Polytope of Type {10,16,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,16,6}*1920
Also Known As : {{10,16|2},{16,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,203901)
Rank : 4
Schlafli Type : {10,16,6}
Number of vertices, edges, etc : 10, 80, 48, 6
Order of s0s1s2s3 : 240
Order of s0s1s2s3s2s1 : 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 : {10,8,6}*960
   3-fold quotients : {10,16,2}*640
   4-fold quotients : {10,4,6}*480
   5-fold quotients : {2,16,6}*384
   6-fold quotients : {10,8,2}*320
   8-fold quotients : {10,2,6}*240
   10-fold quotients : {2,8,6}*192
   12-fold quotients : {10,4,2}*160
   15-fold quotients : {2,16,2}*128
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {2,4,6}*96a
   24-fold quotients : {10,2,2}*80
   30-fold quotients : {2,8,2}*64
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  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);;
s1 := (  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)( 31,167)( 32,166)
( 33,170)( 34,169)( 35,168)( 36,172)( 37,171)( 38,175)( 39,174)( 40,173)
( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,152)( 47,151)( 48,155)
( 49,154)( 50,153)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)( 56,162)
( 57,161)( 58,165)( 59,164)( 60,163)( 61,212)( 62,211)( 63,215)( 64,214)
( 65,213)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,222)( 72,221)
( 73,225)( 74,224)( 75,223)( 76,227)( 77,226)( 78,230)( 79,229)( 80,228)
( 81,232)( 82,231)( 83,235)( 84,234)( 85,233)( 86,237)( 87,236)( 88,240)
( 89,239)( 90,238)( 91,182)( 92,181)( 93,185)( 94,184)( 95,183)( 96,187)
( 97,186)( 98,190)( 99,189)(100,188)(101,192)(102,191)(103,195)(104,194)
(105,193)(106,197)(107,196)(108,200)(109,199)(110,198)(111,202)(112,201)
(113,205)(114,204)(115,203)(116,207)(117,206)(118,210)(119,209)(120,208)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(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)(301,452)(302,451)(303,455)(304,454)
(305,453)(306,457)(307,456)(308,460)(309,459)(310,458)(311,462)(312,461)
(313,465)(314,464)(315,463)(316,467)(317,466)(318,470)(319,469)(320,468)
(321,472)(322,471)(323,475)(324,474)(325,473)(326,477)(327,476)(328,480)
(329,479)(330,478)(331,422)(332,421)(333,425)(334,424)(335,423)(336,427)
(337,426)(338,430)(339,429)(340,428)(341,432)(342,431)(343,435)(344,434)
(345,433)(346,437)(347,436)(348,440)(349,439)(350,438)(351,442)(352,441)
(353,445)(354,444)(355,443)(356,447)(357,446)(358,450)(359,449)(360,448)
(481,662)(482,661)(483,665)(484,664)(485,663)(486,667)(487,666)(488,670)
(489,669)(490,668)(491,672)(492,671)(493,675)(494,674)(495,673)(496,677)
(497,676)(498,680)(499,679)(500,678)(501,682)(502,681)(503,685)(504,684)
(505,683)(506,687)(507,686)(508,690)(509,689)(510,688)(511,707)(512,706)
(513,710)(514,709)(515,708)(516,712)(517,711)(518,715)(519,714)(520,713)
(521,717)(522,716)(523,720)(524,719)(525,718)(526,692)(527,691)(528,695)
(529,694)(530,693)(531,697)(532,696)(533,700)(534,699)(535,698)(536,702)
(537,701)(538,705)(539,704)(540,703)(541,602)(542,601)(543,605)(544,604)
(545,603)(546,607)(547,606)(548,610)(549,609)(550,608)(551,612)(552,611)
(553,615)(554,614)(555,613)(556,617)(557,616)(558,620)(559,619)(560,618)
(561,622)(562,621)(563,625)(564,624)(565,623)(566,627)(567,626)(568,630)
(569,629)(570,628)(571,647)(572,646)(573,650)(574,649)(575,648)(576,652)
(577,651)(578,655)(579,654)(580,653)(581,657)(582,656)(583,660)(584,659)
(585,658)(586,632)(587,631)(588,635)(589,634)(590,633)(591,637)(592,636)
(593,640)(594,639)(595,638)(596,642)(597,641)(598,645)(599,644)(600,643)
(721,902)(722,901)(723,905)(724,904)(725,903)(726,907)(727,906)(728,910)
(729,909)(730,908)(731,912)(732,911)(733,915)(734,914)(735,913)(736,917)
(737,916)(738,920)(739,919)(740,918)(741,922)(742,921)(743,925)(744,924)
(745,923)(746,927)(747,926)(748,930)(749,929)(750,928)(751,947)(752,946)
(753,950)(754,949)(755,948)(756,952)(757,951)(758,955)(759,954)(760,953)
(761,957)(762,956)(763,960)(764,959)(765,958)(766,932)(767,931)(768,935)
(769,934)(770,933)(771,937)(772,936)(773,940)(774,939)(775,938)(776,942)
(777,941)(778,945)(779,944)(780,943)(781,842)(782,841)(783,845)(784,844)
(785,843)(786,847)(787,846)(788,850)(789,849)(790,848)(791,852)(792,851)
(793,855)(794,854)(795,853)(796,857)(797,856)(798,860)(799,859)(800,858)
(801,862)(802,861)(803,865)(804,864)(805,863)(806,867)(807,866)(808,870)
(809,869)(810,868)(811,887)(812,886)(813,890)(814,889)(815,888)(816,892)
(817,891)(818,895)(819,894)(820,893)(821,897)(822,896)(823,900)(824,899)
(825,898)(826,872)(827,871)(828,875)(829,874)(830,873)(831,877)(832,876)
(833,880)(834,879)(835,878)(836,882)(837,881)(838,885)(839,884)(840,883);;
s2 := (  1,721)(  2,722)(  3,723)(  4,724)(  5,725)(  6,731)(  7,732)(  8,733)
(  9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)( 16,736)
( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)( 24,749)
( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,766)( 32,767)
( 33,768)( 34,769)( 35,770)( 36,776)( 37,777)( 38,778)( 39,779)( 40,780)
( 41,771)( 42,772)( 43,773)( 44,774)( 45,775)( 46,751)( 47,752)( 48,753)
( 49,754)( 50,755)( 51,761)( 52,762)( 53,763)( 54,764)( 55,765)( 56,756)
( 57,757)( 58,758)( 59,759)( 60,760)( 61,811)( 62,812)( 63,813)( 64,814)
( 65,815)( 66,821)( 67,822)( 68,823)( 69,824)( 70,825)( 71,816)( 72,817)
( 73,818)( 74,819)( 75,820)( 76,826)( 77,827)( 78,828)( 79,829)( 80,830)
( 81,836)( 82,837)( 83,838)( 84,839)( 85,840)( 86,831)( 87,832)( 88,833)
( 89,834)( 90,835)( 91,781)( 92,782)( 93,783)( 94,784)( 95,785)( 96,791)
( 97,792)( 98,793)( 99,794)(100,795)(101,786)(102,787)(103,788)(104,789)
(105,790)(106,796)(107,797)(108,798)(109,799)(110,800)(111,806)(112,807)
(113,808)(114,809)(115,810)(116,801)(117,802)(118,803)(119,804)(120,805)
(121,841)(122,842)(123,843)(124,844)(125,845)(126,851)(127,852)(128,853)
(129,854)(130,855)(131,846)(132,847)(133,848)(134,849)(135,850)(136,856)
(137,857)(138,858)(139,859)(140,860)(141,866)(142,867)(143,868)(144,869)
(145,870)(146,861)(147,862)(148,863)(149,864)(150,865)(151,886)(152,887)
(153,888)(154,889)(155,890)(156,896)(157,897)(158,898)(159,899)(160,900)
(161,891)(162,892)(163,893)(164,894)(165,895)(166,871)(167,872)(168,873)
(169,874)(170,875)(171,881)(172,882)(173,883)(174,884)(175,885)(176,876)
(177,877)(178,878)(179,879)(180,880)(181,931)(182,932)(183,933)(184,934)
(185,935)(186,941)(187,942)(188,943)(189,944)(190,945)(191,936)(192,937)
(193,938)(194,939)(195,940)(196,946)(197,947)(198,948)(199,949)(200,950)
(201,956)(202,957)(203,958)(204,959)(205,960)(206,951)(207,952)(208,953)
(209,954)(210,955)(211,901)(212,902)(213,903)(214,904)(215,905)(216,911)
(217,912)(218,913)(219,914)(220,915)(221,906)(222,907)(223,908)(224,909)
(225,910)(226,916)(227,917)(228,918)(229,919)(230,920)(231,926)(232,927)
(233,928)(234,929)(235,930)(236,921)(237,922)(238,923)(239,924)(240,925)
(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)(248,493)
(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)(256,496)
(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)(264,509)
(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,526)(272,527)
(273,528)(274,529)(275,530)(276,536)(277,537)(278,538)(279,539)(280,540)
(281,531)(282,532)(283,533)(284,534)(285,535)(286,511)(287,512)(288,513)
(289,514)(290,515)(291,521)(292,522)(293,523)(294,524)(295,525)(296,516)
(297,517)(298,518)(299,519)(300,520)(301,571)(302,572)(303,573)(304,574)
(305,575)(306,581)(307,582)(308,583)(309,584)(310,585)(311,576)(312,577)
(313,578)(314,579)(315,580)(316,586)(317,587)(318,588)(319,589)(320,590)
(321,596)(322,597)(323,598)(324,599)(325,600)(326,591)(327,592)(328,593)
(329,594)(330,595)(331,541)(332,542)(333,543)(334,544)(335,545)(336,551)
(337,552)(338,553)(339,554)(340,555)(341,546)(342,547)(343,548)(344,549)
(345,550)(346,556)(347,557)(348,558)(349,559)(350,560)(351,566)(352,567)
(353,568)(354,569)(355,570)(356,561)(357,562)(358,563)(359,564)(360,565)
(361,601)(362,602)(363,603)(364,604)(365,605)(366,611)(367,612)(368,613)
(369,614)(370,615)(371,606)(372,607)(373,608)(374,609)(375,610)(376,616)
(377,617)(378,618)(379,619)(380,620)(381,626)(382,627)(383,628)(384,629)
(385,630)(386,621)(387,622)(388,623)(389,624)(390,625)(391,646)(392,647)
(393,648)(394,649)(395,650)(396,656)(397,657)(398,658)(399,659)(400,660)
(401,651)(402,652)(403,653)(404,654)(405,655)(406,631)(407,632)(408,633)
(409,634)(410,635)(411,641)(412,642)(413,643)(414,644)(415,645)(416,636)
(417,637)(418,638)(419,639)(420,640)(421,691)(422,692)(423,693)(424,694)
(425,695)(426,701)(427,702)(428,703)(429,704)(430,705)(431,696)(432,697)
(433,698)(434,699)(435,700)(436,706)(437,707)(438,708)(439,709)(440,710)
(441,716)(442,717)(443,718)(444,719)(445,720)(446,711)(447,712)(448,713)
(449,714)(450,715)(451,661)(452,662)(453,663)(454,664)(455,665)(456,671)
(457,672)(458,673)(459,674)(460,675)(461,666)(462,667)(463,668)(464,669)
(465,670)(466,676)(467,677)(468,678)(469,679)(470,680)(471,686)(472,687)
(473,688)(474,689)(475,690)(476,681)(477,682)(478,683)(479,684)(480,685);;
s3 := (  1,246)(  2,247)(  3,248)(  4,249)(  5,250)(  6,241)(  7,242)(  8,243)
(  9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,261)
( 17,262)( 18,263)( 19,264)( 20,265)( 21,256)( 22,257)( 23,258)( 24,259)
( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,276)( 32,277)
( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)( 40,275)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,291)( 47,292)( 48,293)
( 49,294)( 50,295)( 51,286)( 52,287)( 53,288)( 54,289)( 55,290)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,306)( 62,307)( 63,308)( 64,309)
( 65,310)( 66,301)( 67,302)( 68,303)( 69,304)( 70,305)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)
( 81,316)( 82,317)( 83,318)( 84,319)( 85,320)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,331)
( 97,332)( 98,333)( 99,334)(100,335)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,351)(107,352)(108,353)(109,354)(110,355)(111,346)(112,347)
(113,348)(114,349)(115,350)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)(128,363)
(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)(144,379)
(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,396)(152,397)
(153,398)(154,399)(155,400)(156,391)(157,392)(158,393)(159,394)(160,395)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,411)(167,412)(168,413)
(169,414)(170,415)(171,406)(172,407)(173,408)(174,409)(175,410)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,426)(182,427)(183,428)(184,429)
(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)(200,445)
(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)(216,451)
