Polytope of Type {8,10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,12}*1920
Also Known As : {{8,10|2},{10,12|2}}. if this polytope has another name.
Group : SmallGroup(1920,182101)
Rank : 4
Schlafli Type : {8,10,12}
Number of vertices, edges, etc : 8, 40, 60, 12
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 : {4,10,12}*960, {8,10,6}*960
   3-fold quotients : {8,10,4}*640
   4-fold quotients : {2,10,12}*480, {4,10,6}*480
   5-fold quotients : {8,2,12}*384
   6-fold quotients : {4,10,4}*320, {8,10,2}*320
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {4,2,12}*192, {8,2,6}*192
   12-fold quotients : {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {8,2,4}*128
   20-fold quotients : {8,2,3}*96, {2,2,12}*96, {4,2,6}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,2,4}*64, {8,2,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*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 := (  1,481)(  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)(  6,126)(  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)( 61,196)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,201)( 67,205)( 68,204)( 69,203)( 70,202)( 71,206)( 72,210)
( 73,209)( 74,208)( 75,207)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)
( 81,186)( 82,190)( 83,189)( 84,188)( 85,187)( 86,191)( 87,195)( 88,194)
( 89,193)( 90,192)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)( 96,231)
( 97,235)( 98,234)( 99,233)(100,232)(101,236)(102,240)(103,239)(104,238)
(105,237)(106,211)(107,215)(108,214)(109,213)(110,212)(111,216)(112,220)
(113,219)(114,218)(115,217)(116,221)(117,225)(118,224)(119,223)(120,222)
(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)(301,436)(302,440)(303,439)(304,438)
(305,437)(306,441)(307,445)(308,444)(309,443)(310,442)(311,446)(312,450)
(313,449)(314,448)(315,447)(316,421)(317,425)(318,424)(319,423)(320,422)
(321,426)(322,430)(323,429)(324,428)(325,427)(326,431)(327,435)(328,434)
(329,433)(330,432)(331,466)(332,470)(333,469)(334,468)(335,467)(336,471)
(337,475)(338,474)(339,473)(340,472)(341,476)(342,480)(343,479)(344,478)
(345,477)(346,451)(347,455)(348,454)(349,453)(350,452)(351,456)(352,460)
(353,459)(354,458)(355,457)(356,461)(357,465)(358,464)(359,463)(360,462)
(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)(541,676)(542,680)(543,679)(544,678)
(545,677)(546,681)(547,685)(548,684)(549,683)(550,682)(551,686)(552,690)
(553,689)(554,688)(555,687)(556,661)(557,665)(558,664)(559,663)(560,662)
(561,666)(562,670)(563,669)(564,668)(565,667)(566,671)(567,675)(568,674)
(569,673)(570,672)(571,706)(572,710)(573,709)(574,708)(575,707)(576,711)
(577,715)(578,714)(579,713)(580,712)(581,716)(582,720)(583,719)(584,718)
(585,717)(586,691)(587,695)(588,694)(589,693)(590,692)(591,696)(592,700)
(593,699)(594,698)(595,697)(596,701)(597,705)(598,704)(599,703)(600,702)
(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)(781,916)(782,920)(783,919)(784,918)
(785,917)(786,921)(787,925)(788,924)(789,923)(790,922)(791,926)(792,930)
(793,929)(794,928)(795,927)(796,901)(797,905)(798,904)(799,903)(800,902)
(801,906)(802,910)(803,909)(804,908)(805,907)(806,911)(807,915)(808,914)
(809,913)(810,912)(811,946)(812,950)(813,949)(814,948)(815,947)(816,951)
(817,955)(818,954)(819,953)(820,952)(821,956)(822,960)(823,959)(824,958)
(825,957)(826,931)(827,935)(828,934)(829,933)(830,932)(831,936)(832,940)
(833,939)(834,938)(835,937)(836,941)(837,945)(838,944)(839,943)(840,942);;
s2 := (  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,192)(  7,191)(  8,195)
(  9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)( 16,197)
( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)( 24,209)
( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)( 32,211)
( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)( 40,223)
( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,137)( 62,136)( 63,140)( 64,139)
( 65,138)( 66,147)( 67,146)( 68,150)( 69,149)( 70,148)( 71,142)( 72,141)
( 73,145)( 74,144)( 75,143)( 76,122)( 77,121)( 78,125)( 79,124)( 80,123)
( 81,132)( 82,131)( 83,135)( 84,134)( 85,133)( 86,127)( 87,126)( 88,130)
( 89,129)( 90,128)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)( 96,177)
( 97,176)( 98,180)( 99,179)(100,178)(101,172)(102,171)(103,175)(104,174)
(105,173)(106,152)(107,151)(108,155)(109,154)(110,153)(111,162)(112,161)
(113,165)(114,164)(115,163)(116,157)(117,156)(118,160)(119,159)(120,158)
(241,452)(242,451)(243,455)(244,454)(245,453)(246,462)(247,461)(248,465)
(249,464)(250,463)(251,457)(252,456)(253,460)(254,459)(255,458)(256,467)
(257,466)(258,470)(259,469)(260,468)(261,477)(262,476)(263,480)(264,479)
(265,478)(266,472)(267,471)(268,475)(269,474)(270,473)(271,422)(272,421)
(273,425)(274,424)(275,423)(276,432)(277,431)(278,435)(279,434)(280,433)
(281,427)(282,426)(283,430)(284,429)(285,428)(286,437)(287,436)(288,440)
(289,439)(290,438)(291,447)(292,446)(293,450)(294,449)(295,448)(296,442)
(297,441)(298,445)(299,444)(300,443)(301,407)(302,406)(303,410)(304,409)
(305,408)(306,417)(307,416)(308,420)(309,419)(310,418)(311,412)(312,411)
(313,415)(314,414)(315,413)(316,392)(317,391)(318,395)(319,394)(320,393)
(321,402)(322,401)(323,405)(324,404)(325,403)(326,397)(327,396)(328,400)
(329,399)(330,398)(331,377)(332,376)(333,380)(334,379)(335,378)(336,387)
(337,386)(338,390)(339,389)(340,388)(341,382)(342,381)(343,385)(344,384)
(345,383)(346,362)(347,361)(348,365)(349,364)(350,363)(351,372)(352,371)
(353,375)(354,374)(355,373)(356,367)(357,366)(358,370)(359,369)(360,368)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,612)(487,611)(488,615)
(489,614)(490,613)(491,607)(492,606)(493,610)(494,609)(495,608)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,627)(502,626)(503,630)(504,629)
(505,628)(506,622)(507,621)(508,625)(509,624)(510,623)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,642)(517,641)(518,645)(519,644)(520,643)
(521,637)(522,636)(523,640)(524,639)(525,638)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,657)(532,656)(533,660)(534,659)(535,658)(536,652)
(537,651)(538,655)(539,654)(540,653)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,672)(547,671)(548,675)(549,674)(550,673)(551,667)(552,666)
(553,670)(554,669)(555,668)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,687)(562,686)(563,690)(564,689)(565,688)(566,682)(567,681)(568,685)
(569,684)(570,683)(571,692)(572,691)(573,695)(574,694)(575,693)(576,702)
(577,701)(578,705)(579,704)(580,703)(581,697)(582,696)(583,700)(584,699)
(585,698)(586,707)(587,706)(588,710)(589,709)(590,708)(591,717)(592,716)
(593,720)(594,719)(595,718)(596,712)(597,711)(598,715)(599,714)(600,713)
(721,872)(722,871)(723,875)(724,874)(725,873)(726,882)(727,881)(728,885)
(729,884)(730,883)(731,877)(732,876)(733,880)(734,879)(735,878)(736,887)
(737,886)(738,890)(739,889)(740,888)(741,897)(742,896)(743,900)(744,899)
(745,898)(746,892)(747,891)(748,895)(749,894)(750,893)(751,842)(752,841)
(753,845)(754,844)(755,843)(756,852)(757,851)(758,855)(759,854)(760,853)
(761,847)(762,846)(763,850)(764,849)(765,848)(766,857)(767,856)(768,860)
(769,859)(770,858)(771,867)(772,866)(773,870)(774,869)(775,868)(776,862)
(777,861)(778,865)(779,864)(780,863)(781,932)(782,931)(783,935)(784,934)
(785,933)(786,942)(787,941)(788,945)(789,944)(790,943)(791,937)(792,936)
(793,940)(794,939)(795,938)(796,947)(797,946)(798,950)(799,949)(800,948)
