(356,464)(357,462)(358,461)(359,459)(360,460)(481,649)
(482,650)(483,655)(484,656)(485,654)(486,653)(487,651)(488,652)(489,641)
(490,642)(491,647)(492,648)(493,646)(494,645)(495,643)(496,644)(497,673)
(498,674)(499,679)(500,680)(501,678)(502,677)(503,675)(504,676)(505,665)
(506,666)(507,671)(508,672)(509,670)(510,669)(511,667)(512,668)(513,657)
(514,658)(515,663)(516,664)(517,662)(518,661)(519,659)(520,660)(521,609)
(522,610)(523,615)(524,616)(525,614)(526,613)(527,611)(528,612)(529,601)
(530,602)(531,607)(532,608)(533,606)(534,605)(535,603)(536,604)(537,633)
(538,634)(539,639)(540,640)(541,638)(542,637)(543,635)(544,636)(545,625)
(546,626)(547,631)(548,632)(549,630)(550,629)(551,627)(552,628)(553,617)
(554,618)(555,623)(556,624)(557,622)(558,621)(559,619)(560,620)(561,689)
(562,690)(563,695)(564,696)(565,694)(566,693)(567,691)(568,692)(569,681)
(570,682)(571,687)(572,688)(573,686)(574,685)(575,683)(576,684)(577,713)
(578,714)(579,719)(580,720)(581,718)(582,717)(583,715)(584,716)(585,705)
(586,706)(587,711)(588,712)(589,710)(590,709)(591,707)(592,708)(593,697)
(594,698)(595,703)(596,704)(597,702)(598,701)(599,699)(600,700)(721,769)
(722,770)(723,775)(724,776)(725,774)(726,773)(727,771)(728,772)(729,761)
(730,762)(731,767)(732,768)(733,766)(734,765)(735,763)(736,764)(737,793)
(738,794)(739,799)(740,800)(741,798)(742,797)(743,795)(744,796)(745,785)
(746,786)(747,791)(748,792)(749,790)(750,789)(751,787)(752,788)(753,777)
(754,778)(755,783)(756,784)(757,782)(758,781)(759,779)(760,780)(801,809)
(802,810)(803,815)(804,816)(805,814)(806,813)(807,811)(808,812)(817,833)
(818,834)(819,839)(820,840)(821,838)(822,837)(823,835)(824,836)(827,831)
(828,832)(829,830)(841,889)(842,890)(843,895)(844,896)(845,894)(846,893)
(847,891)(848,892)(849,881)(850,882)(851,887)(852,888)(853,886)(854,885)
(855,883)(856,884)(857,913)(858,914)(859,919)(860,920)(861,918)(862,917)
(863,915)(864,916)(865,905)(866,906)(867,911)(868,912)(869,910)(870,909)
(871,907)(872,908)(873,897)(874,898)(875,903)(876,904)(877,902)(878,901)
(879,899)(880,900)(921,929)(922,930)(923,935)(924,936)(925,934)(926,933)
(927,931)(928,932)(937,953)(938,954)(939,959)(940,960)(941,958)(942,957)
(943,955)(944,956)(947,951)(948,952)(949,950);
s2 := Sym(960)!(  1,723)(  2,724)(  3,722)(  4,721)(  5,727)(  6,728)(  7,726)
(  8,725)(  9,731)( 10,732)( 11,730)( 12,729)( 13,735)( 14,736)( 15,734)
( 16,733)( 17,739)( 18,740)( 19,738)( 20,737)( 21,743)( 22,744)( 23,742)
( 24,741)( 25,747)( 26,748)( 27,746)( 28,745)( 29,751)( 30,752)( 31,750)
( 32,749)( 33,755)( 34,756)( 35,754)( 36,753)( 37,759)( 38,760)( 39,758)
( 40,757)( 41,763)( 42,764)( 43,762)( 44,761)( 45,767)( 46,768)( 47,766)
( 48,765)( 49,771)( 50,772)( 51,770)( 52,769)( 53,775)( 54,776)( 55,774)
( 56,773)( 57,779)( 58,780)( 59,778)( 60,777)( 61,783)( 62,784)( 63,782)
( 64,781)( 65,787)( 66,788)( 67,786)( 68,785)( 69,791)( 70,792)( 71,790)
( 72,789)( 73,795)( 74,796)( 75,794)( 76,793)( 77,799)( 78,800)( 79,798)
( 80,797)( 81,803)( 82,804)( 83,802)( 84,801)( 85,807)( 86,808)( 87,806)
( 88,805)( 89,811)( 90,812)( 91,810)( 92,809)( 93,815)( 94,816)( 95,814)
( 96,813)( 97,819)( 98,820)( 99,818)(100,817)(101,823)(102,824)(103,822)
(104,821)(105,827)(106,828)(107,826)(108,825)(109,831)(110,832)(111,830)
(112,829)(113,835)(114,836)(115,834)(116,833)(117,839)(118,840)(119,838)
(120,837)(121,843)(122,844)(123,842)(124,841)(125,847)(126,848)(127,846)
(128,845)(129,851)(130,852)(131,850)(132,849)(133,855)(134,856)(135,854)
(136,853)(137,859)(138,860)(139,858)(140,857)(141,863)(142,864)(143,862)
(144,861)(145,867)(146,868)(147,866)(148,865)(149,871)(150,872)(151,870)
(152,869)(153,875)(154,876)(155,874)(156,873)(157,879)(158,880)(159,878)
(160,877)(161,883)(162,884)(163,882)(164,881)(165,887)(166,888)(167,886)
(168,885)(169,891)(170,892)(171,890)(172,889)(173,895)(174,896)(175,894)
(176,893)(177,899)(178,900)(179,898)(180,897)(181,903)(182,904)(183,902)
(184,901)(185,907)(186,908)(187,906)(188,905)(189,911)(190,912)(191,910)
(192,909)(193,915)(194,916)(195,914)(196,913)(197,919)(198,920)(199,918)
(200,917)(201,923)(202,924)(203,922)(204,921)(205,927)(206,928)(207,926)
(208,925)(209,931)(210,932)(211,930)(212,929)(213,935)(214,936)(215,934)
(216,933)(217,939)(218,940)(219,938)(220,937)(221,943)(222,944)(223,942)
(224,941)(225,947)(226,948)(227,946)(228,945)(229,951)(230,952)(231,950)
(232,949)(233,955)(234,956)(235,954)(236,953)(237,959)(238,960)(239,958)
(240,957)(241,604)(242,603)(243,601)(244,602)(245,608)(246,607)(247,605)
(248,606)(249,612)(250,611)(251,609)(252,610)(253,616)(254,615)(255,613)
(256,614)(257,620)(258,619)(259,617)(260,618)(261,624)(262,623)(263,621)
(264,622)(265,628)(266,627)(267,625)(268,626)(269,632)(270,631)(271,629)
(272,630)(273,636)(274,635)(275,633)(276,634)(277,640)(278,639)(279,637)
(280,638)(281,644)(282,643)(283,641)(284,642)(285,648)(286,647)(287,645)
(288,646)(289,652)(290,651)(291,649)(292,650)(293,656)(294,655)(295,653)
(296,654)(297,660)(298,659)(299,657)(300,658)(301,664)(302,663)(303,661)
(304,662)(305,668)(306,667)(307,665)(308,666)(309,672)(310,671)(311,669)
(312,670)(313,676)(314,675)(315,673)(316,674)(317,680)(318,679)(319,677)
(320,678)(321,684)(322,683)(323,681)(324,682)(325,688)(326,687)(327,685)
(328,686)(329,692)(330,691)(331,689)(332,690)(333,696)(334,695)(335,693)
(336,694)(337,700)(338,699)(339,697)(340,698)(341,704)(342,703)(343,701)
(344,702)(345,708)(346,707)(347,705)(348,706)(349,712)(350,711)(351,709)
(352,710)(353,716)(354,715)(355,713)(356,714)(357,720)(358,719)(359,717)
(360,718)(361,484)(362,483)(363,481)(364,482)(365,488)(366,487)(367,485)
(368,486)(369,492)(370,491)(371,489)(372,490)(373,496)(374,495)(375,493)
(376,494)(377,500)(378,499)(379,497)(380,498)(381,504)(382,503)(383,501)
(384,502)(385,508)(386,507)(387,505)(388,506)(389,512)(390,511)(391,509)
(392,510)(393,516)(394,515)(395,513)(396,514)(397,520)(398,519)(399,517)
(400,518)(401,524)(402,523)(403,521)(404,522)(405,528)(406,527)(407,525)
(408,526)(409,532)(410,531)(411,529)(412,530)(413,536)(414,535)(415,533)
(416,534)(417,540)(418,539)(419,537)(420,538)(421,544)(422,543)(423,541)
(424,542)(425,548)(426,547)(427,545)(428,546)(429,552)(430,551)(431,549)
(432,550)(433,556)(434,555)(435,553)(436,554)(437,560)(438,559)(439,557)
(440,558)(441,564)(442,563)(443,561)(444,562)(445,568)(446,567)(447,565)
(448,566)(449,572)(450,571)(451,569)(452,570)(453,576)(454,575)(455,573)
(456,574)(457,580)(458,579)(459,577)(460,578)(461,584)(462,583)(463,581)
(464,582)(465,588)(466,587)(467,585)(468,586)(469,592)(470,591)(471,589)
(472,590)(473,596)(474,595)(475,593)(476,594)(477,600)(478,599)(479,597)
(480,598);
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope