Polytope of Type {40,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6,4}*1920a
Also Known As : {{40,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,182124)
Rank : 4
Schlafli Type : {40,6,4}
Number of vertices, edges, etc : 40, 120, 12, 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 : {20,6,4}*960a, {40,6,2}*960
   3-fold quotients : {40,2,4}*640
   4-fold quotients : {20,6,2}*480a, {10,6,4}*480a
   5-fold quotients : {8,6,4}*384a
   6-fold quotients : {20,2,4}*320, {40,2,2}*320
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {4,6,4}*192a, {8,6,2}*192
   12-fold quotients : {20,2,2}*160, {10,2,4}*160
   15-fold quotients : {8,2,4}*128
   20-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {4,2,4}*64, {8,2,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {5,2,2}*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)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)(  8,489)
(  9,488)( 10,487)( 11,491)( 12,495)( 13,494)( 14,493)( 15,492)( 16,496)
( 17,500)( 18,499)( 19,498)( 20,497)( 21,501)( 22,505)( 23,504)( 24,503)
( 25,502)( 26,506)( 27,510)( 28,509)( 29,508)( 30,507)( 31,511)( 32,515)
( 33,514)( 34,513)( 35,512)( 36,516)( 37,520)( 38,519)( 39,518)( 40,517)
( 41,521)( 42,525)( 43,524)( 44,523)( 45,522)( 46,526)( 47,530)( 48,529)
( 49,528)( 50,527)( 51,531)( 52,535)( 53,534)( 54,533)( 55,532)( 56,536)
( 57,540)( 58,539)( 59,538)( 60,537)( 61,556)( 62,560)( 63,559)( 64,558)
( 65,557)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,566)( 72,570)
( 73,569)( 74,568)( 75,567)( 76,541)( 77,545)( 78,544)( 79,543)( 80,542)
( 81,546)( 82,550)( 83,549)( 84,548)( 85,547)( 86,551)( 87,555)( 88,554)
( 89,553)( 90,552)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)( 96,591)
( 97,595)( 98,594)( 99,593)(100,592)(101,596)(102,600)(103,599)(104,598)
(105,597)(106,571)(107,575)(108,574)(109,573)(110,572)(111,576)(112,580)
(113,579)(114,578)(115,577)(116,581)(117,585)(118,584)(119,583)(120,582)
(121,661)(122,665)(123,664)(124,663)(125,662)(126,666)(127,670)(128,669)
(129,668)(130,667)(131,671)(132,675)(133,674)(134,673)(135,672)(136,676)
(137,680)(138,679)(139,678)(140,677)(141,681)(142,685)(143,684)(144,683)
(145,682)(146,686)(147,690)(148,689)(149,688)(150,687)(151,691)(152,695)
(153,694)(154,693)(155,692)(156,696)(157,700)(158,699)(159,698)(160,697)
(161,701)(162,705)(163,704)(164,703)(165,702)(166,706)(167,710)(168,709)
(169,708)(170,707)(171,711)(172,715)(173,714)(174,713)(175,712)(176,716)
(177,720)(178,719)(179,718)(180,717)(181,601)(182,605)(183,604)(184,603)
(185,602)(186,606)(187,610)(188,609)(189,608)(190,607)(191,611)(192,615)
(193,614)(194,613)(195,612)(196,616)(197,620)(198,619)(199,618)(200,617)
(201,621)(202,625)(203,624)(204,623)(205,622)(206,626)(207,630)(208,629)
(209,628)(210,627)(211,631)(212,635)(213,634)(214,633)(215,632)(216,636)
(217,640)(218,639)(219,638)(220,637)(221,641)(222,645)(223,644)(224,643)
(225,642)(226,646)(227,650)(228,649)(229,648)(230,647)(231,651)(232,655)
(233,654)(234,653)(235,652)(236,656)(237,660)(238,659)(239,658)(240,657)
(241,721)(242,725)(243,724)(244,723)(245,722)(246,726)(247,730)(248,729)
(249,728)(250,727)(251,731)(252,735)(253,734)(254,733)(255,732)(256,736)
(257,740)(258,739)(259,738)(260,737)(261,741)(262,745)(263,744)(264,743)
(265,742)(266,746)(267,750)(268,749)(269,748)(270,747)(271,751)(272,755)
(273,754)(274,753)(275,752)(276,756)(277,760)(278,759)(279,758)(280,757)
(281,761)(282,765)(283,764)(284,763)(285,762)(286,766)(287,770)(288,769)
(289,768)(290,767)(291,771)(292,775)(293,774)(294,773)(295,772)(296,776)
(297,780)(298,779)(299,778)(300,777)(301,796)(302,800)(303,799)(304,798)
(305,797)(306,801)(307,805)(308,804)(309,803)(310,802)(311,806)(312,810)
(313,809)(314,808)(315,807)(316,781)(317,785)(318,784)(319,783)(320,782)
(321,786)(322,790)(323,789)(324,788)(325,787)(326,791)(327,795)(328,794)
(329,793)(330,792)(331,826)(332,830)(333,829)(334,828)(335,827)(336,831)
(337,835)(338,834)(339,833)(340,832)(341,836)(342,840)(343,839)(344,838)
(345,837)(346,811)(347,815)(348,814)(349,813)(350,812)(351,816)(352,820)
(353,819)(354,818)(355,817)(356,821)(357,825)(358,824)(359,823)(360,822)
(361,901)(362,905)(363,904)(364,903)(365,902)(366,906)(367,910)(368,909)
(369,908)(370,907)(371,911)(372,915)(373,914)(374,913)(375,912)(376,916)
(377,920)(378,919)(379,918)(380,917)(381,921)(382,925)(383,924)(384,923)
(385,922)(386,926)(387,930)(388,929)(389,928)(390,927)(391,931)(392,935)
(393,934)(394,933)(395,932)(396,936)(397,940)(398,939)(399,938)(400,937)
(401,941)(402,945)(403,944)(404,943)(405,942)(406,946)(407,950)(408,949)
(409,948)(410,947)(411,951)(412,955)(413,954)(414,953)(415,952)(416,956)
(417,960)(418,959)(419,958)(420,957)(421,841)(422,845)(423,844)(424,843)
(425,842)(426,846)(427,850)(428,849)(429,848)(430,847)(431,851)(432,855)
(433,854)(434,853)(435,852)(436,856)(437,860)(438,859)(439,858)(440,857)
(441,861)(442,865)(443,864)(444,863)(445,862)(446,866)(447,870)(448,869)
(449,868)(450,867)(451,871)(452,875)(453,874)(454,873)(455,872)(456,876)
(457,880)(458,879)(459,878)(460,877)(461,881)(462,885)(463,884)(464,883)
(465,882)(466,886)(467,890)(468,889)(469,888)(470,887)(471,891)(472,895)
(473,894)(474,893)(475,892)(476,896)(477,900)(478,899)(479,898)(480,897);;
s1 := (  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,132)(  7,131)(  8,135)
(  9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)( 24,149)
( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,162)( 37,161)( 38,165)( 39,164)( 40,163)
( 41,157)( 42,156)( 43,160)( 44,159)( 45,158)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)( 56,172)
( 57,171)( 58,175)( 59,174)( 60,173)( 61,197)( 62,196)( 63,200)( 64,199)
( 65,198)( 66,207)( 67,206)( 68,210)( 69,209)( 70,208)( 71,202)( 72,201)
( 73,205)( 74,204)( 75,203)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)
( 81,192)( 82,191)( 83,195)( 84,194)( 85,193)( 86,187)( 87,186)( 88,190)
( 89,189)( 90,188)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)( 96,237)
( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)(104,234)
(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)(112,221)
(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)(120,218)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,372)(247,371)(248,375)
(249,374)(250,373)(251,367)(252,366)(253,370)(254,369)(255,368)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,387)(262,386)(263,390)(264,389)
(265,388)(266,382)(267,381)(268,385)(269,384)(270,383)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,402)(277,401)(278,405)(279,404)(280,403)
(281,397)(282,396)(283,400)(284,399)(285,398)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,417)(292,416)(293,420)(294,419)(295,418)(296,412)
(297,411)(298,415)(299,414)(300,413)(301,437)(302,436)(303,440)(304,439)
(305,438)(306,447)(307,446)(308,450)(309,449)(310,448)(311,442)(312,441)
(313,445)(314,444)(315,443)(316,422)(317,421)(318,425)(319,424)(320,423)
(321,432)(322,431)(323,435)(324,434)(325,433)(326,427)(327,426)(328,430)
(329,429)(330,428)(331,467)(332,466)(333,470)(334,469)(335,468)(336,477)
(337,476)(338,480)(339,479)(340,478)(341,472)(342,471)(343,475)(344,474)
(345,473)(346,452)(347,451)(348,455)(349,454)(350,453)(351,462)(352,461)
(353,465)(354,464)(355,463)(356,457)(357,456)(358,460)(359,459)(360,458)
(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)(541,677)(542,676)(543,680)(544,679)
(545,678)(546,687)(547,686)(548,690)(549,689)(550,688)(551,682)(552,681)
(553,685)(554,684)(555,683)(556,662)(557,661)(558,665)(559,664)(560,663)
(561,672)(562,671)(563,675)(564,674)(565,673)(566,667)(567,666)(568,670)
(569,669)(570,668)(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)
(577,716)(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)
(585,713)(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)
(593,705)(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,852)(727,851)(728,855)
(729,854)(730,853)(731,847)(732,846)(733,850)(734,849)(735,848)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,867)(742,866)(743,870)(744,869)
(745,868)(746,862)(747,861)(748,865)(749,864)(750,863)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,882)(757,881)(758,885)(759,884)(760,883)
(761,877)(762,876)(763,880)(764,879)(765,878)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,897)(772,896)(773,900)(774,899)(775,898)(776,892)
(777,891)(778,895)(779,894)(780,893)(781,917)(782,916)(783,920)(784,919)
(785,918)(786,927)(787,926)(788,930)(789,929)(790,928)(791,922)(792,921)
(793,925)(794,924)(795,923)(796,902)(797,901)(798,905)(799,904)(800,903)
(801,912)(802,911)(803,915)(804,914)(805,913)(806,907)(807,906)(808,910)
(809,909)(810,908)(811,947)(812,946)(813,950)(814,949)(815,948)(816,957)
(817,956)(818,960)(819,959)(820,958)(821,952)(822,951)(823,955)(824,954)
(825,953)(826,932)(827,931)(828,935)(829,934)(830,933)(831,942)(832,941)
(833,945)(834,944)(835,943)(836,937)(837,936)(838,940)(839,939)(840,938);;
s2 := (  1,186)(  2,187)(  3,188)(  4,189)(  5,190)(  6,181)(  7,182)(  8,183)
(  9,184)( 10,185)( 11,191)( 12,192)( 13,193)( 14,194)( 15,195)( 16,201)
( 17,202)( 18,203)( 19,204)( 20,205)( 21,196)( 22,197)( 23,198)( 24,199)
( 25,200)( 26,206)( 27,207)( 28,208)( 29,209)( 30,210)( 31,216)( 32,217)
( 33,218)( 34,219)( 35,220)( 36,211)( 37,212)( 38,213)( 39,214)( 40,215)
( 41,221)( 42,222)( 43,223)( 44,224)( 45,225)( 46,231)( 47,232)( 48,233)
( 49,234)( 50,235)( 51,226)( 52,227)( 53,228)( 54,229)( 55,230)( 56,236)
( 57,237)( 58,238)( 59,239)( 60,240)( 61,141)( 62,142)( 63,143)( 64,144)
( 65,145)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,146)( 72,147)
( 73,148)( 74,149)( 75,150)( 76,126)( 77,127)( 78,128)( 79,129)( 80,130)
( 81,121)( 82,122)( 83,123)( 84,124)( 85,125)( 86,131)( 87,132)( 88,133)
( 89,134)( 90,135)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)( 96,166)
( 97,167)( 98,168)( 99,169)(100,170)(101,176)(102,177)(103,178)(104,179)
(105,180)(106,156)(107,157)(108,158)(109,159)(110,160)(111,151)(112,152)
(113,153)(114,154)(115,155)(116,161)(117,162)(118,163)(119,164)(120,165)
(241,456)(242,457)(243,458)(244,459)(245,460)(246,451)(247,452)(248,453)
(249,454)(250,455)(251,461)(252,462)(253,463)(254,464)(255,465)(256,471)
(257,472)(258,473)(259,474)(260,475)(261,466)(262,467)(263,468)(264,469)
(265,470)(266,476)(267,477)(268,478)(269,479)(270,480)(271,426)(272,427)
(273,428)(274,429)(275,430)(276,421)(277,422)(278,423)(279,424)(280,425)
(281,431)(282,432)(283,433)(284,434)(285,435)(286,441)(287,442)(288,443)
(289,444)(290,445)(291,436)(292,437)(293,438)(294,439)(295,440)(296,446)
(297,447)(298,448)(299,449)(300,450)(301,411)(302,412)(303,413)(304,414)
(305,415)(306,406)(307,407)(308,408)(309,409)(310,410)(311,416)(312,417)
(313,418)(314,419)(315,420)(316,396)(317,397)(318,398)(319,399)(320,400)
(321,391)(322,392)(323,393)(324,394)(325,395)(326,401)(327,402)(328,403)
(329,404)(330,405)(331,381)(332,382)(333,383)(334,384)(335,385)(336,376)
(337,377)(338,378)(339,379)(340,380)(341,386)(342,387)(343,388)(344,389)
(345,390)(346,366)(347,367)(348,368)(349,369)(350,370)(351,361)(352,362)
(353,363)(354,364)(355,365)(356,371)(357,372)(358,373)(359,374)(360,375)
(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)
(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)
(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)
(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)
(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)
(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)
(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)
(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)
(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)
(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)
(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)
(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)
(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)
(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)
(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)
(721,876)(722,877)(723,878)(724,879)(725,880)(726,871)(727,872)(728,873)
(729,874)(730,875)(731,881)(732,882)(733,883)(734,884)(735,885)(736,891)
(737,892)(738,893)(739,894)(740,895)(741,886)(742,887)(743,888)(744,889)
(745,890)(746,896)(747,897)(748,898)(749,899)(750,900)(751,846)(752,847)
(753,848)(754,849)(755,850)(756,841)(757,842)(758,843)(759,844)(760,845)
(761,851)(762,852)(763,853)(764,854)(765,855)(766,861)(767,862)(768,863)
(769,864)(770,865)(771,856)(772,857)(773,858)(774,859)(775,860)(776,866)
(777,867)(778,868)(779,869)(780,870)(781,936)(782,937)(783,938)(784,939)
(785,940)(786,931)(787,932)(788,933)(789,934)(790,935)(791,941)(792,942)
(793,943)(794,944)(795,945)(796,951)(797,952)(798,953)(799,954)(800,955)
(801,946)(802,947)(803,948)(804,949)(805,950)(806,956)(807,957)(808,958)
(809,959)(810,960)(811,906)(812,907)(813,908)(814,909)(815,910)(816,901)
(817,902)(818,903)(819,904)(820,905)(821,911)(822,912)(823,913)(824,914)
(825,915)(826,921)(827,922)(828,923)(829,924)(830,925)(831,916)(832,917)
(833,918)(834,919)(835,920)(836,926)(837,927)(838,928)(839,929)(840,930);;
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, 
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*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)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)
(  8,489)(  9,488)( 10,487)( 11,491)( 12,495)( 13,494)( 14,493)( 15,492)
( 16,496)( 17,500)( 18,499)( 19,498)( 20,497)( 21,501)( 22,505)( 23,504)
( 24,503)( 25,502)( 26,506)( 27,510)( 28,509)( 29,508)( 30,507)( 31,511)
( 32,515)( 33,514)( 34,513)( 35,512)( 36,516)( 37,520)( 38,519)( 39,518)
( 40,517)( 41,521)( 42,525)( 43,524)( 44,523)( 45,522)( 46,526)( 47,530)
( 48,529)( 49,528)( 50,527)( 51,531)( 52,535)( 53,534)( 54,533)( 55,532)
( 56,536)( 57,540)( 58,539)( 59,538)( 60,537)( 61,556)( 62,560)( 63,559)
( 64,558)( 65,557)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,566)
( 72,570)( 73,569)( 74,568)( 75,567)( 76,541)( 77,545)( 78,544)( 79,543)
( 80,542)( 81,546)( 82,550)( 83,549)( 84,548)( 85,547)( 86,551)( 87,555)
( 88,554)( 89,553)( 90,552)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)
( 96,591)( 97,595)( 98,594)( 99,593)(100,592)(101,596)(102,600)(103,599)
(104,598)(105,597)(106,571)(107,575)(108,574)(109,573)(110,572)(111,576)
(112,580)(113,579)(114,578)(115,577)(116,581)(117,585)(118,584)(119,583)
(120,582)(121,661)(122,665)(123,664)(124,663)(125,662)(126,666)(127,670)
(128,669)(129,668)(130,667)(131,671)(132,675)(133,674)(134,673)(135,672)
(136,676)(137,680)(138,679)(139,678)(140,677)(141,681)(142,685)(143,684)
(144,683)(145,682)(146,686)(147,690)(148,689)(149,688)(150,687)(151,691)
(152,695)(153,694)(154,693)(155,692)(156,696)(157,700)(158,699)(159,698)
(160,697)(161,701)(162,705)(163,704)(164,703)(165,702)(166,706)(167,710)
(168,709)(169,708)(170,707)(171,711)(172,715)(173,714)(174,713)(175,712)
(176,716)(177,720)(178,719)(179,718)(180,717)(181,601)(182,605)(183,604)
(184,603)(185,602)(186,606)(187,610)(188,609)(189,608)(190,607)(191,611)
(192,615)(193,614)(194,613)(195,612)(196,616)(197,620)(198,619)(199,618)
(200,617)(201,621)(202,625)(203,624)(204,623)(205,622)(206,626)(207,630)
(208,629)(209,628)(210,627)(211,631)(212,635)(213,634)(214,633)(215,632)
(216,636)(217,640)(218,639)(219,638)(220,637)(221,641)(222,645)(223,644)
(224,643)(225,642)(226,646)(227,650)(228,649)(229,648)(230,647)(231,651)
(232,655)(233,654)(234,653)(235,652)(236,656)(237,660)(238,659)(239,658)
(240,657)(241,721)(242,725)(243,724)(244,723)(245,722)(246,726)(247,730)
(248,729)(249,728)(250,727)(251,731)(252,735)(253,734)(254,733)(255,732)
(256,736)(257,740)(258,739)(259,738)(260,737)(261,741)(262,745)(263,744)
(264,743)(265,742)(266,746)(267,750)(268,749)(269,748)(270,747)(271,751)
(272,755)(273,754)(274,753)(275,752)(276,756)(277,760)(278,759)(279,758)
(280,757)(281,761)(282,765)(283,764)(284,763)(285,762)(286,766)(287,770)
(288,769)(289,768)(290,767)(291,771)(292,775)(293,774)(294,773)(295,772)
(296,776)(297,780)(298,779)(299,778)(300,777)(301,796)(302,800)(303,799)
(304,798)(305,797)(306,801)(307,805)(308,804)(309,803)(310,802)(311,806)
(312,810)(313,809)(314,808)(315,807)(316,781)(317,785)(318,784)(319,783)
(320,782)(321,786)(322,790)(323,789)(324,788)(325,787)(326,791)(327,795)
(328,794)(329,793)(330,792)(331,826)(332,830)(333,829)(334,828)(335,827)
(336,831)(337,835)(338,834)(339,833)(340,832)(341,836)(342,840)(343,839)
(344,838)(345,837)(346,811)(347,815)(348,814)(349,813)(350,812)(351,816)
(352,820)(353,819)(354,818)(355,817)(356,821)(357,825)(358,824)(359,823)
(360,822)(361,901)(362,905)(363,904)(364,903)(365,902)(366,906)(367,910)
(368,909)(369,908)(370,907)(371,911)(372,915)(373,914)(374,913)(375,912)
(376,916)(377,920)(378,919)(379,918)(380,917)(381,921)(382,925)(383,924)
(384,923)(385,922)(386,926)(387,930)(388,929)(389,928)(390,927)(391,931)
(392,935)(393,934)(394,933)(395,932)(396,936)(397,940)(398,939)(399,938)
(400,937)(401,941)(402,945)(403,944)(404,943)(405,942)(406,946)(407,950)
(408,949)(409,948)(410,947)(411,951)(412,955)(413,954)(414,953)(415,952)
(416,956)(417,960)(418,959)(419,958)(420,957)(421,841)(422,845)(423,844)
(424,843)(425,842)(426,846)(427,850)(428,849)(429,848)(430,847)(431,851)
(432,855)(433,854)(434,853)(435,852)(436,856)(437,860)(438,859)(439,858)
(440,857)(441,861)(442,865)(443,864)(444,863)(445,862)(446,866)(447,870)
(448,869)(449,868)(450,867)(451,871)(452,875)(453,874)(454,873)(455,872)
(456,876)(457,880)(458,879)(459,878)(460,877)(461,881)(462,885)(463,884)
(464,883)(465,882)(466,886)(467,890)(468,889)(469,888)(470,887)(471,891)
(472,895)(473,894)(474,893)(475,892)(476,896)(477,900)(478,899)(479,898)
(480,897);
s1 := Sym(960)!(  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,132)(  7,131)
(  8,135)(  9,134)( 10,133)( 11,127)( 12,126)( 13,130)( 14,129)( 15,128)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,147)( 22,146)( 23,150)
( 24,149)( 25,148)( 26,142)( 27,141)( 28,145)( 29,144)( 30,143)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,162)( 37,161)( 38,165)( 39,164)
( 40,163)( 41,157)( 42,156)( 43,160)( 44,159)( 45,158)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,177)( 52,176)( 53,180)( 54,179)( 55,178)
( 56,172)( 57,171)( 58,175)( 59,174)( 60,173)( 61,197)( 62,196)( 63,200)
( 64,199)( 65,198)( 66,207)( 67,206)( 68,210)( 69,209)( 70,208)( 71,202)
( 72,201)( 73,205)( 74,204)( 75,203)( 76,182)( 77,181)( 78,185)( 79,184)
( 80,183)( 81,192)( 82,191)( 83,195)( 84,194)( 85,193)( 86,187)( 87,186)
( 88,190)( 89,189)( 90,188)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)
( 96,237)( 97,236)( 98,240)( 99,239)(100,238)(101,232)(102,231)(103,235)
(104,234)(105,233)(106,212)(107,211)(108,215)(109,214)(110,213)(111,222)
(112,221)(113,225)(114,224)(115,223)(116,217)(117,216)(118,220)(119,219)
(120,218)(241,362)(242,361)(243,365)(244,364)(245,363)(246,372)(247,371)
(248,375)(249,374)(250,373)(251,367)(252,366)(253,370)(254,369)(255,368)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,387)(262,386)(263,390)
(264,389)(265,388)(266,382)(267,381)(268,385)(269,384)(270,383)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,402)(277,401)(278,405)(279,404)
(280,403)(281,397)(282,396)(283,400)(284,399)(285,398)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,417)(292,416)(293,420)(294,419)(295,418)
(296,412)(297,411)(298,415)(299,414)(300,413)(301,437)(302,436)(303,440)
(304,439)(305,438)(306,447)(307,446)(308,450)(309,449)(310,448)(311,442)
(312,441)(313,445)(314,444)(315,443)(316,422)(317,421)(318,425)(319,424)
(320,423)(321,432)(322,431)(323,435)(324,434)(325,433)(326,427)(327,426)
(328,430)(329,429)(330,428)(331,467)(332,466)(333,470)(334,469)(335,468)
(336,477)(337,476)(338,480)(339,479)(340,478)(341,472)(342,471)(343,475)
(344,474)(345,473)(346,452)(347,451)(348,455)(349,454)(350,453)(351,462)
(352,461)(353,465)(354,464)(355,463)(356,457)(357,456)(358,460)(359,459)
(360,458)(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)(541,677)(542,676)(543,680)
(544,679)(545,678)(546,687)(547,686)(548,690)(549,689)(550,688)(551,682)
(552,681)(553,685)(554,684)(555,683)(556,662)(557,661)(558,665)(559,664)
(560,663)(561,672)(562,671)(563,675)(564,674)(565,673)(566,667)(567,666)
(568,670)(569,669)(570,668)(571,707)(572,706)(573,710)(574,709)(575,708)
(576,717)(577,716)(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)
(584,714)(585,713)(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)
(592,701)(593,705)(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)
(600,698)(721,842)(722,841)(723,845)(724,844)(725,843)(726,852)(727,851)
(728,855)(729,854)(730,853)(731,847)(732,846)(733,850)(734,849)(735,848)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,867)(742,866)(743,870)
(744,869)(745,868)(746,862)(747,861)(748,865)(749,864)(750,863)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,882)(757,881)(758,885)(759,884)
(760,883)(761,877)(762,876)(763,880)(764,879)(765,878)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,897)(772,896)(773,900)(774,899)(775,898)
(776,892)(777,891)(778,895)(779,894)(780,893)(781,917)(782,916)(783,920)
(784,919)(785,918)(786,927)(787,926)(788,930)(789,929)(790,928)(791,922)
(792,921)(793,925)(794,924)(795,923)(796,902)(797,901)(798,905)(799,904)
(800,903)(801,912)(802,911)(803,915)(804,914)(805,913)(806,907)(807,906)
(808,910)(809,909)(810,908)(811,947)(812,946)(813,950)(814,949)(815,948)
(816,957)(817,956)(818,960)(819,959)(820,958)(821,952)(822,951)(823,955)
(824,954)(825,953)(826,932)(827,931)(828,935)(829,934)(830,933)(831,942)
(832,941)(833,945)(834,944)(835,943)(836,937)(837,936)(838,940)(839,939)
(840,938);
s2 := Sym(960)!(  1,186)(  2,187)(  3,188)(  4,189)(  5,190)(  6,181)(  7,182)
(  8,183)(  9,184)( 10,185)( 11,191)( 12,192)( 13,193)( 14,194)( 15,195)
( 16,201)( 17,202)( 18,203)( 19,204)( 20,205)( 21,196)( 22,197)( 23,198)
( 24,199)( 25,200)( 26,206)( 27,207)( 28,208)( 29,209)( 30,210)( 31,216)
( 32,217)( 33,218)( 34,219)( 35,220)( 36,211)( 37,212)( 38,213)( 39,214)
( 40,215)( 41,221)( 42,222)( 43,223)( 44,224)( 45,225)( 46,231)( 47,232)
( 48,233)( 49,234)( 50,235)( 51,226)( 52,227)( 53,228)( 54,229)( 55,230)
( 56,236)( 57,237)( 58,238)( 59,239)( 60,240)( 61,141)( 62,142)( 63,143)
( 64,144)( 65,145)( 66,136)( 67,137)( 68,138)( 69,139)( 70,140)( 71,146)
( 72,147)( 73,148)( 74,149)( 75,150)( 76,126)( 77,127)( 78,128)( 79,129)
( 80,130)( 81,121)( 82,122)( 83,123)( 84,124)( 85,125)( 86,131)( 87,132)
( 88,133)( 89,134)( 90,135)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)
( 96,166)( 97,167)( 98,168)( 99,169)(100,170)(101,176)(102,177)(103,178)
(104,179)(105,180)(106,156)(107,157)(108,158)(109,159)(110,160)(111,151)
(112,152)(113,153)(114,154)(115,155)(116,161)(117,162)(118,163)(119,164)
(120,165)(241,456)(242,457)(243,458)(244,459)(245,460)(246,451)(247,452)
(248,453)(249,454)(250,455)(251,461)(252,462)(253,463)(254,464)(255,465)
(256,471)(257,472)(258,473)(259,474)(260,475)(261,466)(262,467)(263,468)
(264,469)(265,470)(266,476)(267,477)(268,478)(269,479)(270,480)(271,426)
(272,427)(273,428)(274,429)(275,430)(276,421)(277,422)(278,423)(279,424)
(280,425)(281,431)(282,432)(283,433)(284,434)(285,435)(286,441)(287,442)
(288,443)(289,444)(290,445)(291,436)(292,437)(293,438)(294,439)(295,440)
(296,446)(297,447)(298,448)(299,449)(300,450)(301,411)(302,412)(303,413)
(304,414)(305,415)(306,406)(307,407)(308,408)(309,409)(310,410)(311,416)
(312,417)(313,418)(314,419)(315,420)(316,396)(317,397)(318,398)(319,399)
(320,400)(321,391)(322,392)(323,393)(324,394)(325,395)(326,401)(327,402)
(328,403)(329,404)(330,405)(331,381)(332,382)(333,383)(334,384)(335,385)
(336,376)(337,377)(338,378)(339,379)(340,380)(341,386)(342,387)(343,388)
(344,389)(345,390)(346,366)(347,367)(348,368)(349,369)(350,370)(351,361)
(352,362)(353,363)(354,364)(355,365)(356,371)(357,372)(358,373)(359,374)
(360,375)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)
(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)
(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)
(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)
(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)
(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)
(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)
(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)
(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)
(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)
(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)
(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)
(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)
(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)
(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)
(600,720)(721,876)(722,877)(723,878)(724,879)(725,880)(726,871)(727,872)
(728,873)(729,874)(730,875)(731,881)(732,882)(733,883)(734,884)(735,885)
(736,891)(737,892)(738,893)(739,894)(740,895)(741,886)(742,887)(743,888)
(744,889)(745,890)(746,896)(747,897)(748,898)(749,899)(750,900)(751,846)
(752,847)(753,848)(754,849)(755,850)(756,841)(757,842)(758,843)(759,844)
(760,845)(761,851)(762,852)(763,853)(764,854)(765,855)(766,861)(767,862)
(768,863)(769,864)(770,865)(771,856)(772,857)(773,858)(774,859)(775,860)
(776,866)(777,867)(778,868)(779,869)(780,870)(781,936)(782,937)(783,938)
(784,939)(785,940)(786,931)(787,932)(788,933)(789,934)(790,935)(791,941)
(792,942)(793,943)(794,944)(795,945)(796,951)(797,952)(798,953)(799,954)
(800,955)(801,946)(802,947)(803,948)(804,949)(805,950)(806,956)(807,957)
(808,958)(809,959)(810,960)(811,906)(812,907)(813,908)(814,909)(815,910)
(816,901)(817,902)(818,903)(819,904)(820,905)(821,911)(822,912)(823,913)
(824,914)(825,915)(826,921)(827,922)(828,923)(829,924)(830,925)(831,916)
(832,917)(833,918)(834,919)(835,920)(836,926)(837,927)(838,928)(839,929)
(840,930);
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, 
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*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