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Polytope of Type {8,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30,4}*1920a
Also Known As : {{8,30|2},{30,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,182073)
Rank : 4
Schlafli Type : {8,30,4}
Number of vertices, edges, etc : 8, 120, 60, 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 : {4,30,4}*960a, {8,30,2}*960
   3-fold quotients : {8,10,4}*640
   4-fold quotients : {2,30,4}*480a, {4,30,2}*480a
   5-fold quotients : {8,6,4}*384a
   6-fold quotients : {4,10,4}*320, {8,10,2}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {4,6,4}*192a, {8,6,2}*192
   12-fold quotients : {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {8,2,4}*128
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,2,4}*64, {8,2,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {2,3,2}*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)(  6,486)(  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)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)(128,668)
(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)(136,676)
(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)(144,684)
(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)(152,692)
(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)(160,700)
(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)(168,708)
(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)(176,716)
(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)(184,604)
(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)(192,612)
(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)(200,620)
(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)
(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)(216,636)
(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)(224,644)
(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)(232,652)
(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)(240,660)
(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)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)(368,908)
(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)(376,916)
(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)(384,924)
(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)(392,932)
(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)(400,940)
(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)(408,948)
(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)(416,956)
(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)(424,844)
(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)
(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)
(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868)
(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)(456,876)
(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)(464,884)
(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)(472,892)
(473,893)(474,894)(475,895)(476,896)(477,897)(478,898)(479,899)(480,900);;
s1 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)(  8,134)
(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)
( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)
( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)
( 57,175)( 58,174)( 59,173)( 60,172)( 61,196)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,201)( 72,205)
( 73,204)( 74,203)( 75,202)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)
( 81,191)( 82,195)( 83,194)( 84,193)( 85,192)( 86,186)( 87,190)( 88,189)
( 89,188)( 90,187)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)( 96,236)
( 97,240)( 98,239)( 99,238)(100,237)(101,231)(102,235)(103,234)(104,233)
(105,232)(106,211)(107,215)(108,214)(109,213)(110,212)(111,221)(112,225)
(113,224)(114,223)(115,222)(116,216)(117,220)(118,219)(119,218)(120,217)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)(248,374)
(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)(264,388)
(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)(280,402)
(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)
(297,415)(298,414)(299,413)(300,412)(301,436)(302,440)(303,439)(304,438)
(305,437)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)(312,445)
(313,444)(314,443)(315,442)(316,421)(317,425)(318,424)(319,423)(320,422)
(321,431)(322,435)(323,434)(324,433)(325,432)(326,426)(327,430)(328,429)
(329,428)(330,427)(331,466)(332,470)(333,469)(334,468)(335,467)(336,476)
(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)(344,473)
(345,472)(346,451)(347,455)(348,454)(349,453)(350,452)(351,461)(352,465)
(353,464)(354,463)(355,462)(356,456)(357,460)(358,459)(359,458)(360,457)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)
(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)
(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)(520,642)
(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)(536,651)
(537,655)(538,654)(539,653)(540,652)(541,676)(542,680)(543,679)(544,678)
(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)(552,685)
(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)(560,662)
(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)(568,669)
(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)
(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)
(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)
(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)(728,854)
(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)(744,868)
(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)(760,882)
(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)(776,891)
(777,895)(778,894)(779,893)(780,892)(781,916)(782,920)(783,919)(784,918)
(785,917)(786,926)(787,930)(788,929)(789,928)(790,927)(791,921)(792,925)
(793,924)(794,923)(795,922)(796,901)(797,905)(798,904)(799,903)(800,902)
(801,911)(802,915)(803,914)(804,913)(805,912)(806,906)(807,910)(808,909)
(809,908)(810,907)(811,946)(812,950)(813,949)(814,948)(815,947)(816,956)
(817,960)(818,959)(819,958)(820,957)(821,951)(822,955)(823,954)(824,953)
(825,952)(826,931)(827,935)(828,934)(829,933)(830,932)(831,941)(832,945)
(833,944)(834,943)(835,942)(836,936)(837,940)(838,939)(839,938)(840,937);;
s2 := (  1,187)(  2,186)(  3,190)(  4,189)(  5,188)(  6,182)(  7,181)(  8,185)
(  9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,202)
( 17,201)( 18,205)( 19,204)( 20,203)( 21,197)( 22,196)( 23,200)( 24,199)
( 25,198)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,217)( 32,216)
( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)( 40,213)
( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,232)( 47,231)( 48,235)
( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)( 56,237)
( 57,236)( 58,240)( 59,239)( 60,238)( 61,142)( 62,141)( 63,145)( 64,144)
( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,147)( 72,146)
( 73,150)( 74,149)( 75,148)( 76,127)( 77,126)( 78,130)( 79,129)( 80,128)
( 81,122)( 82,121)( 83,125)( 84,124)( 85,123)( 86,132)( 87,131)( 88,135)
( 89,134)( 90,133)( 91,172)( 92,171)( 93,175)( 94,174)( 95,173)( 96,167)
( 97,166)( 98,170)( 99,169)(100,168)(101,177)(102,176)(103,180)(104,179)
(105,178)(106,157)(107,156)(108,160)(109,159)(110,158)(111,152)(112,151)
(113,155)(114,154)(115,153)(116,162)(117,161)(118,165)(119,164)(120,163)
(241,457)(242,456)(243,460)(244,459)(245,458)(246,452)(247,451)(248,455)
(249,454)(250,453)(251,462)(252,461)(253,465)(254,464)(255,463)(256,472)
(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)(264,469)
(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,427)(272,426)
(273,430)(274,429)(275,428)(276,422)(277,421)(278,425)(279,424)(280,423)
(281,432)(282,431)(283,435)(284,434)(285,433)(286,442)(287,441)(288,445)
(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)(296,447)
(297,446)(298,450)(299,449)(300,448)(301,412)(302,411)(303,415)(304,414)
(305,413)(306,407)(307,406)(308,410)(309,409)(310,408)(311,417)(312,416)
(313,420)(314,419)(315,418)(316,397)(317,396)(318,400)(319,399)(320,398)
(321,392)(322,391)(323,395)(324,394)(325,393)(326,402)(327,401)(328,405)
(329,404)(330,403)(331,382)(332,381)(333,385)(334,384)(335,383)(336,377)
(337,376)(338,380)(339,379)(340,378)(341,387)(342,386)(343,390)(344,389)
(345,388)(346,367)(347,366)(348,370)(349,369)(350,368)(351,362)(352,361)
(353,365)(354,364)(355,363)(356,372)(357,371)(358,375)(359,374)(360,373)
(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)
(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)
(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)
(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)(512,636)
(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)
(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)(544,669)
(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)
(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)(576,692)
(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)(592,706)
(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,877)(722,876)(723,880)(724,879)(725,878)(726,872)(727,871)(728,875)
(729,874)(730,873)(731,882)(732,881)(733,885)(734,884)(735,883)(736,892)
(737,891)(738,895)(739,894)(740,893)(741,887)(742,886)(743,890)(744,889)
(745,888)(746,897)(747,896)(748,900)(749,899)(750,898)(751,847)(752,846)
(753,850)(754,849)(755,848)(756,842)(757,841)(758,845)(759,844)(760,843)
(761,852)(762,851)(763,855)(764,854)(765,853)(766,862)(767,861)(768,865)
(769,864)(770,863)(771,857)(772,856)(773,860)(774,859)(775,858)(776,867)
(777,866)(778,870)(779,869)(780,868)(781,937)(782,936)(783,940)(784,939)
(785,938)(786,932)(787,931)(788,935)(789,934)(790,933)(791,942)(792,941)
(793,945)(794,944)(795,943)(796,952)(797,951)(798,955)(799,954)(800,953)
(801,947)(802,946)(803,950)(804,949)(805,948)(806,957)(807,956)(808,960)
(809,959)(810,958)(811,907)(812,906)(813,910)(814,909)(815,908)(816,902)
(817,901)(818,905)(819,904)(820,903)(821,912)(822,911)(823,915)(824,914)
(825,913)(826,922)(827,921)(828,925)(829,924)(830,923)(831,917)(832,916)
(833,920)(834,919)(835,918)(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, 
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*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)!(  1,481)(  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)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)
(128,668)(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)
(136,676)(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)
(144,684)(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)
(152,692)(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)
(160,700)(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)
(168,708)(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)
(176,716)(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)
(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)
(192,612)(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)
(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)
(208,628)(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)
(216,636)(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)
(224,644)(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)
(232,652)(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)
(240,660)(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)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)
(368,908)(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)
(376,916)(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)
(384,924)(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)
(392,932)(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)
(400,940)(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)
(408,948)(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)
(416,956)(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)
(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)
(432,852)(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)
(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)
(448,868)(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)
(456,876)(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)
(464,884)(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)
(472,892)(473,893)(474,894)(475,895)(476,896)(477,897)(478,898)(479,899)
(480,900);
s1 := Sym(960)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)
(  8,134)(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)
( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)
( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,196)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,201)
( 72,205)( 73,204)( 74,203)( 75,202)( 76,181)( 77,185)( 78,184)( 79,183)
( 80,182)( 81,191)( 82,195)( 83,194)( 84,193)( 85,192)( 86,186)( 87,190)
( 88,189)( 89,188)( 90,187)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)
( 96,236)( 97,240)( 98,239)( 99,238)(100,237)(101,231)(102,235)(103,234)
(104,233)(105,232)(106,211)(107,215)(108,214)(109,213)(110,212)(111,221)
(112,225)(113,224)(114,223)(115,222)(116,216)(117,220)(118,219)(119,218)
(120,217)(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)
(248,374)(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)
(264,388)(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)
(280,402)(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)
(296,411)(297,415)(298,414)(299,413)(300,412)(301,436)(302,440)(303,439)
(304,438)(305,437)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)
(312,445)(313,444)(314,443)(315,442)(316,421)(317,425)(318,424)(319,423)
(320,422)(321,431)(322,435)(323,434)(324,433)(325,432)(326,426)(327,430)
(328,429)(329,428)(330,427)(331,466)(332,470)(333,469)(334,468)(335,467)
(336,476)(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)
(344,473)(345,472)(346,451)(347,455)(348,454)(349,453)(350,452)(351,461)
(352,465)(353,464)(354,463)(355,462)(356,456)(357,460)(358,459)(359,458)
(360,457)(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)
(488,614)(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)
(504,628)(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)
(520,642)(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)
(536,651)(537,655)(538,654)(539,653)(540,652)(541,676)(542,680)(543,679)
(544,678)(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)
(552,685)(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)
(560,662)(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)
(568,669)(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)
(576,716)(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)
(584,713)(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)
(592,705)(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)
(600,697)(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)
(728,854)(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)
(744,868)(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)
(760,882)(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)
(776,891)(777,895)(778,894)(779,893)(780,892)(781,916)(782,920)(783,919)
(784,918)(785,917)(786,926)(787,930)(788,929)(789,928)(790,927)(791,921)
(792,925)(793,924)(794,923)(795,922)(796,901)(797,905)(798,904)(799,903)
(800,902)(801,911)(802,915)(803,914)(804,913)(805,912)(806,906)(807,910)
(808,909)(809,908)(810,907)(811,946)(812,950)(813,949)(814,948)(815,947)
(816,956)(817,960)(818,959)(819,958)(820,957)(821,951)(822,955)(823,954)
(824,953)(825,952)(826,931)(827,935)(828,934)(829,933)(830,932)(831,941)
(832,945)(833,944)(834,943)(835,942)(836,936)(837,940)(838,939)(839,938)
(840,937);
s2 := Sym(960)!(  1,187)(  2,186)(  3,190)(  4,189)(  5,188)(  6,182)(  7,181)
(  8,185)(  9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)
( 16,202)( 17,201)( 18,205)( 19,204)( 20,203)( 21,197)( 22,196)( 23,200)
( 24,199)( 25,198)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,217)
( 32,216)( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)
( 40,213)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,232)( 47,231)
( 48,235)( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)
( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,142)( 62,141)( 63,145)
( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,147)
( 72,146)( 73,150)( 74,149)( 75,148)( 76,127)( 77,126)( 78,130)( 79,129)
( 80,128)( 81,122)( 82,121)( 83,125)( 84,124)( 85,123)( 86,132)( 87,131)
( 88,135)( 89,134)( 90,133)( 91,172)( 92,171)( 93,175)( 94,174)( 95,173)
( 96,167)( 97,166)( 98,170)( 99,169)(100,168)(101,177)(102,176)(103,180)
(104,179)(105,178)(106,157)(107,156)(108,160)(109,159)(110,158)(111,152)
(112,151)(113,155)(114,154)(115,153)(116,162)(117,161)(118,165)(119,164)
(120,163)(241,457)(242,456)(243,460)(244,459)(245,458)(246,452)(247,451)
(248,455)(249,454)(250,453)(251,462)(252,461)(253,465)(254,464)(255,463)
(256,472)(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)
(264,469)(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,427)
(272,426)(273,430)(274,429)(275,428)(276,422)(277,421)(278,425)(279,424)
(280,423)(281,432)(282,431)(283,435)(284,434)(285,433)(286,442)(287,441)
(288,445)(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)
(296,447)(297,446)(298,450)(299,449)(300,448)(301,412)(302,411)(303,415)
(304,414)(305,413)(306,407)(307,406)(308,410)(309,409)(310,408)(311,417)
(312,416)(313,420)(314,419)(315,418)(316,397)(317,396)(318,400)(319,399)
(320,398)(321,392)(322,391)(323,395)(324,394)(325,393)(326,402)(327,401)
(328,405)(329,404)(330,403)(331,382)(332,381)(333,385)(334,384)(335,383)
(336,377)(337,376)(338,380)(339,379)(340,378)(341,387)(342,386)(343,390)
(344,389)(345,388)(346,367)(347,366)(348,370)(349,369)(350,368)(351,362)
(352,361)(353,365)(354,364)(355,363)(356,372)(357,371)(358,375)(359,374)
(360,373)(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)
(488,605)(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,622)(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)
(504,619)(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)
(512,636)(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)
(520,633)(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)
(528,655)(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)
(544,669)(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)
(560,683)(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)
(576,692)(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)
(592,706)(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,877)(722,876)(723,880)(724,879)(725,878)(726,872)(727,871)
(728,875)(729,874)(730,873)(731,882)(732,881)(733,885)(734,884)(735,883)
(736,892)(737,891)(738,895)(739,894)(740,893)(741,887)(742,886)(743,890)
(744,889)(745,888)(746,897)(747,896)(748,900)(749,899)(750,898)(751,847)
(752,846)(753,850)(754,849)(755,848)(756,842)(757,841)(758,845)(759,844)
(760,843)(761,852)(762,851)(763,855)(764,854)(765,853)(766,862)(767,861)
(768,865)(769,864)(770,863)(771,857)(772,856)(773,860)(774,859)(775,858)
(776,867)(777,866)(778,870)(779,869)(780,868)(781,937)(782,936)(783,940)
(784,939)(785,938)(786,932)(787,931)(788,935)(789,934)(790,933)(791,942)
(792,941)(793,945)(794,944)(795,943)(796,952)(797,951)(798,955)(799,954)
(800,953)(801,947)(802,946)(803,950)(804,949)(805,948)(806,957)(807,956)
(808,960)(809,959)(810,958)(811,907)(812,906)(813,910)(814,909)(815,908)
(816,902)(817,901)(818,905)(819,904)(820,903)(821,912)(822,911)(823,915)
(824,914)(825,913)(826,922)(827,921)(828,925)(829,924)(830,923)(831,917)
(832,916)(833,920)(834,919)(835,918)(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, 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*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