(801,957)(802,956)(803,960)(804,959)(805,958)(806,952)(807,951)(808,955)
(809,954)(810,953)(811,902)(812,901)(813,905)(814,904)(815,903)(816,912)
(817,911)(818,915)(819,914)(820,913)(821,907)(822,906)(823,910)(824,909)
(825,908)(826,917)(827,916)(828,920)(829,919)(830,918)(831,927)(832,926)
(833,930)(834,929)(835,928)(836,922)(837,921)(838,925)(839,924)(840,923);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)(  6,126)(  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)( 61,196)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,201)( 67,205)( 68,204)( 69,203)( 70,202)( 71,206)
( 72,210)( 73,209)( 74,208)( 75,207)( 76,181)( 77,185)( 78,184)( 79,183)
( 80,182)( 81,186)( 82,190)( 83,189)( 84,188)( 85,187)( 86,191)( 87,195)
( 88,194)( 89,193)( 90,192)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)
( 96,231)( 97,235)( 98,234)( 99,233)(100,232)(101,236)(102,240)(103,239)
(104,238)(105,237)(106,211)(107,215)(108,214)(109,213)(110,212)(111,216)
(112,220)(113,219)(114,218)(115,217)(116,221)(117,225)(118,224)(119,223)
(120,222)(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)(301,436)(302,440)(303,439)
(304,438)(305,437)(306,441)(307,445)(308,444)(309,443)(310,442)(311,446)
(312,450)(313,449)(314,448)(315,447)(316,421)(317,425)(318,424)(319,423)
(320,422)(321,426)(322,430)(323,429)(324,428)(325,427)(326,431)(327,435)
(328,434)(329,433)(330,432)(331,466)(332,470)(333,469)(334,468)(335,467)
(336,471)(337,475)(338,474)(339,473)(340,472)(341,476)(342,480)(343,479)
(344,478)(345,477)(346,451)(347,455)(348,454)(349,453)(350,452)(351,456)
(352,460)(353,459)(354,458)(355,457)(356,461)(357,465)(358,464)(359,463)
(360,462)(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)(541,676)(542,680)(543,679)
(544,678)(545,677)(546,681)(547,685)(548,684)(549,683)(550,682)(551,686)
(552,690)(553,689)(554,688)(555,687)(556,661)(557,665)(558,664)(559,663)
(560,662)(561,666)(562,670)(563,669)(564,668)(565,667)(566,671)(567,675)
(568,674)(569,673)(570,672)(571,706)(572,710)(573,709)(574,708)(575,707)
(576,711)(577,715)(578,714)(579,713)(580,712)(581,716)(582,720)(583,719)
(584,718)(585,717)(586,691)(587,695)(588,694)(589,693)(590,692)(591,696)
(592,700)(593,699)(594,698)(595,697)(596,701)(597,705)(598,704)(599,703)
(600,702)(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)(781,916)(782,920)(783,919)
(784,918)(785,917)(786,921)(787,925)(788,924)(789,923)(790,922)(791,926)
(792,930)(793,929)(794,928)(795,927)(796,901)(797,905)(798,904)(799,903)
(800,902)(801,906)(802,910)(803,909)(804,908)(805,907)(806,911)(807,915)
(808,914)(809,913)(810,912)(811,946)(812,950)(813,949)(814,948)(815,947)
(816,951)(817,955)(818,954)(819,953)(820,952)(821,956)(822,960)(823,959)
(824,958)(825,957)(826,931)(827,935)(828,934)(829,933)(830,932)(831,936)
(832,940)(833,939)(834,938)(835,937)(836,941)(837,945)(838,944)(839,943)
(840,942);
s2 := Sym(960)!(  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,192)(  7,191)
(  8,195)(  9,194)( 10,193)( 11,187)( 12,186)( 13,190)( 14,189)( 15,188)
( 16,197)( 17,196)( 18,200)( 19,199)( 20,198)( 21,207)( 22,206)( 23,210)
( 24,209)( 25,208)( 26,202)( 27,201)( 28,205)( 29,204)( 30,203)( 31,212)
( 32,211)( 33,215)( 34,214)( 35,213)( 36,222)( 37,221)( 38,225)( 39,224)
( 40,223)( 41,217)( 42,216)( 43,220)( 44,219)( 45,218)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,137)( 62,136)( 63,140)
( 64,139)( 65,138)( 66,147)( 67,146)( 68,150)( 69,149)( 70,148)( 71,142)
( 72,141)( 73,145)( 74,144)( 75,143)( 76,122)( 77,121)( 78,125)( 79,124)
( 80,123)( 81,132)( 82,131)( 83,135)( 84,134)( 85,133)( 86,127)( 87,126)
( 88,130)( 89,129)( 90,128)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)
( 96,177)( 97,176)( 98,180)( 99,179)(100,178)(101,172)(102,171)(103,175)
(104,174)(105,173)(106,152)(107,151)(108,155)(109,154)(110,153)(111,162)
(112,161)(113,165)(114,164)(115,163)(116,157)(117,156)(118,160)(119,159)
(120,158)(241,452)(242,451)(243,455)(244,454)(245,453)(246,462)(247,461)
(248,465)(249,464)(250,463)(251,457)(252,456)(253,460)(254,459)(255,458)
(256,467)(257,466)(258,470)(259,469)(260,468)(261,477)(262,476)(263,480)
(264,479)(265,478)(266,472)(267,471)(268,475)(269,474)(270,473)(271,422)
(272,421)(273,425)(274,424)(275,423)(276,432)(277,431)(278,435)(279,434)
(280,433)(281,427)(282,426)(283,430)(284,429)(285,428)(286,437)(287,436)
(288,440)(289,439)(290,438)(291,447)(292,446)(293,450)(294,449)(295,448)
(296,442)(297,441)(298,445)(299,444)(300,443)(301,407)(302,406)(303,410)
(304,409)(305,408)(306,417)(307,416)(308,420)(309,419)(310,418)(311,412)
(312,411)(313,415)(314,414)(315,413)(316,392)(317,391)(318,395)(319,394)
(320,393)(321,402)(322,401)(323,405)(324,404)(325,403)(326,397)(327,396)
(328,400)(329,399)(330,398)(331,377)(332,376)(333,380)(334,379)(335,378)
(336,387)(337,386)(338,390)(339,389)(340,388)(341,382)(342,381)(343,385)
(344,384)(345,383)(346,362)(347,361)(348,365)(349,364)(350,363)(351,372)
(352,371)(353,375)(354,374)(355,373)(356,367)(357,366)(358,370)(359,369)
(360,368)(481,602)(482,601)(483,605)(484,604)(485,603)(486,612)(487,611)
(488,615)(489,614)(490,613)(491,607)(492,606)(493,610)(494,609)(495,608)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,627)(502,626)(503,630)
(504,629)(505,628)(506,622)(507,621)(508,625)(509,624)(510,623)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,642)(517,641)(518,645)(519,644)
(520,643)(521,637)(522,636)(523,640)(524,639)(525,638)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,657)(532,656)(533,660)(534,659)(535,658)
(536,652)(537,651)(538,655)(539,654)(540,653)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,672)(547,671)(548,675)(549,674)(550,673)(551,667)
(552,666)(553,670)(554,669)(555,668)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,687)(562,686)(563,690)(564,689)(565,688)(566,682)(567,681)
(568,685)(569,684)(570,683)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,702)(577,701)(578,705)(579,704)(580,703)(581,697)(582,696)(583,700)
(584,699)(585,698)(586,707)(587,706)(588,710)(589,709)(590,708)(591,717)
(592,716)(593,720)(594,719)(595,718)(596,712)(597,711)(598,715)(599,714)
(600,713)(721,872)(722,871)(723,875)(724,874)(725,873)(726,882)(727,881)
(728,885)(729,884)(730,883)(731,877)(732,876)(733,880)(734,879)(735,878)
(736,887)(737,886)(738,890)(739,889)(740,888)(741,897)(742,896)(743,900)
(744,899)(745,898)(746,892)(747,891)(748,895)(749,894)(750,893)(751,842)
(752,841)(753,845)(754,844)(755,843)(756,852)(757,851)(758,855)(759,854)
(760,853)(761,847)(762,846)(763,850)(764,849)(765,848)(766,857)(767,856)
(768,860)(769,859)(770,858)(771,867)(772,866)(773,870)(774,869)(775,868)
(776,862)(777,861)(778,865)(779,864)(780,863)(781,932)(782,931)(783,935)
(784,934)(785,933)(786,942)(787,941)(788,945)(789,944)(790,943)(791,937)
(792,936)(793,940)(794,939)(795,938)(796,947)(797,946)(798,950)(799,949)
(800,948)(801,957)(802,956)(803,960)(804,959)(805,958)(806,952)(807,951)
(808,955)(809,954)(810,953)(811,902)(812,901)(813,905)(814,904)(815,903)
(816,912)(817,911)(818,915)(819,914)(820,913)(821,907)(822,906)(823,910)
(824,909)(825,908)(826,917)(827,916)(828,920)(829,919)(830,918)(831,927)
(832,926)(833,930)(834,929)(835,928)(836,922)(837,921)(838,925)(839,924)
(840,923);
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, 
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope