Polytope of Type {24,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,10,4}*1920
Also Known As : {{24,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,182123)
Rank : 4
Schlafli Type : {24,10,4}
Number of vertices, edges, etc : 24, 120, 20, 4
Order of s0s1s2s3 : 120
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 : {12,10,4}*960, {24,10,2}*960
   3-fold quotients : {8,10,4}*640
   4-fold quotients : {12,10,2}*480, {6,10,4}*480
   5-fold quotients : {24,2,4}*384
   6-fold quotients : {4,10,4}*320, {8,10,2}*320
   8-fold quotients : {6,10,2}*240
   10-fold quotients : {12,2,4}*192, {24,2,2}*192
   12-fold quotients : {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {8,2,4}*128
   20-fold quotients : {12,2,2}*96, {6,2,4}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,2,4}*64, {8,2,2}*64
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,491)(  7,492)(  8,493)
(  9,494)( 10,495)( 11,486)( 12,487)( 13,488)( 14,489)( 15,490)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)
( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,521)( 37,522)( 38,523)( 39,524)( 40,525)
( 41,516)( 42,517)( 43,518)( 44,519)( 45,520)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)( 56,531)
( 57,532)( 58,533)( 59,534)( 60,535)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,566)( 67,567)( 68,568)( 69,569)( 70,570)( 71,561)( 72,562)
( 73,563)( 74,564)( 75,565)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,551)( 82,552)( 83,553)( 84,554)( 85,555)( 86,546)( 87,547)( 88,548)
( 89,549)( 90,550)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,596)
( 97,597)( 98,598)( 99,599)(100,600)(101,591)(102,592)(103,593)(104,594)
(105,595)(106,571)(107,572)(108,573)(109,574)(110,575)(111,581)(112,582)
(113,583)(114,584)(115,585)(116,576)(117,577)(118,578)(119,579)(120,580)
(121,661)(122,662)(123,663)(124,664)(125,665)(126,671)(127,672)(128,673)
(129,674)(130,675)(131,666)(132,667)(133,668)(134,669)(135,670)(136,676)
(137,677)(138,678)(139,679)(140,680)(141,686)(142,687)(143,688)(144,689)
(145,690)(146,681)(147,682)(148,683)(149,684)(150,685)(151,691)(152,692)
(153,693)(154,694)(155,695)(156,701)(157,702)(158,703)(159,704)(160,705)
(161,696)(162,697)(163,698)(164,699)(165,700)(166,706)(167,707)(168,708)
(169,709)(170,710)(171,716)(172,717)(173,718)(174,719)(175,720)(176,711)
(177,712)(178,713)(179,714)(180,715)(181,601)(182,602)(183,603)(184,604)
(185,605)(186,611)(187,612)(188,613)(189,614)(190,615)(191,606)(192,607)
(193,608)(194,609)(195,610)(196,616)(197,617)(198,618)(199,619)(200,620)
(201,626)(202,627)(203,628)(204,629)(205,630)(206,621)(207,622)(208,623)
(209,624)(210,625)(211,631)(212,632)(213,633)(214,634)(215,635)(216,641)
(217,642)(218,643)(219,644)(220,645)(221,636)(222,637)(223,638)(224,639)
(225,640)(226,646)(227,647)(228,648)(229,649)(230,650)(231,656)(232,657)
(233,658)(234,659)(235,660)(236,651)(237,652)(238,653)(239,654)(240,655)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,731)(247,732)(248,733)
(249,734)(250,735)(251,726)(252,727)(253,728)(254,729)(255,730)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,746)(262,747)(263,748)(264,749)
(265,750)(266,741)(267,742)(268,743)(269,744)(270,745)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,761)(277,762)(278,763)(279,764)(280,765)
(281,756)(282,757)(283,758)(284,759)(285,760)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,776)(292,777)(293,778)(294,779)(295,780)(296,771)
(297,772)(298,773)(299,774)(300,775)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,806)(307,807)(308,808)(309,809)(310,810)(311,801)(312,802)
(313,803)(314,804)(315,805)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,791)(322,792)(323,793)(324,794)(325,795)(326,786)(327,787)(328,788)
(329,789)(330,790)(331,826)(332,827)(333,828)(334,829)(335,830)(336,836)
(337,837)(338,838)(339,839)(340,840)(341,831)(342,832)(343,833)(344,834)
(345,835)(346,811)(347,812)(348,813)(349,814)(350,815)(351,821)(352,822)
(353,823)(354,824)(355,825)(356,816)(357,817)(358,818)(359,819)(360,820)
(361,901)(362,902)(363,903)(364,904)(365,905)(366,911)(367,912)(368,913)
(369,914)(370,915)(371,906)(372,907)(373,908)(374,909)(375,910)(376,916)
(377,917)(378,918)(379,919)(380,920)(381,926)(382,927)(383,928)(384,929)
(385,930)(386,921)(387,922)(388,923)(389,924)(390,925)(391,931)(392,932)
(393,933)(394,934)(395,935)(396,941)(397,942)(398,943)(399,944)(400,945)
(401,936)(402,937)(403,938)(404,939)(405,940)(406,946)(407,947)(408,948)
(409,949)(410,950)(411,956)(412,957)(413,958)(414,959)(415,960)(416,951)
(417,952)(418,953)(419,954)(420,955)(421,841)(422,842)(423,843)(424,844)
(425,845)(426,851)(427,852)(428,853)(429,854)(430,855)(431,846)(432,847)
(433,848)(434,849)(435,850)(436,856)(437,857)(438,858)(439,859)(440,860)
(441,866)(442,867)(443,868)(444,869)(445,870)(446,861)(447,862)(448,863)
(449,864)(450,865)(451,871)(452,872)(453,873)(454,874)(455,875)(456,881)
(457,882)(458,883)(459,884)(460,885)(461,876)(462,877)(463,878)(464,879)
(465,880)(466,886)(467,887)(468,888)(469,889)(470,890)(471,896)(472,897)
(473,898)(474,899)(475,900)(476,891)(477,892)(478,893)(479,894)(480,895);;
s1 := (  1,126)(  2,130)(  3,129)(  4,128)(  5,127)(  6,121)(  7,125)(  8,124)
(  9,123)( 10,122)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,141)
( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)( 24,138)
( 25,137)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,156)( 32,160)
( 33,159)( 34,158)( 35,157)( 36,151)( 37,155)( 38,154)( 39,153)( 40,152)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,171)( 47,175)( 48,174)
( 49,173)( 50,172)( 51,166)( 52,170)( 53,169)( 54,168)( 55,167)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,201)( 62,205)( 63,204)( 64,203)
( 65,202)( 66,196)( 67,200)( 68,199)( 69,198)( 70,197)( 71,206)( 72,210)
( 73,209)( 74,208)( 75,207)( 76,186)( 77,190)( 78,189)( 79,188)( 80,187)
( 81,181)( 82,185)( 83,184)( 84,183)( 85,182)( 86,191)( 87,195)( 88,194)
( 89,193)( 90,192)( 91,231)( 92,235)( 93,234)( 94,233)( 95,232)( 96,226)
( 97,230)( 98,229)( 99,228)(100,227)(101,236)(102,240)(103,239)(104,238)
(105,237)(106,216)(107,220)(108,219)(109,218)(110,217)(111,211)(112,215)
(113,214)(114,213)(115,212)(116,221)(117,225)(118,224)(119,223)(120,222)
(241,366)(242,370)(243,369)(244,368)(245,367)(246,361)(247,365)(248,364)
(249,363)(250,362)(251,371)(252,375)(253,374)(254,373)(255,372)(256,381)
(257,385)(258,384)(259,383)(260,382)(261,376)(262,380)(263,379)(264,378)
(265,377)(266,386)(267,390)(268,389)(269,388)(270,387)(271,396)(272,400)
(273,399)(274,398)(275,397)(276,391)(277,395)(278,394)(279,393)(280,392)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,411)(287,415)(288,414)
(289,413)(290,412)(291,406)(292,410)(293,409)(294,408)(295,407)(296,416)
(297,420)(298,419)(299,418)(300,417)(301,441)(302,445)(303,444)(304,443)
(305,442)(306,436)(307,440)(308,439)(309,438)(310,437)(311,446)(312,450)
(313,449)(314,448)(315,447)(316,426)(317,430)(318,429)(319,428)(320,427)
(321,421)(322,425)(323,424)(324,423)(325,422)(326,431)(327,435)(328,434)
(329,433)(330,432)(331,471)(332,475)(333,474)(334,473)(335,472)(336,466)