(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)(232,467)
(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,726)(482,727)(483,728)(484,729)(485,730)(486,721)(487,722)(488,723)
(489,724)(490,725)(491,731)(492,732)(493,733)(494,734)(495,735)(496,741)
(497,742)(498,743)(499,744)(500,745)(501,736)(502,737)(503,738)(504,739)
(505,740)(506,746)(507,747)(508,748)(509,749)(510,750)(511,756)(512,757)
(513,758)(514,759)(515,760)(516,751)(517,752)(518,753)(519,754)(520,755)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,771)(527,772)(528,773)
(529,774)(530,775)(531,766)(532,767)(533,768)(534,769)(535,770)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,786)(542,787)(543,788)(544,789)
(545,790)(546,781)(547,782)(548,783)(549,784)(550,785)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,801)(557,802)(558,803)(559,804)(560,805)
(561,796)(562,797)(563,798)(564,799)(565,800)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,816)(572,817)(573,818)(574,819)(575,820)(576,811)
(577,812)(578,813)(579,814)(580,815)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,831)(587,832)(588,833)(589,834)(590,835)(591,826)(592,827)
(593,828)(594,829)(595,830)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,846)(602,847)(603,848)(604,849)(605,850)(606,841)(607,842)(608,843)
(609,844)(610,845)(611,851)(612,852)(613,853)(614,854)(615,855)(616,861)
(617,862)(618,863)(619,864)(620,865)(621,856)(622,857)(623,858)(624,859)
(625,860)(626,866)(627,867)(628,868)(629,869)(630,870)(631,876)(632,877)
(633,878)(634,879)(635,880)(636,871)(637,872)(638,873)(639,874)(640,875)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,891)(647,892)(648,893)
(649,894)(650,895)(651,886)(652,887)(653,888)(654,889)(655,890)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,906)(662,907)(663,908)(664,909)
(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)(680,925)
(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)(696,931)
(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)(712,947)
(713,948)(714,949)(715,950)(716,956)(717,957)(718,958)(719,959)(720,960);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, 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*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
s1 := 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)( 31,167)
( 32,166)( 33,170)( 34,169)( 35,168)( 36,172)( 37,171)( 38,175)( 39,174)
( 40,173)( 41,177)( 42,176)( 43,180)( 44,179)( 45,178)( 46,152)( 47,151)
( 48,155)( 49,154)( 50,153)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)
( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,212)( 62,211)( 63,215)
( 64,214)( 65,213)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,222)
( 72,221)( 73,225)( 74,224)( 75,223)( 76,227)( 77,226)( 78,230)( 79,229)
( 80,228)( 81,232)( 82,231)( 83,235)( 84,234)( 85,233)( 86,237)( 87,236)
( 88,240)( 89,239)( 90,238)( 91,182)( 92,181)( 93,185)( 94,184)( 95,183)
( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(101,192)(102,191)(103,195)
(104,194)(105,193)(106,197)(107,196)(108,200)(109,199)(110,198)(111,202)
(112,201)(113,205)(114,204)(115,203)(116,207)(117,206)(118,210)(119,209)
(120,208)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(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)(301,452)(302,451)(303,455)
(304,454)(305,453)(306,457)(307,456)(308,460)(309,459)(310,458)(311,462)
(312,461)(313,465)(314,464)(315,463)(316,467)(317,466)(318,470)(319,469)
(320,468)(321,472)(322,471)(323,475)(324,474)(325,473)(326,477)(327,476)
(328,480)(329,479)(330,478)(331,422)(332,421)(333,425)(334,424)(335,423)
(336,427)(337,426)(338,430)(339,429)(340,428)(341,432)(342,431)(343,435)
(344,434)(345,433)(346,437)(347,436)(348,440)(349,439)(350,438)(351,442)
(352,441)(353,445)(354,444)(355,443)(356,447)(357,446)(358,450)(359,449)
(360,448)(481,662)(482,661)(483,665)(484,664)(485,663)(486,667)(487,666)
(488,670)(489,669)(490,668)(491,672)(492,671)(493,675)(494,674)(495,673)
(496,677)(497,676)(498,680)(499,679)(500,678)(501,682)(502,681)(503,685)
(504,684)(505,683)(506,687)(507,686)(508,690)(509,689)(510,688)(511,707)
(512,706)(513,710)(514,709)(515,708)(516,712)(517,711)(518,715)(519,714)
(520,713)(521,717)(522,716)(523,720)(524,719)(525,718)(526,692)(527,691)
(528,695)(529,694)(530,693)(531,697)(532,696)(533,700)(534,699)(535,698)
(536,702)(537,701)(538,705)(539,704)(540,703)(541,602)(542,601)(543,605)
(544,604)(545,603)(546,607)(547,606)(548,610)(549,609)(550,608)(551,612)
(552,611)(553,615)(554,614)(555,613)(556,617)(557,616)(558,620)(559,619)
(560,618)(561,622)(562,621)(563,625)(564,624)(565,623)(566,627)(567,626)
(568,630)(569,629)(570,628)(571,647)(572,646)(573,650)(574,649)(575,648)
(576,652)(577,651)(578,655)(579,654)(580,653)(581,657)(582,656)(583,660)
(584,659)(585,658)(586,632)(587,631)(588,635)(589,634)(590,633)(591,637)
(592,636)(593,640)(594,639)(595,638)(596,642)(597,641)(598,645)(599,644)
(600,643)(721,902)(722,901)(723,905)(724,904)(725,903)(726,907)(727,906)
(728,910)(729,909)(730,908)(731,912)(732,911)(733,915)(734,914)(735,913)
(736,917)(737,916)(738,920)(739,919)(740,918)(741,922)(742,921)(743,925)
(744,924)(745,923)(746,927)(747,926)(748,930)(749,929)(750,928)(751,947)
(752,946)(753,950)(754,949)(755,948)(756,952)(757,951)(758,955)(759,954)
(760,953)(761,957)(762,956)(763,960)(764,959)(765,958)(766,932)(767,931)
(768,935)(769,934)(770,933)(771,937)(772,936)(773,940)(774,939)(775,938)
(776,942)(777,941)(778,945)(779,944)(780,943)(781,842)(782,841)(783,845)
(784,844)(785,843)(786,847)(787,846)(788,850)(789,849)(790,848)(791,852)
(792,851)(793,855)(794,854)(795,853)(796,857)(797,856)(798,860)(799,859)
(800,858)(801,862)(802,861)(803,865)(804,864)(805,863)(806,867)(807,866)
(808,870)(809,869)(810,868)(811,887)(812,886)(813,890)(814,889)(815,888)
(816,892)(817,891)(818,895)(819,894)(820,893)(821,897)(822,896)(823,900)
(824,899)(825,898)(826,872)(827,871)(828,875)(829,874)(830,873)(831,877)
(832,876)(833,880)(834,879)(835,878)(836,882)(837,881)(838,885)(839,884)
(840,883);
s2 := Sym(960)!(  1,721)(  2,722)(  3,723)(  4,724)(  5,725)(  6,731)(  7,732)
(  8,733)(  9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)
( 16,736)( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)
( 24,749)( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,766)
( 32,767)( 33,768)( 34,769)( 35,770)( 36,776)( 37,777)( 38,778)( 39,779)
( 40,780)( 41,771)( 42,772)( 43,773)( 44,774)( 45,775)( 46,751)( 47,752)
( 48,753)( 49,754)( 50,755)( 51,761)( 52,762)( 53,763)( 54,764)( 55,765)
( 56,756)( 57,757)( 58,758)( 59,759)( 60,760)( 61,811)( 62,812)( 63,813)
( 64,814)( 65,815)( 66,821)( 67,822)( 68,823)( 69,824)( 70,825)( 71,816)
( 72,817)( 73,818)( 74,819)( 75,820)( 76,826)( 77,827)( 78,828)( 79,829)
( 80,830)( 81,836)( 82,837)( 83,838)( 84,839)( 85,840)( 86,831)( 87,832)
( 88,833)( 89,834)( 90,835)( 91,781)( 92,782)( 93,783)( 94,784)( 95,785)
( 96,791)( 97,792)( 98,793)( 99,794)(100,795)(101,786)(102,787)(103,788)
(104,789)(105,790)(106,796)(107,797)(108,798)(109,799)(110,800)(111,806)
(112,807)(113,808)(114,809)(115,810)(116,801)(117,802)(118,803)(119,804)
(120,805)(121,841)(122,842)(123,843)(124,844)(125,845)(126,851)(127,852)
(128,853)(129,854)(130,855)(131,846)(132,847)(133,848)(134,849)(135,850)
(136,856)(137,857)(138,858)(139,859)(140,860)(141,866)(142,867)(143,868)
(144,869)(145,870)(146,861)(147,862)(148,863)(149,864)(150,865)(151,886)
(152,887)(153,888)(154,889)(155,890)(156,896)(157,897)(158,898)(159,899)
(160,900)(161,891)(162,892)(163,893)(164,894)(165,895)(166,871)(167,872)
(168,873)(169,874)(170,875)(171,881)(172,882)(173,883)(174,884)(175,885)
(176,876)(177,877)(178,878)(179,879)(180,880)(181,931)(182,932)(183,933)
(184,934)(185,935)(186,941)(187,942)(188,943)(189,944)(190,945)(191,936)
(192,937)(193,938)(194,939)(195,940)(196,946)(197,947)(198,948)(199,949)
(200,950)(201,956)(202,957)(203,958)(204,959)(205,960)(206,951)(207,952)
(208,953)(209,954)(210,955)(211,901)(212,902)(213,903)(214,904)(215,905)
(216,911)(217,912)(218,913)(219,914)(220,915)(221,906)(222,907)(223,908)
(224,909)(225,910)(226,916)(227,917)(228,918)(229,919)(230,920)(231,926)
(232,927)(233,928)(234,929)(235,930)(236,921)(237,922)(238,923)(239,924)
(240,925)(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)
(248,493)(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)
(256,496)(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)
(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,526)
(272,527)(273,528)(274,529)(275,530)(276,536)(277,537)(278,538)(279,539)
(280,540)(281,531)(282,532)(283,533)(284,534)(285,535)(286,511)(287,512)
(288,513)(289,514)(290,515)(291,521)(292,522)(293,523)(294,524)(295,525)
(296,516)(297,517)(298,518)(299,519)(300,520)(301,571)(302,572)(303,573)
(304,574)(305,575)(306,581)(307,582)(308,583)(309,584)(310,585)(311,576)
(312,577)(313,578)(314,579)(315,580)(316,586)(317,587)(318,588)(319,589)
(320,590)(321,596)(322,597)(323,598)(324,599)(325,600)(326,591)(327,592)
(328,593)(329,594)(330,595)(331,541)(332,542)(333,543)(334,544)(335,545)
(336,551)(337,552)(338,553)(339,554)(340,555)(341,546)(342,547)(343,548)
(344,549)(345,550)(346,556)(347,557)(348,558)(349,559)(350,560)(351,566)
(352,567)(353,568)(354,569)(355,570)(356,561)(357,562)(358,563)(359,564)
(360,565)(361,601)(362,602)(363,603)(364,604)(365,605)(366,611)(367,612)
(368,613)(369,614)(370,615)(371,606)(372,607)(373,608)(374,609)(375,610)
(376,616)(377,617)(378,618)(379,619)(380,620)(381,626)(382,627)(383,628)
(384,629)(385,630)(386,621)(387,622)(388,623)(389,624)(390,625)(391,646)
(392,647)(393,648)(394,649)(395,650)(396,656)(397,657)(398,658)(399,659)
(400,660)(401,651)(402,652)(403,653)(404,654)(405,655)(406,631)(407,632)
(408,633)(409,634)(410,635)(411,641)(412,642)(413,643)(414,644)(415,645)
(416,636)(417,637)(418,638)(419,639)(420,640)(421,691)(422,692)(423,693)
(424,694)(425,695)(426,701)(427,702)(428,703)(429,704)(430,705)(431,696)
(432,697)(433,698)(434,699)(435,700)(436,706)(437,707)(438,708)(439,709)
(440,710)(441,716)(442,717)(443,718)(444,719)(445,720)(446,711)(447,712)
(448,713)(449,714)(450,715)(451,661)(452,662)(453,663)(454,664)(455,665)
(456,671)(457,672)(458,673)(459,674)(460,675)(461,666)(462,667)(463,668)
(464,669)(465,670)(466,676)(467,677)(468,678)(469,679)(470,680)(471,686)
(472,687)(473,688)(474,689)(475,690)(476,681)(477,682)(478,683)(479,684)
(480,685);
s3 := Sym(960)!(  1,246)(  2,247)(  3,248)(  4,249)(  5,250)(  6,241)(  7,242)
(  8,243)(  9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,261)( 17,262)( 18,263)( 19,264)( 20,265)( 21,256)( 22,257)( 23,258)
( 24,259)( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,276)
( 32,277)( 33,278)( 34,279)( 35,280)( 36,271)( 37,272)( 38,273)( 39,274)
( 40,275)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,291)( 47,292)
( 48,293)( 49,294)( 50,295)( 51,286)( 52,287)( 53,288)( 54,289)( 55,290)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,306)( 62,307)( 63,308)
( 64,309)( 65,310)( 66,301)( 67,302)( 68,303)( 69,304)( 70,305)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,321)( 77,322)( 78,323)( 79,324)
( 80,325)( 81,316)( 82,317)( 83,318)( 84,319)( 85,320)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)
( 96,331)( 97,332)( 98,333)( 99,334)(100,335)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,351)(107,352)(108,353)(109,354)(110,355)(111,346)
(112,347)(113,348)(114,349)(115,350)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)
(128,363)(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)
(144,379)(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,396)
(152,397)(153,398)(154,399)(155,400)(156,391)(157,392)(158,393)(159,394)
(160,395)(161,401)(162,402)(163,403)(164,404)(165,405)(166,411)(167,412)
(168,413)(169,414)(170,415)(171,406)(172,407)(173,408)(174,409)(175,410)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,426)(182,427)(183,428)
(184,429)(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)
(200,445)(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)
(216,451)(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)
(232,467)(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,726)(482,727)(483,728)(484,729)(485,730)(486,721)(487,722)
(488,723)(489,724)(490,725)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,741)(497,742)(498,743)(499,744)(500,745)(501,736)(502,737)(503,738)
(504,739)(505,740)(506,746)(507,747)(508,748)(509,749)(510,750)(511,756)
(512,757)(513,758)(514,759)(515,760)(516,751)(517,752)(518,753)(519,754)
(520,755)(521,761)(522,762)(523,763)(524,764)(525,765)(526,771)(527,772)
(528,773)(529,774)(530,775)(531,766)(532,767)(533,768)(534,769)(535,770)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,786)(542,787)(543,788)
(544,789)(545,790)(546,781)(547,782)(548,783)(549,784)(550,785)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,801)(557,802)(558,803)(559,804)
(560,805)(561,796)(562,797)(563,798)(564,799)(565,800)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,816)(572,817)(573,818)(574,819)(575,820)
(576,811)(577,812)(578,813)(579,814)(580,815)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,831)(587,832)(588,833)(589,834)(590,835)(591,826)
(592,827)(593,828)(594,829)(595,830)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,846)(602,847)(603,848)(604,849)(605,850)(606,841)(607,842)
(608,843)(609,844)(610,845)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,861)(617,862)(618,863)(619,864)(620,865)(621,856)(622,857)(623,858)
(624,859)(625,860)(626,866)(627,867)(628,868)(629,869)(630,870)(631,876)
(632,877)(633,878)(634,879)(635,880)(636,871)(637,872)(638,873)(639,874)
(640,875)(641,881)(642,882)(643,883)(644,884)(645,885)(646,891)(647,892)
(648,893)(649,894)(650,895)(651,886)(652,887)(653,888)(654,889)(655,890)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,906)(662,907)(663,908)
(664,909)(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)
(680,925)(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)
(696,931)(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)
(712,947)(713,948)(714,949)(715,950)(716,956)(717,957)(718,958)(719,959)
(720,960);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope