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Polytope of Type {4,10,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,4,6}*1920
Also Known As : {{4,10|2},{10,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,208118)
Rank : 5
Schlafli Type : {4,10,4,6}
Number of vertices, edges, etc : 4, 20, 20, 12, 6
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Universal
   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 : {2,10,4,6}*960, {4,10,2,6}*960
   3-fold quotients : {4,10,4,2}*640
   4-fold quotients : {4,10,2,3}*480, {2,10,2,6}*480
   5-fold quotients : {4,2,4,6}*384a
   6-fold quotients : {2,10,4,2}*320, {4,10,2,2}*320
   8-fold quotients : {2,5,2,6}*240, {2,10,2,3}*240
   10-fold quotients : {2,2,4,6}*192a, {4,2,2,6}*192
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {4,2,4,2}*128
   16-fold quotients : {2,5,2,3}*120
   20-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)
(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,541)( 62,542)( 63,543)( 64,544)
( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)( 72,552)
( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)( 80,560)
( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)( 88,568)
( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)( 96,576)
( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)(112,592)
(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)(120,600)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)(184,694)
(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)(192,702)
(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)(200,710)
(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)(208,718)
(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)(216,666)
(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)(224,674)
(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)(232,682)
(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)(240,690)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,781)(302,782)(303,783)(304,784)
(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)(312,792)
(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)(320,800)
(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)(328,808)
(329,809)(330,810)(331,811)(332,812)(333,813)(334,814)(335,815)(336,816)
(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)(344,824)
(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)(352,832)
(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)(360,840)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)(424,934)
(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)(432,942)
(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)(440,950)
(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)(448,958)
(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)(456,906)
(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)(464,914)
(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)(472,922)
(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)(480,930);;
s1 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)(  8,129)
(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)( 24,143)
( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)(248,369)
(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)(264,383)
(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)(280,397)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)(296,416)
(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)(304,423)
(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)(312,435)
(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)(328,449)
(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)(336,456)
(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)(344,463)
(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)(352,475)
(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)(360,477)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)
(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)(504,623)
(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)(520,637)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)(552,675)
(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)(568,689)
(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)(576,696)
(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)(584,703)
(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)(592,715)
(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)(600,717)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)(728,849)
(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)(744,863)
(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)(760,877)
(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)(776,896)
(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)(784,903)
(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)(792,915)
(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)(800,917)
(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)(808,929)
(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)(816,936)
(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)(824,943)
(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)(832,955)
(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)(840,957);;
s2 := (  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)(  8,130)
(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,377)(242,376)(243,380)(244,379)(245,378)(246,382)(247,381)(248,385)
(249,384)(250,383)(251,387)(252,386)(253,390)(254,389)(255,388)(256,362)
(257,361)(258,365)(259,364)(260,363)(261,367)(262,366)(263,370)(264,369)
(265,368)(266,372)(267,371)(268,375)(269,374)(270,373)(271,407)(272,406)
(273,410)(274,409)(275,408)(276,412)(277,411)(278,415)(279,414)(280,413)
(281,417)(282,416)(283,420)(284,419)(285,418)(286,392)(287,391)(288,395)
(289,394)(290,393)(291,397)(292,396)(293,400)(294,399)(295,398)(296,402)
(297,401)(298,405)(299,404)(300,403)(301,437)(302,436)(303,440)(304,439)
(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)(312,446)
(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)(320,423)
(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)(328,435)
(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)(336,472)
(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)(344,479)
(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)(352,456)
(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)(360,463)
(481,632)(482,631)(483,635)(484,634)(485,633)(486,637)(487,636)(488,640)
(489,639)(490,638)(491,642)(492,641)(493,645)(494,644)(495,643)(496,647)
(497,646)(498,650)(499,649)(500,648)(501,652)(502,651)(503,655)(504,654)
(505,653)(506,657)(507,656)(508,660)(509,659)(510,658)(511,602)(512,601)
(513,605)(514,604)(515,603)(516,607)(517,606)(518,610)(519,609)(520,608)
(521,612)(522,611)(523,615)(524,614)(525,613)(526,617)(527,616)(528,620)
(529,619)(530,618)(531,622)(532,621)(533,625)(534,624)(535,623)(536,627)
(537,626)(538,630)(539,629)(540,628)(541,692)(542,691)(543,695)(544,694)
(545,693)(546,697)(547,696)(548,700)(549,699)(550,698)(551,702)(552,701)
(553,705)(554,704)(555,703)(556,707)(557,706)(558,710)(559,709)(560,708)
(561,712)(562,711)(563,715)(564,714)(565,713)(566,717)(567,716)(568,720)
(569,719)(570,718)(571,662)(572,661)(573,665)(574,664)(575,663)(576,667)
(577,666)(578,670)(579,669)(580,668)(581,672)(582,671)(583,675)(584,674)
(585,673)(586,677)(587,676)(588,680)(589,679)(590,678)(591,682)(592,681)
(593,685)(594,684)(595,683)(596,687)(597,686)(598,690)(599,689)(600,688)
(721,887)(722,886)(723,890)(724,889)(725,888)(726,892)(727,891)(728,895)
(729,894)(730,893)(731,897)(732,896)(733,900)(734,899)(735,898)(736,872)
(737,871)(738,875)(739,874)(740,873)(741,877)(742,876)(743,880)(744,879)
(745,878)(746,882)(747,881)(748,885)(749,884)(750,883)(751,857)(752,856)
(753,860)(754,859)(755,858)(756,862)(757,861)(758,865)(759,864)(760,863)
(761,867)(762,866)(763,870)(764,869)(765,868)(766,842)(767,841)(768,845)
(769,844)(770,843)(771,847)(772,846)(773,850)(774,849)(775,848)(776,852)
(777,851)(778,855)(779,854)(780,853)(781,947)(782,946)(783,950)(784,949)
(785,948)(786,952)(787,951)(788,955)(789,954)(790,953)(791,957)(792,956)
(793,960)(794,959)(795,958)(796,932)(797,931)(798,935)(799,934)(800,933)
(801,937)(802,936)(803,940)(804,939)(805,938)(806,942)(807,941)(808,945)
(809,944)(810,943)(811,917)(812,916)(813,920)(814,919)(815,918)(816,922)
(817,921)(818,925)(819,924)(820,923)(821,927)(822,926)(823,930)(824,929)
(825,928)(826,902)(827,901)(828,905)(829,904)(830,903)(831,907)(832,906)
(833,910)(834,909)(835,908)(836,912)(837,911)(838,915)(839,914)(840,913);;
s3 := (  1,301)(  2,302)(  3,303)(  4,304)(  5,305)(  6,311)(  7,312)(  8,313)
(  9,314)( 10,315)( 11,306)( 12,307)( 13,308)( 14,309)( 15,310)( 16,316)
( 17,317)( 18,318)( 19,319)( 20,320)( 21,326)( 22,327)( 23,328)( 24,329)
( 25,330)( 26,321)( 27,322)( 28,323)( 29,324)( 30,325)( 31,331)( 32,332)
( 33,333)( 34,334)( 35,335)( 36,341)( 37,342)( 38,343)( 39,344)( 40,345)
( 41,336)( 42,337)( 43,338)( 44,339)( 45,340)( 46,346)( 47,347)( 48,348)
( 49,349)( 50,350)( 51,356)( 52,357)( 53,358)( 54,359)( 55,360)( 56,351)
( 57,352)( 58,353)( 59,354)( 60,355)( 61,241)( 62,242)( 63,243)( 64,244)
( 65,245)( 66,251)( 67,252)( 68,253)( 69,254)( 70,255)( 71,246)( 72,247)
( 73,248)( 74,249)( 75,250)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,266)( 82,267)( 83,268)( 84,269)( 85,270)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,281)
( 97,282)( 98,283)( 99,284)(100,285)(101,276)(102,277)(103,278)(104,279)
(105,280)(106,286)(107,287)(108,288)(109,289)(110,290)(111,296)(112,297)
(113,298)(114,299)(115,300)(116,291)(117,292)(118,293)(119,294)(120,295)
(121,421)(122,422)(123,423)(124,424)(125,425)(126,431)(127,432)(128,433)
(129,434)(130,435)(131,426)(132,427)(133,428)(134,429)(135,430)(136,436)
(137,437)(138,438)(139,439)(140,440)(141,446)(142,447)(143,448)(144,449)
(145,450)(146,441)(147,442)(148,443)(149,444)(150,445)(151,451)(152,452)
(153,453)(154,454)(155,455)(156,461)(157,462)(158,463)(159,464)(160,465)
(161,456)(162,457)(163,458)(164,459)(165,460)(166,466)(167,467)(168,468)
(169,469)(170,470)(171,476)(172,477)(173,478)(174,479)(175,480)(176,471)
(177,472)(178,473)(179,474)(180,475)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,371)(187,372)(188,373)(189,374)(190,375)(191,366)(192,367)
(193,368)(194,369)(195,370)(196,376)(197,377)(198,378)(199,379)(200,380)
(201,386)(202,387)(203,388)(204,389)(205,390)(206,381)(207,382)(208,383)
(209,384)(210,385)(211,391)(212,392)(213,393)(214,394)(215,395)(216,401)
(217,402)(218,403)(219,404)(220,405)(221,396)(222,397)(223,398)(224,399)
(225,400)(226,406)(227,407)(228,408)(229,409)(230,410)(231,416)(232,417)
(233,418)(234,419)(235,420)(236,411)(237,412)(238,413)(239,414)(240,415)
(481,781)(482,782)(483,783)(484,784)(485,785)(486,791)(487,792)(488,793)
(489,794)(490,795)(491,786)(492,787)(493,788)(494,789)(495,790)(496,796)
(497,797)(498,798)(499,799)(500,800)(501,806)(502,807)(503,808)(504,809)
(505,810)(506,801)(507,802)(508,803)(509,804)(510,805)(511,811)(512,812)
(513,813)(514,814)(515,815)(516,821)(517,822)(518,823)(519,824)(520,825)
(521,816)(522,817)(523,818)(524,819)(525,820)(526,826)(527,827)(528,828)
(529,829)(530,830)(531,836)(532,837)(533,838)(534,839)(535,840)(536,831)
(537,832)(538,833)(539,834)(540,835)(541,721)(542,722)(543,723)(544,724)
(545,725)(546,731)(547,732)(548,733)(549,734)(550,735)(551,726)(552,727)
(553,728)(554,729)(555,730)(556,736)(557,737)(558,738)(559,739)(560,740)
(561,746)(562,747)(563,748)(564,749)(565,750)(566,741)(567,742)(568,743)
(569,744)(570,745)(571,751)(572,752)(573,753)(574,754)(575,755)(576,761)
(577,762)(578,763)(579,764)(580,765)(581,756)(582,757)(583,758)(584,759)
(585,760)(586,766)(587,767)(588,768)(589,769)(590,770)(591,776)(592,777)
(593,778)(594,779)(595,780)(596,771)(597,772)(598,773)(599,774)(600,775)
(601,901)(602,902)(603,903)(604,904)(605,905)(606,911)(607,912)(608,913)
(609,914)(610,915)(611,906)(612,907)(613,908)(614,909)(615,910)(616,916)
(617,917)(618,918)(619,919)(620,920)(621,926)(622,927)(623,928)(624,929)
(625,930)(626,921)(627,922)(628,923)(629,924)(630,925)(631,931)(632,932)
(633,933)(634,934)(635,935)(636,941)(637,942)(638,943)(639,944)(640,945)
(641,936)(642,937)(643,938)(644,939)(645,940)(646,946)(647,947)(648,948)
(649,949)(650,950)(651,956)(652,957)(653,958)(654,959)(655,960)(656,951)
(657,952)(658,953)(659,954)(660,955)(661,841)(662,842)(663,843)(664,844)
(665,845)(666,851)(667,852)(668,853)(669,854)(670,855)(671,846)(672,847)
(673,848)(674,849)(675,850)(676,856)(677,857)(678,858)(679,859)(680,860)
(681,866)(682,867)(683,868)(684,869)(685,870)(686,861)(687,862)(688,863)
(689,864)(690,865)(691,871)(692,872)(693,873)(694,874)(695,875)(696,881)
(697,882)(698,883)(699,884)(700,885)(701,876)(702,877)(703,878)(704,879)
(705,880)(706,886)(707,887)(708,888)(709,889)(710,890)(711,896)(712,897)
(713,898)(714,899)(715,900)(716,891)(717,892)(718,893)(719,894)(720,895);;
s4 := (  1, 66)(  2, 67)(  3, 68)(  4, 69)(  5, 70)(  6, 61)(  7, 62)(  8, 63)
(  9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 81)
( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)( 24, 79)
( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 96)( 32, 97)
( 33, 98)( 34, 99)( 35,100)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)
( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,111)( 47,112)( 48,113)
( 49,114)( 50,115)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)( 56,116)
( 57,117)( 58,118)( 59,119)( 60,120)(121,186)(122,187)(123,188)(124,189)
(125,190)(126,181)(127,182)(128,183)(129,184)(130,185)(131,191)(132,192)
(133,193)(134,194)(135,195)(136,201)(137,202)(138,203)(139,204)(140,205)
(141,196)(142,197)(143,198)(144,199)(145,200)(146,206)(147,207)(148,208)
(149,209)(150,210)(151,216)(152,217)(153,218)(154,219)(155,220)(156,211)
(157,212)(158,213)(159,214)(160,215)(161,221)(162,222)(163,223)(164,224)
(165,225)(166,231)(167,232)(168,233)(169,234)(170,235)(171,226)(172,227)
(173,228)(174,229)(175,230)(176,236)(177,237)(178,238)(179,239)(180,240)
(241,306)(242,307)(243,308)(244,309)(245,310)(246,301)(247,302)(248,303)
(249,304)(250,305)(251,311)(252,312)(253,313)(254,314)(255,315)(256,321)
(257,322)(258,323)(259,324)(260,325)(261,316)(262,317)(263,318)(264,319)
(265,320)(266,326)(267,327)(268,328)(269,329)(270,330)(271,336)(272,337)
(273,338)(274,339)(275,340)(276,331)(277,332)(278,333)(279,334)(280,335)
(281,341)(282,342)(283,343)(284,344)(285,345)(286,351)(287,352)(288,353)
(289,354)(290,355)(291,346)(292,347)(293,348)(294,349)(295,350)(296,356)
(297,357)(298,358)(299,359)(300,360)(361,426)(362,427)(363,428)(364,429)
(365,430)(366,421)(367,422)(368,423)(369,424)(370,425)(371,431)(372,432)
(373,433)(374,434)(375,435)(376,441)(377,442)(378,443)(379,444)(380,445)
(381,436)(382,437)(383,438)(384,439)(385,440)(386,446)(387,447)(388,448)
(389,449)(390,450)(391,456)(392,457)(393,458)(394,459)(395,460)(396,451)
(397,452)(398,453)(399,454)(400,455)(401,461)(402,462)(403,463)(404,464)
(405,465)(406,471)(407,472)(408,473)(409,474)(410,475)(411,466)(412,467)
(413,468)(414,469)(415,470)(416,476)(417,477)(418,478)(419,479)(420,480)
(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)(488,543)
(489,544)(490,545)(491,551)(492,552)(493,553)(494,554)(495,555)(496,561)
(497,562)(498,563)(499,564)(500,565)(501,556)(502,557)(503,558)(504,559)
(505,560)(506,566)(507,567)(508,568)(509,569)(510,570)(511,576)(512,577)
(513,578)(514,579)(515,580)(516,571)(517,572)(518,573)(519,574)(520,575)
(521,581)(522,582)(523,583)(524,584)(525,585)(526,591)(527,592)(528,593)
(529,594)(530,595)(531,586)(532,587)(533,588)(534,589)(535,590)(536,596)
(537,597)(538,598)(539,599)(540,600)(601,666)(602,667)(603,668)(604,669)
(605,670)(606,661)(607,662)(608,663)(609,664)(610,665)(611,671)(612,672)
(613,673)(614,674)(615,675)(616,681)(617,682)(618,683)(619,684)(620,685)
(621,676)(622,677)(623,678)(624,679)(625,680)(626,686)(627,687)(628,688)
(629,689)(630,690)(631,696)(632,697)(633,698)(634,699)(635,700)(636,691)
(637,692)(638,693)(639,694)(640,695)(641,701)(642,702)(643,703)(644,704)
(645,705)(646,711)(647,712)(648,713)(649,714)(650,715)(651,706)(652,707)
(653,708)(654,709)(655,710)(656,716)(657,717)(658,718)(659,719)(660,720)
(721,786)(722,787)(723,788)(724,789)(725,790)(726,781)(727,782)(728,783)
(729,784)(730,785)(731,791)(732,792)(733,793)(734,794)(735,795)(736,801)
(737,802)(738,803)(739,804)(740,805)(741,796)(742,797)(743,798)(744,799)
(745,800)(746,806)(747,807)(748,808)(749,809)(750,810)(751,816)(752,817)
(753,818)(754,819)(755,820)(756,811)(757,812)(758,813)(759,814)(760,815)
(761,821)(762,822)(763,823)(764,824)(765,825)(766,831)(767,832)(768,833)
(769,834)(770,835)(771,826)(772,827)(773,828)(774,829)(775,830)(776,836)
(777,837)(778,838)(779,839)(780,840)(841,906)(842,907)(843,908)(844,909)
(845,910)(846,901)(847,902)(848,903)(849,904)(850,905)(851,911)(852,912)
(853,913)(854,914)(855,915)(856,921)(857,922)(858,923)(859,924)(860,925)
(861,916)(862,917)(863,918)(864,919)(865,920)(866,926)(867,927)(868,928)
(869,929)(870,930)(871,936)(872,937)(873,938)(874,939)(875,940)(876,931)
(877,932)(878,933)(879,934)(880,935)(881,941)(882,942)(883,943)(884,944)
(885,945)(886,951)(887,952)(888,953)(889,954)(890,955)(891,946)(892,947)
(893,948)(894,949)(895,950)(896,956)(897,957)(898,958)(899,959)(900,960);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)
(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,541)( 62,542)( 63,543)
( 64,544)( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)
( 72,552)( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)
( 80,560)( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)
( 88,568)( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)
( 96,576)( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)
(112,592)(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)
(120,600)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)
(184,694)(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)
(192,702)(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)
(200,710)(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)
(208,718)(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)
(216,666)(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)
(224,674)(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)
(232,682)(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)
(240,690)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(301,781)(302,782)(303,783)
(304,784)(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)
(312,792)(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)
(320,800)(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)
(328,808)(329,809)(330,810)(331,811)(332,812)(333,813)(334,814)(335,815)
(336,816)(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)
(344,824)(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)
(352,832)(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)
(360,840)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)
(424,934)(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)
(432,942)(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)
(440,950)(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)
(448,958)(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)
(456,906)(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)
(464,914)(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)
(472,922)(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)
(480,930);
s1 := Sym(960)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)
(  8,129)(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)
( 24,143)( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237)(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)
(248,369)(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)
(264,383)(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)
(280,397)(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)
(296,416)(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)
(304,423)(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)
(312,435)(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)
(328,449)(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)
(336,456)(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)
(344,463)(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)
(352,475)(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)
(360,477)(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)
(488,609)(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)
(504,623)(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)
(520,637)(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)
(552,675)(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)
(568,689)(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,696)(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)
(584,703)(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)
(592,715)(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)
(600,717)(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)
(728,849)(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)
(744,863)(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)
(760,877)(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)
(776,896)(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)
(784,903)(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)
(792,915)(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)
(800,917)(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)
(808,929)(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)
(816,936)(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)
(824,943)(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)
(832,955)(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)
(840,957);
s2 := Sym(960)!(  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)
(  8,130)(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,377)(242,376)(243,380)(244,379)(245,378)(246,382)(247,381)
(248,385)(249,384)(250,383)(251,387)(252,386)(253,390)(254,389)(255,388)
(256,362)(257,361)(258,365)(259,364)(260,363)(261,367)(262,366)(263,370)
(264,369)(265,368)(266,372)(267,371)(268,375)(269,374)(270,373)(271,407)
(272,406)(273,410)(274,409)(275,408)(276,412)(277,411)(278,415)(279,414)
(280,413)(281,417)(282,416)(283,420)(284,419)(285,418)(286,392)(287,391)
(288,395)(289,394)(290,393)(291,397)(292,396)(293,400)(294,399)(295,398)
(296,402)(297,401)(298,405)(299,404)(300,403)(301,437)(302,436)(303,440)
(304,439)(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)
(312,446)(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)
(320,423)(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)
(328,435)(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)
(336,472)(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)
(344,479)(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)
(352,456)(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)
(360,463)(481,632)(482,631)(483,635)(484,634)(485,633)(486,637)(487,636)
(488,640)(489,639)(490,638)(491,642)(492,641)(493,645)(494,644)(495,643)
(496,647)(497,646)(498,650)(499,649)(500,648)(501,652)(502,651)(503,655)
(504,654)(505,653)(506,657)(507,656)(508,660)(509,659)(510,658)(511,602)
(512,601)(513,605)(514,604)(515,603)(516,607)(517,606)(518,610)(519,609)
(520,608)(521,612)(522,611)(523,615)(524,614)(525,613)(526,617)(527,616)
(528,620)(529,619)(530,618)(531,622)(532,621)(533,625)(534,624)(535,623)
(536,627)(537,626)(538,630)(539,629)(540,628)(541,692)(542,691)(543,695)
(544,694)(545,693)(546,697)(547,696)(548,700)(549,699)(550,698)(551,702)
(552,701)(553,705)(554,704)(555,703)(556,707)(557,706)(558,710)(559,709)
(560,708)(561,712)(562,711)(563,715)(564,714)(565,713)(566,717)(567,716)
(568,720)(569,719)(570,718)(571,662)(572,661)(573,665)(574,664)(575,663)
(576,667)(577,666)(578,670)(579,669)(580,668)(581,672)(582,671)(583,675)
(584,674)(585,673)(586,677)(587,676)(588,680)(589,679)(590,678)(591,682)
(592,681)(593,685)(594,684)(595,683)(596,687)(597,686)(598,690)(599,689)
(600,688)(721,887)(722,886)(723,890)(724,889)(725,888)(726,892)(727,891)
(728,895)(729,894)(730,893)(731,897)(732,896)(733,900)(734,899)(735,898)
(736,872)(737,871)(738,875)(739,874)(740,873)(741,877)(742,876)(743,880)
(744,879)(745,878)(746,882)(747,881)(748,885)(749,884)(750,883)(751,857)
(752,856)(753,860)(754,859)(755,858)(756,862)(757,861)(758,865)(759,864)
(760,863)(761,867)(762,866)(763,870)(764,869)(765,868)(766,842)(767,841)
(768,845)(769,844)(770,843)(771,847)(772,846)(773,850)(774,849)(775,848)
(776,852)(777,851)(778,855)(779,854)(780,853)(781,947)(782,946)(783,950)
(784,949)(785,948)(786,952)(787,951)(788,955)(789,954)(790,953)(791,957)
(792,956)(793,960)(794,959)(795,958)(796,932)(797,931)(798,935)(799,934)
(800,933)(801,937)(802,936)(803,940)(804,939)(805,938)(806,942)(807,941)
(808,945)(809,944)(810,943)(811,917)(812,916)(813,920)(814,919)(815,918)
(816,922)(817,921)(818,925)(819,924)(820,923)(821,927)(822,926)(823,930)
(824,929)(825,928)(826,902)(827,901)(828,905)(829,904)(830,903)(831,907)
(832,906)(833,910)(834,909)(835,908)(836,912)(837,911)(838,915)(839,914)
(840,913);
s3 := Sym(960)!(  1,301)(  2,302)(  3,303)(  4,304)(  5,305)(  6,311)(  7,312)
(  8,313)(  9,314)( 10,315)( 11,306)( 12,307)( 13,308)( 14,309)( 15,310)
( 16,316)( 17,317)( 18,318)( 19,319)( 20,320)( 21,326)( 22,327)( 23,328)
( 24,329)( 25,330)( 26,321)( 27,322)( 28,323)( 29,324)( 30,325)( 31,331)
( 32,332)( 33,333)( 34,334)( 35,335)( 36,341)( 37,342)( 38,343)( 39,344)
( 40,345)( 41,336)( 42,337)( 43,338)( 44,339)( 45,340)( 46,346)( 47,347)
( 48,348)( 49,349)( 50,350)( 51,356)( 52,357)( 53,358)( 54,359)( 55,360)
( 56,351)( 57,352)( 58,353)( 59,354)( 60,355)( 61,241)( 62,242)( 63,243)
( 64,244)( 65,245)( 66,251)( 67,252)( 68,253)( 69,254)( 70,255)( 71,246)
( 72,247)( 73,248)( 74,249)( 75,250)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,266)( 82,267)( 83,268)( 84,269)( 85,270)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,281)( 97,282)( 98,283)( 99,284)(100,285)(101,276)(102,277)(103,278)
(104,279)(105,280)(106,286)(107,287)(108,288)(109,289)(110,290)(111,296)
(112,297)(113,298)(114,299)(115,300)(116,291)(117,292)(118,293)(119,294)
(120,295)(121,421)(122,422)(123,423)(124,424)(125,425)(126,431)(127,432)
(128,433)(129,434)(130,435)(131,426)(132,427)(133,428)(134,429)(135,430)
(136,436)(137,437)(138,438)(139,439)(140,440)(141,446)(142,447)(143,448)
(144,449)(145,450)(146,441)(147,442)(148,443)(149,444)(150,445)(151,451)
(152,452)(153,453)(154,454)(155,455)(156,461)(157,462)(158,463)(159,464)
(160,465)(161,456)(162,457)(163,458)(164,459)(165,460)(166,466)(167,467)
(168,468)(169,469)(170,470)(171,476)(172,477)(173,478)(174,479)(175,480)
(176,471)(177,472)(178,473)(179,474)(180,475)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,371)(187,372)(188,373)(189,374)(190,375)(191,366)
(192,367)(193,368)(194,369)(195,370)(196,376)(197,377)(198,378)(199,379)
(200,380)(201,386)(202,387)(203,388)(204,389)(205,390)(206,381)(207,382)
(208,383)(209,384)(210,385)(211,391)(212,392)(213,393)(214,394)(215,395)
(216,401)(217,402)(218,403)(219,404)(220,405)(221,396)(222,397)(223,398)
(224,399)(225,400)(226,406)(227,407)(228,408)(229,409)(230,410)(231,416)
(232,417)(233,418)(234,419)(235,420)(236,411)(237,412)(238,413)(239,414)
(240,415)(481,781)(482,782)(483,783)(484,784)(485,785)(486,791)(487,792)
(488,793)(489,794)(490,795)(491,786)(492,787)(493,788)(494,789)(495,790)
(496,796)(497,797)(498,798)(499,799)(500,800)(501,806)(502,807)(503,808)
(504,809)(505,810)(506,801)(507,802)(508,803)(509,804)(510,805)(511,811)
(512,812)(513,813)(514,814)(515,815)(516,821)(517,822)(518,823)(519,824)
(520,825)(521,816)(522,817)(523,818)(524,819)(525,820)(526,826)(527,827)
(528,828)(529,829)(530,830)(531,836)(532,837)(533,838)(534,839)(535,840)
(536,831)(537,832)(538,833)(539,834)(540,835)(541,721)(542,722)(543,723)
(544,724)(545,725)(546,731)(547,732)(548,733)(549,734)(550,735)(551,726)
(552,727)(553,728)(554,729)(555,730)(556,736)(557,737)(558,738)(559,739)
(560,740)(561,746)(562,747)(563,748)(564,749)(565,750)(566,741)(567,742)
(568,743)(569,744)(570,745)(571,751)(572,752)(573,753)(574,754)(575,755)
(576,761)(577,762)(578,763)(579,764)(580,765)(581,756)(582,757)(583,758)
(584,759)(585,760)(586,766)(587,767)(588,768)(589,769)(590,770)(591,776)
(592,777)(593,778)(594,779)(595,780)(596,771)(597,772)(598,773)(599,774)
(600,775)(601,901)(602,902)(603,903)(604,904)(605,905)(606,911)(607,912)
(608,913)(609,914)(610,915)(611,906)(612,907)(613,908)(614,909)(615,910)
(616,916)(617,917)(618,918)(619,919)(620,920)(621,926)(622,927)(623,928)
(624,929)(625,930)(626,921)(627,922)(628,923)(629,924)(630,925)(631,931)
(632,932)(633,933)(634,934)(635,935)(636,941)(637,942)(638,943)(639,944)
(640,945)(641,936)(642,937)(643,938)(644,939)(645,940)(646,946)(647,947)
(648,948)(649,949)(650,950)(651,956)(652,957)(653,958)(654,959)(655,960)
(656,951)(657,952)(658,953)(659,954)(660,955)(661,841)(662,842)(663,843)
(664,844)(665,845)(666,851)(667,852)(668,853)(669,854)(670,855)(671,846)
(672,847)(673,848)(674,849)(675,850)(676,856)(677,857)(678,858)(679,859)
(680,860)(681,866)(682,867)(683,868)(684,869)(685,870)(686,861)(687,862)
(688,863)(689,864)(690,865)(691,871)(692,872)(693,873)(694,874)(695,875)
(696,881)(697,882)(698,883)(699,884)(700,885)(701,876)(702,877)(703,878)
(704,879)(705,880)(706,886)(707,887)(708,888)(709,889)(710,890)(711,896)
(712,897)(713,898)(714,899)(715,900)(716,891)(717,892)(718,893)(719,894)
(720,895);
s4 := Sym(960)!(  1, 66)(  2, 67)(  3, 68)(  4, 69)(  5, 70)(  6, 61)(  7, 62)
(  8, 63)(  9, 64)( 10, 65)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)
( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 76)( 22, 77)( 23, 78)
( 24, 79)( 25, 80)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 96)
( 32, 97)( 33, 98)( 34, 99)( 35,100)( 36, 91)( 37, 92)( 38, 93)( 39, 94)
( 40, 95)( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,111)( 47,112)
( 48,113)( 49,114)( 50,115)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)
( 56,116)( 57,117)( 58,118)( 59,119)( 60,120)(121,186)(122,187)(123,188)
(124,189)(125,190)(126,181)(127,182)(128,183)(129,184)(130,185)(131,191)
(132,192)(133,193)(134,194)(135,195)(136,201)(137,202)(138,203)(139,204)
(140,205)(141,196)(142,197)(143,198)(144,199)(145,200)(146,206)(147,207)
(148,208)(149,209)(150,210)(151,216)(152,217)(153,218)(154,219)(155,220)
(156,211)(157,212)(158,213)(159,214)(160,215)(161,221)(162,222)(163,223)
(164,224)(165,225)(166,231)(167,232)(168,233)(169,234)(170,235)(171,226)
(172,227)(173,228)(174,229)(175,230)(176,236)(177,237)(178,238)(179,239)
(180,240)(241,306)(242,307)(243,308)(244,309)(245,310)(246,301)(247,302)
(248,303)(249,304)(250,305)(251,311)(252,312)(253,313)(254,314)(255,315)
(256,321)(257,322)(258,323)(259,324)(260,325)(261,316)(262,317)(263,318)
(264,319)(265,320)(266,326)(267,327)(268,328)(269,329)(270,330)(271,336)
(272,337)(273,338)(274,339)(275,340)(276,331)(277,332)(278,333)(279,334)
(280,335)(281,341)(282,342)(283,343)(284,344)(285,345)(286,351)(287,352)
(288,353)(289,354)(290,355)(291,346)(292,347)(293,348)(294,349)(295,350)
(296,356)(297,357)(298,358)(299,359)(300,360)(361,426)(362,427)(363,428)
(364,429)(365,430)(366,421)(367,422)(368,423)(369,424)(370,425)(371,431)
(372,432)(373,433)(374,434)(375,435)(376,441)(377,442)(378,443)(379,444)
(380,445)(381,436)(382,437)(383,438)(384,439)(385,440)(386,446)(387,447)
(388,448)(389,449)(390,450)(391,456)(392,457)(393,458)(394,459)(395,460)
(396,451)(397,452)(398,453)(399,454)(400,455)(401,461)(402,462)(403,463)
(404,464)(405,465)(406,471)(407,472)(408,473)(409,474)(410,475)(411,466)
(412,467)(413,468)(414,469)(415,470)(416,476)(417,477)(418,478)(419,479)
(420,480)(481,546)(482,547)(483,548)(484,549)(485,550)(486,541)(487,542)
(488,543)(489,544)(490,545)(491,551)(492,552)(493,553)(494,554)(495,555)
(496,561)(497,562)(498,563)(499,564)(500,565)(501,556)(502,557)(503,558)
(504,559)(505,560)(506,566)(507,567)(508,568)(509,569)(510,570)(511,576)
(512,577)(513,578)(514,579)(515,580)(516,571)(517,572)(518,573)(519,574)
(520,575)(521,581)(522,582)(523,583)(524,584)(525,585)(526,591)(527,592)
(528,593)(529,594)(530,595)(531,586)(532,587)(533,588)(534,589)(535,590)
(536,596)(537,597)(538,598)(539,599)(540,600)(601,666)(602,667)(603,668)
(604,669)(605,670)(606,661)(607,662)(608,663)(609,664)(610,665)(611,671)
(612,672)(613,673)(614,674)(615,675)(616,681)(617,682)(618,683)(619,684)
(620,685)(621,676)(622,677)(623,678)(624,679)(625,680)(626,686)(627,687)
(628,688)(629,689)(630,690)(631,696)(632,697)(633,698)(634,699)(635,700)
(636,691)(637,692)(638,693)(639,694)(640,695)(641,701)(642,702)(643,703)
(644,704)(645,705)(646,711)(647,712)(648,713)(649,714)(650,715)(651,706)
(652,707)(653,708)(654,709)(655,710)(656,716)(657,717)(658,718)(659,719)
(660,720)(721,786)(722,787)(723,788)(724,789)(725,790)(726,781)(727,782)
(728,783)(729,784)(730,785)(731,791)(732,792)(733,793)(734,794)(735,795)
(736,801)(737,802)(738,803)(739,804)(740,805)(741,796)(742,797)(743,798)
(744,799)(745,800)(746,806)(747,807)(748,808)(749,809)(750,810)(751,816)
(752,817)(753,818)(754,819)(755,820)(756,811)(757,812)(758,813)(759,814)
(760,815)(761,821)(762,822)(763,823)(764,824)(765,825)(766,831)(767,832)
(768,833)(769,834)(770,835)(771,826)(772,827)(773,828)(774,829)(775,830)
(776,836)(777,837)(778,838)(779,839)(780,840)(841,906)(842,907)(843,908)
(844,909)(845,910)(846,901)(847,902)(848,903)(849,904)(850,905)(851,911)
(852,912)(853,913)(854,914)(855,915)(856,921)(857,922)(858,923)(859,924)
(860,925)(861,916)(862,917)(863,918)(864,919)(865,920)(866,926)(867,927)
(868,928)(869,929)(870,930)(871,936)(872,937)(873,938)(874,939)(875,940)
(876,931)(877,932)(878,933)(879,934)(880,935)(881,941)(882,942)(883,943)
(884,944)(885,945)(886,951)(887,952)(888,953)(889,954)(890,955)(891,946)
(892,947)(893,948)(894,949)(895,950)(896,956)(897,957)(898,958)(899,959)
(900,960);
poly := sub<Sym(960)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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