(337,470)(338,469)(339,468)(340,467)(341,476)(342,480)(343,479)(344,478)
(345,477)(346,456)(347,460)(348,459)(349,458)(350,457)(351,451)(352,455)
(353,454)(354,453)(355,452)(356,461)(357,465)(358,464)(359,463)(360,462)
(481,606)(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)
(489,603)(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)
(497,625)(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)
(505,617)(506,626)(507,630)(508,629)(509,628)(510,627)(511,636)(512,640)
(513,639)(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)
(529,653)(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,681)(542,685)(543,684)(544,683)
(545,682)(546,676)(547,680)(548,679)(549,678)(550,677)(551,686)(552,690)
(553,689)(554,688)(555,687)(556,666)(557,670)(558,669)(559,668)(560,667)
(561,661)(562,665)(563,664)(564,663)(565,662)(566,671)(567,675)(568,674)
(569,673)(570,672)(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)
(577,710)(578,709)(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)
(585,717)(586,696)(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)
(593,694)(594,693)(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)
(721,846)(722,850)(723,849)(724,848)(725,847)(726,841)(727,845)(728,844)
(729,843)(730,842)(731,851)(732,855)(733,854)(734,853)(735,852)(736,861)
(737,865)(738,864)(739,863)(740,862)(741,856)(742,860)(743,859)(744,858)
(745,857)(746,866)(747,870)(748,869)(749,868)(750,867)(751,876)(752,880)
(753,879)(754,878)(755,877)(756,871)(757,875)(758,874)(759,873)(760,872)
(761,881)(762,885)(763,884)(764,883)(765,882)(766,891)(767,895)(768,894)
(769,893)(770,892)(771,886)(772,890)(773,889)(774,888)(775,887)(776,896)
(777,900)(778,899)(779,898)(780,897)(781,921)(782,925)(783,924)(784,923)
(785,922)(786,916)(787,920)(788,919)(789,918)(790,917)(791,926)(792,930)
(793,929)(794,928)(795,927)(796,906)(797,910)(798,909)(799,908)(800,907)
(801,901)(802,905)(803,904)(804,903)(805,902)(806,911)(807,915)(808,914)
(809,913)(810,912)(811,951)(812,955)(813,954)(814,953)(815,952)(816,946)
(817,950)(818,949)(819,948)(820,947)(821,956)(822,960)(823,959)(824,958)
(825,957)(826,936)(827,940)(828,939)(829,938)(830,937)(831,931)(832,935)
(833,934)(834,933)(835,932)(836,941)(837,945)(838,944)(839,943)(840,942);;
s2 := (  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,187)(  7,186)(  8,190)
(  9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,197)
( 17,196)( 18,200)( 19,199)( 20,198)( 21,202)( 22,201)( 23,205)( 24,204)
( 25,203)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,212)( 32,211)
( 33,215)( 34,214)( 35,213)( 36,217)( 37,216)( 38,220)( 39,219)( 40,218)
( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)( 56,237)
( 57,236)( 58,240)( 59,239)( 60,238)( 61,137)( 62,136)( 63,140)( 64,139)
( 65,138)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,147)( 72,146)
( 73,150)( 74,149)( 75,148)( 76,122)( 77,121)( 78,125)( 79,124)( 80,123)
( 81,127)( 82,126)( 83,130)( 84,129)( 85,128)( 86,132)( 87,131)( 88,135)
( 89,134)( 90,133)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)( 96,172)
( 97,171)( 98,175)( 99,174)(100,173)(101,177)(102,176)(103,180)(104,179)
(105,178)(106,152)(107,151)(108,155)(109,154)(110,153)(111,157)(112,156)
(113,160)(114,159)(115,158)(116,162)(117,161)(118,165)(119,164)(120,163)
(241,452)(242,451)(243,455)(244,454)(245,453)(246,457)(247,456)(248,460)
(249,459)(250,458)(251,462)(252,461)(253,465)(254,464)(255,463)(256,467)
(257,466)(258,470)(259,469)(260,468)(261,472)(262,471)(263,475)(264,474)
(265,473)(266,477)(267,476)(268,480)(269,479)(270,478)(271,422)(272,421)
(273,425)(274,424)(275,423)(276,427)(277,426)(278,430)(279,429)(280,428)
(281,432)(282,431)(283,435)(284,434)(285,433)(286,437)(287,436)(288,440)
(289,439)(290,438)(291,442)(292,441)(293,445)(294,444)(295,443)(296,447)
(297,446)(298,450)(299,449)(300,448)(301,407)(302,406)(303,410)(304,409)
(305,408)(306,412)(307,411)(308,415)(309,414)(310,413)(311,417)(312,416)
(313,420)(314,419)(315,418)(316,392)(317,391)(318,395)(319,394)(320,393)
(321,397)(322,396)(323,400)(324,399)(325,398)(326,402)(327,401)(328,405)
(329,404)(330,403)(331,377)(332,376)(333,380)(334,379)(335,378)(336,382)
(337,381)(338,385)(339,384)(340,383)(341,387)(342,386)(343,390)(344,389)
(345,388)(346,362)(347,361)(348,365)(349,364)(350,363)(351,367)(352,366)
(353,370)(354,369)(355,368)(356,372)(357,371)(358,375)(359,374)(360,373)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)(576,697)
(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)(592,711)
(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,872)(722,871)(723,875)(724,874)(725,873)(726,877)(727,876)(728,880)
(729,879)(730,878)(731,882)(732,881)(733,885)(734,884)(735,883)(736,887)
(737,886)(738,890)(739,889)(740,888)(741,892)(742,891)(743,895)(744,894)
(745,893)(746,897)(747,896)(748,900)(749,899)(750,898)(751,842)(752,841)
(753,845)(754,844)(755,843)(756,847)(757,846)(758,850)(759,849)(760,848)
(761,852)(762,851)(763,855)(764,854)(765,853)(766,857)(767,856)(768,860)
(769,859)(770,858)(771,862)(772,861)(773,865)(774,864)(775,863)(776,867)
(777,866)(778,870)(779,869)(780,868)(781,932)(782,931)(783,935)(784,934)
(785,933)(786,937)(787,936)(788,940)(789,939)(790,938)(791,942)(792,941)
(793,945)(794,944)(795,943)(796,947)(797,946)(798,950)(799,949)(800,948)
(801,952)(802,951)(803,955)(804,954)(805,953)(806,957)(807,956)(808,960)
(809,959)(810,958)(811,902)(812,901)(813,905)(814,904)(815,903)(816,907)
(817,906)(818,910)(819,909)(820,908)(821,912)(822,911)(823,915)(824,914)
(825,913)(826,917)(827,916)(828,920)(829,919)(830,918)(831,922)(832,921)
(833,925)(834,924)(835,923)(836,927)(837,926)(838,930)(839,929)(840,928);;
s3 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(  3,483)(  4,484)(  5,485)(  6,491)(  7,492)
(  8,493)(  9,494)( 10,495)( 11,486)( 12,487)( 13,488)( 14,489)( 15,490)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)
( 24,509)( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,521)( 37,522)( 38,523)( 39,524)
( 40,525)( 41,516)( 42,517)( 43,518)( 44,519)( 45,520)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)
( 56,531)( 57,532)( 58,533)( 59,534)( 60,535)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,566)( 67,567)( 68,568)( 69,569)( 70,570)( 71,561)
( 72,562)( 73,563)( 74,564)( 75,565)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,551)( 82,552)( 83,553)( 84,554)( 85,555)( 86,546)( 87,547)
( 88,548)( 89,549)( 90,550)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,596)( 97,597)( 98,598)( 99,599)(100,600)(101,591)(102,592)(103,593)
(104,594)(105,595)(106,571)(107,572)(108,573)(109,574)(110,575)(111,581)
(112,582)(113,583)(114,584)(115,585)(116,576)(117,577)(118,578)(119,579)
(120,580)(121,661)(122,662)(123,663)(124,664)(125,665)(126,671)(127,672)
(128,673)(129,674)(130,675)(131,666)(132,667)(133,668)(134,669)(135,670)
(136,676)(137,677)(138,678)(139,679)(140,680)(141,686)(142,687)(143,688)
(144,689)(145,690)(146,681)(147,682)(148,683)(149,684)(150,685)(151,691)
(152,692)(153,693)(154,694)(155,695)(156,701)(157,702)(158,703)(159,704)
(160,705)(161,696)(162,697)(163,698)(164,699)(165,700)(166,706)(167,707)
(168,708)(169,709)(170,710)(171,716)(172,717)(173,718)(174,719)(175,720)
(176,711)(177,712)(178,713)(179,714)(180,715)(181,601)(182,602)(183,603)
(184,604)(185,605)(186,611)(187,612)(188,613)(189,614)(190,615)(191,606)
(192,607)(193,608)(194,609)(195,610)(196,616)(197,617)(198,618)(199,619)
(200,620)(201,626)(202,627)(203,628)(204,629)(205,630)(206,621)(207,622)
(208,623)(209,624)(210,625)(211,631)(212,632)(213,633)(214,634)(215,635)
(216,641)(217,642)(218,643)(219,644)(220,645)(221,636)(222,637)(223,638)
(224,639)(225,640)(226,646)(227,647)(228,648)(229,649)(230,650)(231,656)
(232,657)(233,658)(234,659)(235,660)(236,651)(237,652)(238,653)(239,654)
(240,655)(241,721)(242,722)(243,723)(244,724)(245,725)(246,731)(247,732)
(248,733)(249,734)(250,735)(251,726)(252,727)(253,728)(254,729)(255,730)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,746)(262,747)(263,748)
(264,749)(265,750)(266,741)(267,742)(268,743)(269,744)(270,745)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,761)(277,762)(278,763)(279,764)
(280,765)(281,756)(282,757)(283,758)(284,759)(285,760)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,776)(292,777)(293,778)(294,779)(295,780)
(296,771)(297,772)(298,773)(299,774)(300,775)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,806)(307,807)(308,808)(309,809)(310,810)(311,801)
(312,802)(313,803)(314,804)(315,805)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,791)(322,792)(323,793)(324,794)(325,795)(326,786)(327,787)
(328,788)(329,789)(330,790)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,836)(337,837)(338,838)(339,839)(340,840)(341,831)(342,832)(343,833)
(344,834)(345,835)(346,811)(347,812)(348,813)(349,814)(350,815)(351,821)
(352,822)(353,823)(354,824)(355,825)(356,816)(357,817)(358,818)(359,819)
(360,820)(361,901)(362,902)(363,903)(364,904)(365,905)(366,911)(367,912)
(368,913)(369,914)(370,915)(371,906)(372,907)(373,908)(374,909)(375,910)
(376,916)(377,917)(378,918)(379,919)(380,920)(381,926)(382,927)(383,928)
(384,929)(385,930)(386,921)(387,922)(388,923)(389,924)(390,925)(391,931)
(392,932)(393,933)(394,934)(395,935)(396,941)(397,942)(398,943)(399,944)
(400,945)(401,936)(402,937)(403,938)(404,939)(405,940)(406,946)(407,947)
(408,948)(409,949)(410,950)(411,956)(412,957)(413,958)(414,959)(415,960)
(416,951)(417,952)(418,953)(419,954)(420,955)(421,841)(422,842)(423,843)
(424,844)(425,845)(426,851)(427,852)(428,853)(429,854)(430,855)(431,846)
(432,847)(433,848)(434,849)(435,850)(436,856)(437,857)(438,858)(439,859)
(440,860)(441,866)(442,867)(443,868)(444,869)(445,870)(446,861)(447,862)
(448,863)(449,864)(450,865)(451,871)(452,872)(453,873)(454,874)(455,875)
(456,881)(457,882)(458,883)(459,884)(460,885)(461,876)(462,877)(463,878)
(464,879)(465,880)(466,886)(467,887)(468,888)(469,889)(470,890)(471,896)
(472,897)(473,898)(474,899)(475,900)(476,891)(477,892)(478,893)(479,894)
(480,895);
s1 := Sym(960)!(  1,126)(  2,130)(  3,129)(  4,128)(  5,127)(  6,121)(  7,125)
(  8,124)(  9,123)( 10,122)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,141)( 17,145)( 18,144)( 19,143)( 20,142)( 21,136)( 22,140)( 23,139)
( 24,138)( 25,137)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,156)
( 32,160)( 33,159)( 34,158)( 35,157)( 36,151)( 37,155)( 38,154)( 39,153)
( 40,152)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,171)( 47,175)
( 48,174)( 49,173)( 50,172)( 51,166)( 52,170)( 53,169)( 54,168)( 55,167)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,201)( 62,205)( 63,204)
( 64,203)( 65,202)( 66,196)( 67,200)( 68,199)( 69,198)( 70,197)( 71,206)
( 72,210)( 73,209)( 74,208)( 75,207)( 76,186)( 77,190)( 78,189)( 79,188)
( 80,187)( 81,181)( 82,185)( 83,184)( 84,183)( 85,182)( 86,191)( 87,195)
( 88,194)( 89,193)( 90,192)( 91,231)( 92,235)( 93,234)( 94,233)( 95,232)
( 96,226)( 97,230)( 98,229)( 99,228)(100,227)(101,236)(102,240)(103,239)
(104,238)(105,237)(106,216)(107,220)(108,219)(109,218)(110,217)(111,211)
(112,215)(113,214)(114,213)(115,212)(116,221)(117,225)(118,224)(119,223)
(120,222)(241,366)(242,370)(243,369)(244,368)(245,367)(246,361)(247,365)
(248,364)(249,363)(250,362)(251,371)(252,375)(253,374)(254,373)(255,372)
(256,381)(257,385)(258,384)(259,383)(260,382)(261,376)(262,380)(263,379)
(264,378)(265,377)(266,386)(267,390)(268,389)(269,388)(270,387)(271,396)
(272,400)(273,399)(274,398)(275,397)(276,391)(277,395)(278,394)(279,393)
(280,392)(281,401)(282,405)(283,404)(284,403)(285,402)(286,411)(287,415)
(288,414)(289,413)(290,412)(291,406)(292,410)(293,409)(294,408)(295,407)
(296,416)(297,420)(298,419)(299,418)(300,417)(301,441)(302,445)(303,444)
(304,443)(305,442)(306,436)(307,440)(308,439)(309,438)(310,437)(311,446)
(312,450)(313,449)(314,448)(315,447)(316,426)(317,430)(318,429)(319,428)
(320,427)(321,421)(322,425)(323,424)(324,423)(325,422)(326,431)(327,435)
(328,434)(329,433)(330,432)(331,471)(332,475)(333,474)(334,473)(335,472)
(336,466)(337,470)(338,469)(339,468)(340,467)(341,476)(342,480)(343,479)
(344,478)(345,477)(346,456)(347,460)(348,459)(349,458)(350,457)(351,451)
(352,455)(353,454)(354,453)(355,452)(356,461)(357,465)(358,464)(359,463)
(360,462)(481,606)(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)
(488,604)(489,603)(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,621)(497,625)(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)
(504,618)(505,617)(506,626)(507,630)(508,629)(509,628)(510,627)(511,636)
(512,640)(513,639)(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)
(520,632)(521,641)(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)
(528,654)(529,653)(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,681)(542,685)(543,684)
(544,683)(545,682)(546,676)(547,680)(548,679)(549,678)(550,677)(551,686)
(552,690)(553,689)(554,688)(555,687)(556,666)(557,670)(558,669)(559,668)
(560,667)(561,661)(562,665)(563,664)(564,663)(565,662)(566,671)(567,675)
(568,674)(569,673)(570,672)(571,711)(572,715)(573,714)(574,713)(575,712)
(576,706)(577,710)(578,709)(579,708)(580,707)(581,716)(582,720)(583,719)
(584,718)(585,717)(586,696)(587,700)(588,699)(589,698)(590,697)(591,691)
(592,695)(593,694)(594,693)(595,692)(596,701)(597,705)(598,704)(599,703)
(600,702)(721,846)(722,850)(723,849)(724,848)(725,847)(726,841)(727,845)
(728,844)(729,843)(730,842)(731,851)(732,855)(733,854)(734,853)(735,852)
(736,861)(737,865)(738,864)(739,863)(740,862)(741,856)(742,860)(743,859)
(744,858)(745,857)(746,866)(747,870)(748,869)(749,868)(750,867)(751,876)
(752,880)(753,879)(754,878)(755,877)(756,871)(757,875)(758,874)(759,873)
(760,872)(761,881)(762,885)(763,884)(764,883)(765,882)(766,891)(767,895)
(768,894)(769,893)(770,892)(771,886)(772,890)(773,889)(774,888)(775,887)
(776,896)(777,900)(778,899)(779,898)(780,897)(781,921)(782,925)(783,924)
(784,923)(785,922)(786,916)(787,920)(788,919)(789,918)(790,917)(791,926)
(792,930)(793,929)(794,928)(795,927)(796,906)(797,910)(798,909)(799,908)
(800,907)(801,901)(802,905)(803,904)(804,903)(805,902)(806,911)(807,915)
(808,914)(809,913)(810,912)(811,951)(812,955)(813,954)(814,953)(815,952)
(816,946)(817,950)(818,949)(819,948)(820,947)(821,956)(822,960)(823,959)
(824,958)(825,957)(826,936)(827,940)(828,939)(829,938)(830,937)(831,931)
(832,935)(833,934)(834,933)(835,932)(836,941)(837,945)(838,944)(839,943)
(840,942);
s2 := Sym(960)!(  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,187)(  7,186)
(  8,190)(  9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)
( 16,197)( 17,196)( 18,200)( 19,199)( 20,198)( 21,202)( 22,201)( 23,205)
( 24,204)( 25,203)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,212)
( 32,211)( 33,215)( 34,214)( 35,213)( 36,217)( 37,216)( 38,220)( 39,219)
( 40,218)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)
( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,137)( 62,136)( 63,140)
( 64,139)( 65,138)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,147)
( 72,146)( 73,150)( 74,149)( 75,148)( 76,122)( 77,121)( 78,125)( 79,124)
( 80,123)( 81,127)( 82,126)( 83,130)( 84,129)( 85,128)( 86,132)( 87,131)
( 88,135)( 89,134)( 90,133)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)
( 96,172)( 97,171)( 98,175)( 99,174)(100,173)(101,177)(102,176)(103,180)
(104,179)(105,178)(106,152)(107,151)(108,155)(109,154)(110,153)(111,157)
(112,156)(113,160)(114,159)(115,158)(116,162)(117,161)(118,165)(119,164)
(120,163)(241,452)(242,451)(243,455)(244,454)(245,453)(246,457)(247,456)
(248,460)(249,459)(250,458)(251,462)(252,461)(253,465)(254,464)(255,463)
(256,467)(257,466)(258,470)(259,469)(260,468)(261,472)(262,471)(263,475)
(264,474)(265,473)(266,477)(267,476)(268,480)(269,479)(270,478)(271,422)
(272,421)(273,425)(274,424)(275,423)(276,427)(277,426)(278,430)(279,429)
(280,428)(281,432)(282,431)(283,435)(284,434)(285,433)(286,437)(287,436)
(288,440)(289,439)(290,438)(291,442)(292,441)(293,445)(294,444)(295,443)
(296,447)(297,446)(298,450)(299,449)(300,448)(301,407)(302,406)(303,410)
(304,409)(305,408)(306,412)(307,411)(308,415)(309,414)(310,413)(311,417)
(312,416)(313,420)(314,419)(315,418)(316,392)(317,391)(318,395)(319,394)
(320,393)(321,397)(322,396)(323,400)(324,399)(325,398)(326,402)(327,401)
(328,405)(329,404)(330,403)(331,377)(332,376)(333,380)(334,379)(335,378)
(336,382)(337,381)(338,385)(339,384)(340,383)(341,387)(342,386)(343,390)
(344,389)(345,388)(346,362)(347,361)(348,365)(349,364)(350,363)(351,367)
(352,366)(353,370)(354,369)(355,368)(356,372)(357,371)(358,375)(359,374)
(360,373)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,697)(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)
(592,711)(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,872)(722,871)(723,875)(724,874)(725,873)(726,877)(727,876)
(728,880)(729,879)(730,878)(731,882)(732,881)(733,885)(734,884)(735,883)
(736,887)(737,886)(738,890)(739,889)(740,888)(741,892)(742,891)(743,895)
(744,894)(745,893)(746,897)(747,896)(748,900)(749,899)(750,898)(751,842)
(752,841)(753,845)(754,844)(755,843)(756,847)(757,846)(758,850)(759,849)
(760,848)(761,852)(762,851)(763,855)(764,854)(765,853)(766,857)(767,856)
(768,860)(769,859)(770,858)(771,862)(772,861)(773,865)(774,864)(775,863)
(776,867)(777,866)(778,870)(779,869)(780,868)(781,932)(782,931)(783,935)
(784,934)(785,933)(786,937)(787,936)(788,940)(789,939)(790,938)(791,942)
(792,941)(793,945)(794,944)(795,943)(796,947)(797,946)(798,950)(799,949)
(800,948)(801,952)(802,951)(803,955)(804,954)(805,953)(806,957)(807,956)
(808,960)(809,959)(810,958)(811,902)(812,901)(813,905)(814,904)(815,903)
(816,907)(817,906)(818,910)(819,909)(820,908)(821,912)(822,911)(823,915)
(824,914)(825,913)(826,917)(827,916)(828,920)(829,919)(830,918)(831,922)
(832,921)(833,925)(834,924)(835,923)(836,927)(837,926)(838,930)(839,929)
(840,928);
s3 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope