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Polytope of Type {6,10,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,4,4}*1920
Also Known As : {{6,10|2},{10,4|2},{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,205028)
Rank : 5
Schlafli Type : {6,10,4,4}
Number of vertices, edges, etc : 6, 30, 20, 8, 4
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 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 : {6,10,2,4}*960, {6,10,4,2}*960
   3-fold quotients : {2,10,4,4}*640
   4-fold quotients : {6,10,2,2}*480
   5-fold quotients : {6,2,4,4}*384
   6-fold quotients : {2,10,2,4}*320, {2,10,4,2}*320
   10-fold quotients : {3,2,4,4}*192, {6,2,2,4}*192, {6,2,4,2}*192
   12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   15-fold quotients : {2,2,4,4}*128
   20-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {6,2,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   40-fold quotients : {3,2,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)(  8,133)
(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)( 24,149)
( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)( 72,187)
( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)( 88,203)
( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,221)
( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)(104,219)
(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)(248,373)
(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)(264,389)
(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)(280,405)
(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)(312,427)
(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)(328,443)
(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)(336,461)
(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)(344,459)
(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)(352,477)
(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)(360,475)
(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)
(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)
(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)
(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)(512,632)
(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)(520,645)
(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)(528,648)
(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)(536,651)
(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)(544,664)
(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)(552,667)
(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)(560,680)
(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)(568,683)
(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)(576,701)
(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)(584,699)
(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)(592,717)
(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)(600,715)
(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)
(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)
(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)
(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)(752,872)
(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)(760,885)
(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)(768,888)
(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)(776,891)
(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)(784,904)
(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)(792,907)
(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)(800,920)
(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)(808,923)
(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)(816,941)
(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)(824,939)
(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)(832,957)
(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)(840,955);;
s1 := (  1,186)(  2,190)(  3,189)(  4,188)(  5,187)(  6,181)(  7,185)(  8,184)
(  9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)( 16,201)
( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)( 24,198)
( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)( 32,220)
( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)( 40,212)
( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)( 48,234)
( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,236)
( 57,240)( 58,239)( 59,238)( 60,237)( 61,126)( 62,130)( 63,129)( 64,128)
( 65,127)( 66,121)( 67,125)( 68,124)( 69,123)( 70,122)( 71,131)( 72,135)
( 73,134)( 74,133)( 75,132)( 76,141)( 77,145)( 78,144)( 79,143)( 80,142)
( 81,136)( 82,140)( 83,139)( 84,138)( 85,137)( 86,146)( 87,150)( 88,149)
( 89,148)( 90,147)( 91,156)( 92,160)( 93,159)( 94,158)( 95,157)( 96,151)
( 97,155)( 98,154)( 99,153)(100,152)(101,161)(102,165)(103,164)(104,163)
(105,162)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)
(113,169)(114,168)(115,167)(116,176)(117,180)(118,179)(119,178)(120,177)
(241,426)(242,430)(243,429)(244,428)(245,427)(246,421)(247,425)(248,424)
(249,423)(250,422)(251,431)(252,435)(253,434)(254,433)(255,432)(256,441)
(257,445)(258,444)(259,443)(260,442)(261,436)(262,440)(263,439)(264,438)
(265,437)(266,446)(267,450)(268,449)(269,448)(270,447)(271,456)(272,460)
(273,459)(274,458)(275,457)(276,451)(277,455)(278,454)(279,453)(280,452)
(281,461)(282,465)(283,464)(284,463)(285,462)(286,471)(287,475)(288,474)
(289,473)(290,472)(291,466)(292,470)(293,469)(294,468)(295,467)(296,476)
(297,480)(298,479)(299,478)(300,477)(301,366)(302,370)(303,369)(304,368)
(305,367)(306,361)(307,365)(308,364)(309,363)(310,362)(311,371)(312,375)
(313,374)(314,373)(315,372)(316,381)(317,385)(318,384)(319,383)(320,382)
(321,376)(322,380)(323,379)(324,378)(325,377)(326,386)(327,390)(328,389)
(329,388)(330,387)(331,396)(332,400)(333,399)(334,398)(335,397)(336,391)
(337,395)(338,394)(339,393)(340,392)(341,401)(342,405)(343,404)(344,403)
(345,402)(346,411)(347,415)(348,414)(349,413)(350,412)(351,406)(352,410)
(353,409)(354,408)(355,407)(356,416)(357,420)(358,419)(359,418)(360,417)
(481,666)(482,670)(483,669)(484,668)(485,667)(486,661)(487,665)(488,664)
(489,663)(490,662)(491,671)(492,675)(493,674)(494,673)(495,672)(496,681)
(497,685)(498,684)(499,683)(500,682)(501,676)(502,680)(503,679)(504,678)
(505,677)(506,686)(507,690)(508,689)(509,688)(510,687)(511,696)(512,700)
(513,699)(514,698)(515,697)(516,691)(517,695)(518,694)(519,693)(520,692)
(521,701)(522,705)(523,704)(524,703)(525,702)(526,711)(527,715)(528,714)
(529,713)(530,712)(531,706)(532,710)(533,709)(534,708)(535,707)(536,716)
(537,720)(538,719)(539,718)(540,717)(541,606)(542,610)(543,609)(544,608)
(545,607)(546,601)(547,605)(548,604)(549,603)(550,602)(551,611)(552,615)
(553,614)(554,613)(555,612)(556,621)(557,625)(558,624)(559,623)(560,622)
(561,616)(562,620)(563,619)(564,618)(565,617)(566,626)(567,630)(568,629)
(569,628)(570,627)(571,636)(572,640)(573,639)(574,638)(575,637)(576,631)
(577,635)(578,634)(579,633)(580,632)(581,641)(582,645)(583,644)(584,643)
(585,642)(586,651)(587,655)(588,654)(589,653)(590,652)(591,646)(592,650)
(593,649)(594,648)(595,647)(596,656)(597,660)(598,659)(599,658)(600,657)
(721,906)(722,910)(723,909)(724,908)(725,907)(726,901)(727,905)(728,904)
(729,903)(730,902)(731,911)(732,915)(733,914)(734,913)(735,912)(736,921)
(737,925)(738,924)(739,923)(740,922)(741,916)(742,920)(743,919)(744,918)
(745,917)(746,926)(747,930)(748,929)(749,928)(750,927)(751,936)(752,940)
(753,939)(754,938)(755,937)(756,931)(757,935)(758,934)(759,933)(760,932)
(761,941)(762,945)(763,944)(764,943)(765,942)(766,951)(767,955)(768,954)
(769,953)(770,952)(771,946)(772,950)(773,949)(774,948)(775,947)(776,956)
(777,960)(778,959)(779,958)(780,957)(781,846)(782,850)(783,849)(784,848)
(785,847)(786,841)(787,845)(788,844)(789,843)(790,842)(791,851)(792,855)
(793,854)(794,853)(795,852)(796,861)(797,865)(798,864)(799,863)(800,862)
(801,856)(802,860)(803,859)(804,858)(805,857)(806,866)(807,870)(808,869)
(809,868)(810,867)(811,876)(812,880)(813,879)(814,878)(815,877)(816,871)
(817,875)(818,874)(819,873)(820,872)(821,881)(822,885)(823,884)(824,883)
(825,882)(826,891)(827,895)(828,894)(829,893)(830,892)(831,886)(832,890)
(833,889)(834,888)(835,887)(836,896)(837,900)(838,899)(839,898)(840,897);;
s2 := (  1,542)(  2,541)(  3,545)(  4,544)(  5,543)(  6,547)(  7,546)(  8,550)
(  9,549)( 10,548)( 11,552)( 12,551)( 13,555)( 14,554)( 15,553)( 16,557)
( 17,556)( 18,560)( 19,559)( 20,558)( 21,562)( 22,561)( 23,565)( 24,564)
( 25,563)( 26,567)( 27,566)( 28,570)( 29,569)( 30,568)( 31,572)( 32,571)
( 33,575)( 34,574)( 35,573)( 36,577)( 37,576)( 38,580)( 39,579)( 40,578)
( 41,582)( 42,581)( 43,585)( 44,584)( 45,583)( 46,587)( 47,586)( 48,590)
( 49,589)( 50,588)( 51,592)( 52,591)( 53,595)( 54,594)( 55,593)( 56,597)
( 57,596)( 58,600)( 59,599)( 60,598)( 61,482)( 62,481)( 63,485)( 64,484)
( 65,483)( 66,487)( 67,486)( 68,490)( 69,489)( 70,488)( 71,492)( 72,491)
( 73,495)( 74,494)( 75,493)( 76,497)( 77,496)( 78,500)( 79,499)( 80,498)
( 81,502)( 82,501)( 83,505)( 84,504)( 85,503)( 86,507)( 87,506)( 88,510)
( 89,509)( 90,508)( 91,512)( 92,511)( 93,515)( 94,514)( 95,513)( 96,517)
( 97,516)( 98,520)( 99,519)(100,518)(101,522)(102,521)(103,525)(104,524)
(105,523)(106,527)(107,526)(108,530)(109,529)(110,528)(111,532)(112,531)
(113,535)(114,534)(115,533)(116,537)(117,536)(118,540)(119,539)(120,538)
(121,662)(122,661)(123,665)(124,664)(125,663)(126,667)(127,666)(128,670)
(129,669)(130,668)(131,672)(132,671)(133,675)(134,674)(135,673)(136,677)
(137,676)(138,680)(139,679)(140,678)(141,682)(142,681)(143,685)(144,684)
(145,683)(146,687)(147,686)(148,690)(149,689)(150,688)(151,692)(152,691)
(153,695)(154,694)(155,693)(156,697)(157,696)(158,700)(159,699)(160,698)
(161,702)(162,701)(163,705)(164,704)(165,703)(166,707)(167,706)(168,710)
(169,709)(170,708)(171,712)(172,711)(173,715)(174,714)(175,713)(176,717)
(177,716)(178,720)(179,719)(180,718)(181,602)(182,601)(183,605)(184,604)
(185,603)(186,607)(187,606)(188,610)(189,609)(190,608)(191,612)(192,611)
(193,615)(194,614)(195,613)(196,617)(197,616)(198,620)(199,619)(200,618)
(201,622)(202,621)(203,625)(204,624)(205,623)(206,627)(207,626)(208,630)
(209,629)(210,628)(211,632)(212,631)(213,635)(214,634)(215,633)(216,637)
(217,636)(218,640)(219,639)(220,638)(221,642)(222,641)(223,645)(224,644)
(225,643)(226,647)(227,646)(228,650)(229,649)(230,648)(231,652)(232,651)
(233,655)(234,654)(235,653)(236,657)(237,656)(238,660)(239,659)(240,658)
(241,782)(242,781)(243,785)(244,784)(245,783)(246,787)(247,786)(248,790)
(249,789)(250,788)(251,792)(252,791)(253,795)(254,794)(255,793)(256,797)
(257,796)(258,800)(259,799)(260,798)(261,802)(262,801)(263,805)(264,804)
(265,803)(266,807)(267,806)(268,810)(269,809)(270,808)(271,812)(272,811)
(273,815)(274,814)(275,813)(276,817)(277,816)(278,820)(279,819)(280,818)
(281,822)(282,821)(283,825)(284,824)(285,823)(286,827)(287,826)(288,830)
(289,829)(290,828)(291,832)(292,831)(293,835)(294,834)(295,833)(296,837)
(297,836)(298,840)(299,839)(300,838)(301,722)(302,721)(303,725)(304,724)
(305,723)(306,727)(307,726)(308,730)(309,729)(310,728)(311,732)(312,731)
(313,735)(314,734)(315,733)(316,737)(317,736)(318,740)(319,739)(320,738)
(321,742)(322,741)(323,745)(324,744)(325,743)(326,747)(327,746)(328,750)
(329,749)(330,748)(331,752)(332,751)(333,755)(334,754)(335,753)(336,757)
(337,756)(338,760)(339,759)(340,758)(341,762)(342,761)(343,765)(344,764)
(345,763)(346,767)(347,766)(348,770)(349,769)(350,768)(351,772)(352,771)
(353,775)(354,774)(355,773)(356,777)(357,776)(358,780)(359,779)(360,778)
(361,902)(362,901)(363,905)(364,904)(365,903)(366,907)(367,906)(368,910)
(369,909)(370,908)(371,912)(372,911)(373,915)(374,914)(375,913)(376,917)
(377,916)(378,920)(379,919)(380,918)(381,922)(382,921)(383,925)(384,924)
(385,923)(386,927)(387,926)(388,930)(389,929)(390,928)(391,932)(392,931)
(393,935)(394,934)(395,933)(396,937)(397,936)(398,940)(399,939)(400,938)
(401,942)(402,941)(403,945)(404,944)(405,943)(406,947)(407,946)(408,950)
(409,949)(410,948)(411,952)(412,951)(413,955)(414,954)(415,953)(416,957)
(417,956)(418,960)(419,959)(420,958)(421,842)(422,841)(423,845)(424,844)
(425,843)(426,847)(427,846)(428,850)(429,849)(430,848)(431,852)(432,851)
(433,855)(434,854)(435,853)(436,857)(437,856)(438,860)(439,859)(440,858)
(441,862)(442,861)(443,865)(444,864)(445,863)(446,867)(447,866)(448,870)
(449,869)(450,868)(451,872)(452,871)(453,875)(454,874)(455,873)(456,877)
(457,876)(458,880)(459,879)(460,878)(461,882)(462,881)(463,885)(464,884)
(465,883)(466,887)(467,886)(468,890)(469,889)(470,888)(471,892)(472,891)
(473,895)(474,894)(475,893)(476,897)(477,896)(478,900)(479,899)(480,898);;
s3 := (241,256)(242,257)(243,258)(244,259)(245,260)(246,261)(247,262)(248,263)
(249,264)(250,265)(251,266)(252,267)(253,268)(254,269)(255,270)(271,286)
(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)
(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,316)(302,317)
(303,318)(304,319)(305,320)(306,321)(307,322)(308,323)(309,324)(310,325)
(311,326)(312,327)(313,328)(314,329)(315,330)(331,346)(332,347)(333,348)
(334,349)(335,350)(336,351)(337,352)(338,353)(339,354)(340,355)(341,356)
(342,357)(343,358)(344,359)(345,360)(361,376)(362,377)(363,378)(364,379)
(365,380)(366,381)(367,382)(368,383)(369,384)(370,385)(371,386)(372,387)
(373,388)(374,389)(375,390)(391,406)(392,407)(393,408)(394,409)(395,410)
(396,411)(397,412)(398,413)(399,414)(400,415)(401,416)(402,417)(403,418)
(404,419)(405,420)(421,436)(422,437)(423,438)(424,439)(425,440)(426,441)
(427,442)(428,443)(429,444)(430,445)(431,446)(432,447)(433,448)(434,449)
(435,450)(451,466)(452,467)(453,468)(454,469)(455,470)(456,471)(457,472)
(458,473)(459,474)(460,475)(461,476)(462,477)(463,478)(464,479)(465,480)
(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)(488,518)
(489,519)(490,520)(491,521)(492,522)(493,523)(494,524)(495,525)(496,526)
(497,527)(498,528)(499,529)(500,530)(501,531)(502,532)(503,533)(504,534)
(505,535)(506,536)(507,537)(508,538)(509,539)(510,540)(541,571)(542,572)
(543,573)(544,574)(545,575)(546,576)(547,577)(548,578)(549,579)(550,580)
(551,581)(552,582)(553,583)(554,584)(555,585)(556,586)(557,587)(558,588)
(559,589)(560,590)(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)
(567,597)(568,598)(569,599)(570,600)(601,631)(602,632)(603,633)(604,634)
(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,641)(612,642)
(613,643)(614,644)(615,645)(616,646)(617,647)(618,648)(619,649)(620,650)
(621,651)(622,652)(623,653)(624,654)(625,655)(626,656)(627,657)(628,658)
(629,659)(630,660)(661,691)(662,692)(663,693)(664,694)(665,695)(666,696)
(667,697)(668,698)(669,699)(670,700)(671,701)(672,702)(673,703)(674,704)
(675,705)(676,706)(677,707)(678,708)(679,709)(680,710)(681,711)(682,712)
(683,713)(684,714)(685,715)(686,716)(687,717)(688,718)(689,719)(690,720)
(721,766)(722,767)(723,768)(724,769)(725,770)(726,771)(727,772)(728,773)
(729,774)(730,775)(731,776)(732,777)(733,778)(734,779)(735,780)(736,751)
(737,752)(738,753)(739,754)(740,755)(741,756)(742,757)(743,758)(744,759)
(745,760)(746,761)(747,762)(748,763)(749,764)(750,765)(781,826)(782,827)
(783,828)(784,829)(785,830)(786,831)(787,832)(788,833)(789,834)(790,835)
(791,836)(792,837)(793,838)(794,839)(795,840)(796,811)(797,812)(798,813)
(799,814)(800,815)(801,816)(802,817)(803,818)(804,819)(805,820)(806,821)
(807,822)(808,823)(809,824)(810,825)(841,886)(842,887)(843,888)(844,889)
(845,890)(846,891)(847,892)(848,893)(849,894)(850,895)(851,896)(852,897)
(853,898)(854,899)(855,900)(856,871)(857,872)(858,873)(859,874)(860,875)
(861,876)(862,877)(863,878)(864,879)(865,880)(866,881)(867,882)(868,883)
(869,884)(870,885)(901,946)(902,947)(903,948)(904,949)(905,950)(906,951)
(907,952)(908,953)(909,954)(910,955)(911,956)(912,957)(913,958)(914,959)
(915,960)(916,931)(917,932)(918,933)(919,934)(920,935)(921,936)(922,937)
(923,938)(924,939)(925,940)(926,941)(927,942)(928,943)(929,944)(930,945);;
s4 := (  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,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)
(  8,133)(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)
( 24,149)( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)
( 72,187)( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)
( 88,203)( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,221)( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)
(248,373)(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)
(264,389)(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)
(280,405)(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)
(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)
(328,443)(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,461)(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)
(344,459)(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)
(352,477)(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)
(360,475)(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)
(488,613)(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)
(496,616)(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)
(504,629)(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)
(512,632)(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)
(520,645)(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)
(528,648)(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)
(536,651)(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)
(544,664)(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)
(552,667)(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)
(560,680)(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)
(568,683)(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)
(576,701)(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)
(584,699)(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)
(592,717)(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)
(600,715)(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)
(728,853)(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)
(736,856)(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)
(744,869)(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)
(752,872)(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)
(760,885)(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)
(768,888)(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)
(776,891)(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)
(784,904)(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)
(792,907)(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)
(800,920)(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)
(808,923)(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)
(816,941)(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)
(824,939)(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)
(832,957)(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)
(840,955);
s1 := Sym(960)!(  1,186)(  2,190)(  3,189)(  4,188)(  5,187)(  6,181)(  7,185)
(  8,184)(  9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)
( 16,201)( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)
( 24,198)( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)
( 32,220)( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)
( 40,212)( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)
( 48,234)( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)
( 56,236)( 57,240)( 58,239)( 59,238)( 60,237)( 61,126)( 62,130)( 63,129)
( 64,128)( 65,127)( 66,121)( 67,125)( 68,124)( 69,123)( 70,122)( 71,131)
( 72,135)( 73,134)( 74,133)( 75,132)( 76,141)( 77,145)( 78,144)( 79,143)
( 80,142)( 81,136)( 82,140)( 83,139)( 84,138)( 85,137)( 86,146)( 87,150)
( 88,149)( 89,148)( 90,147)( 91,156)( 92,160)( 93,159)( 94,158)( 95,157)
( 96,151)( 97,155)( 98,154)( 99,153)(100,152)(101,161)(102,165)(103,164)
(104,163)(105,162)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)
(112,170)(113,169)(114,168)(115,167)(116,176)(117,180)(118,179)(119,178)
(120,177)(241,426)(242,430)(243,429)(244,428)(245,427)(246,421)(247,425)
(248,424)(249,423)(250,422)(251,431)(252,435)(253,434)(254,433)(255,432)
(256,441)(257,445)(258,444)(259,443)(260,442)(261,436)(262,440)(263,439)
(264,438)(265,437)(266,446)(267,450)(268,449)(269,448)(270,447)(271,456)
(272,460)(273,459)(274,458)(275,457)(276,451)(277,455)(278,454)(279,453)
(280,452)(281,461)(282,465)(283,464)(284,463)(285,462)(286,471)(287,475)
(288,474)(289,473)(290,472)(291,466)(292,470)(293,469)(294,468)(295,467)
(296,476)(297,480)(298,479)(299,478)(300,477)(301,366)(302,370)(303,369)
(304,368)(305,367)(306,361)(307,365)(308,364)(309,363)(310,362)(311,371)
(312,375)(313,374)(314,373)(315,372)(316,381)(317,385)(318,384)(319,383)
(320,382)(321,376)(322,380)(323,379)(324,378)(325,377)(326,386)(327,390)
(328,389)(329,388)(330,387)(331,396)(332,400)(333,399)(334,398)(335,397)
(336,391)(337,395)(338,394)(339,393)(340,392)(341,401)(342,405)(343,404)
(344,403)(345,402)(346,411)(347,415)(348,414)(349,413)(350,412)(351,406)
(352,410)(353,409)(354,408)(355,407)(356,416)(357,420)(358,419)(359,418)
(360,417)(481,666)(482,670)(483,669)(484,668)(485,667)(486,661)(487,665)
(488,664)(489,663)(490,662)(491,671)(492,675)(493,674)(494,673)(495,672)
(496,681)(497,685)(498,684)(499,683)(500,682)(501,676)(502,680)(503,679)
(504,678)(505,677)(506,686)(507,690)(508,689)(509,688)(510,687)(511,696)
(512,700)(513,699)(514,698)(515,697)(516,691)(517,695)(518,694)(519,693)
(520,692)(521,701)(522,705)(523,704)(524,703)(525,702)(526,711)(527,715)
(528,714)(529,713)(530,712)(531,706)(532,710)(533,709)(534,708)(535,707)
(536,716)(537,720)(538,719)(539,718)(540,717)(541,606)(542,610)(543,609)
(544,608)(545,607)(546,601)(547,605)(548,604)(549,603)(550,602)(551,611)
(552,615)(553,614)(554,613)(555,612)(556,621)(557,625)(558,624)(559,623)
(560,622)(561,616)(562,620)(563,619)(564,618)(565,617)(566,626)(567,630)
(568,629)(569,628)(570,627)(571,636)(572,640)(573,639)(574,638)(575,637)
(576,631)(577,635)(578,634)(579,633)(580,632)(581,641)(582,645)(583,644)
(584,643)(585,642)(586,651)(587,655)(588,654)(589,653)(590,652)(591,646)
(592,650)(593,649)(594,648)(595,647)(596,656)(597,660)(598,659)(599,658)
(600,657)(721,906)(722,910)(723,909)(724,908)(725,907)(726,901)(727,905)
(728,904)(729,903)(730,902)(731,911)(732,915)(733,914)(734,913)(735,912)
(736,921)(737,925)(738,924)(739,923)(740,922)(741,916)(742,920)(743,919)
(744,918)(745,917)(746,926)(747,930)(748,929)(749,928)(750,927)(751,936)
(752,940)(753,939)(754,938)(755,937)(756,931)(757,935)(758,934)(759,933)
(760,932)(761,941)(762,945)(763,944)(764,943)(765,942)(766,951)(767,955)
(768,954)(769,953)(770,952)(771,946)(772,950)(773,949)(774,948)(775,947)
(776,956)(777,960)(778,959)(779,958)(780,957)(781,846)(782,850)(783,849)
(784,848)(785,847)(786,841)(787,845)(788,844)(789,843)(790,842)(791,851)
(792,855)(793,854)(794,853)(795,852)(796,861)(797,865)(798,864)(799,863)
(800,862)(801,856)(802,860)(803,859)(804,858)(805,857)(806,866)(807,870)
(808,869)(809,868)(810,867)(811,876)(812,880)(813,879)(814,878)(815,877)
(816,871)(817,875)(818,874)(819,873)(820,872)(821,881)(822,885)(823,884)
(824,883)(825,882)(826,891)(827,895)(828,894)(829,893)(830,892)(831,886)
(832,890)(833,889)(834,888)(835,887)(836,896)(837,900)(838,899)(839,898)
(840,897);
s2 := Sym(960)!(  1,542)(  2,541)(  3,545)(  4,544)(  5,543)(  6,547)(  7,546)
(  8,550)(  9,549)( 10,548)( 11,552)( 12,551)( 13,555)( 14,554)( 15,553)
( 16,557)( 17,556)( 18,560)( 19,559)( 20,558)( 21,562)( 22,561)( 23,565)
( 24,564)( 25,563)( 26,567)( 27,566)( 28,570)( 29,569)( 30,568)( 31,572)
( 32,571)( 33,575)( 34,574)( 35,573)( 36,577)( 37,576)( 38,580)( 39,579)
( 40,578)( 41,582)( 42,581)( 43,585)( 44,584)( 45,583)( 46,587)( 47,586)
( 48,590)( 49,589)( 50,588)( 51,592)( 52,591)( 53,595)( 54,594)( 55,593)
( 56,597)( 57,596)( 58,600)( 59,599)( 60,598)( 61,482)( 62,481)( 63,485)
( 64,484)( 65,483)( 66,487)( 67,486)( 68,490)( 69,489)( 70,488)( 71,492)
( 72,491)( 73,495)( 74,494)( 75,493)( 76,497)( 77,496)( 78,500)( 79,499)
( 80,498)( 81,502)( 82,501)( 83,505)( 84,504)( 85,503)( 86,507)( 87,506)
( 88,510)( 89,509)( 90,508)( 91,512)( 92,511)( 93,515)( 94,514)( 95,513)
( 96,517)( 97,516)( 98,520)( 99,519)(100,518)(101,522)(102,521)(103,525)
(104,524)(105,523)(106,527)(107,526)(108,530)(109,529)(110,528)(111,532)
(112,531)(113,535)(114,534)(115,533)(116,537)(117,536)(118,540)(119,539)
(120,538)(121,662)(122,661)(123,665)(124,664)(125,663)(126,667)(127,666)
(128,670)(129,669)(130,668)(131,672)(132,671)(133,675)(134,674)(135,673)
(136,677)(137,676)(138,680)(139,679)(140,678)(141,682)(142,681)(143,685)
(144,684)(145,683)(146,687)(147,686)(148,690)(149,689)(150,688)(151,692)
(152,691)(153,695)(154,694)(155,693)(156,697)(157,696)(158,700)(159,699)
(160,698)(161,702)(162,701)(163,705)(164,704)(165,703)(166,707)(167,706)
(168,710)(169,709)(170,708)(171,712)(172,711)(173,715)(174,714)(175,713)
(176,717)(177,716)(178,720)(179,719)(180,718)(181,602)(182,601)(183,605)
(184,604)(185,603)(186,607)(187,606)(188,610)(189,609)(190,608)(191,612)
(192,611)(193,615)(194,614)(195,613)(196,617)(197,616)(198,620)(199,619)
(200,618)(201,622)(202,621)(203,625)(204,624)(205,623)(206,627)(207,626)
(208,630)(209,629)(210,628)(211,632)(212,631)(213,635)(214,634)(215,633)
(216,637)(217,636)(218,640)(219,639)(220,638)(221,642)(222,641)(223,645)
(224,644)(225,643)(226,647)(227,646)(228,650)(229,649)(230,648)(231,652)
(232,651)(233,655)(234,654)(235,653)(236,657)(237,656)(238,660)(239,659)
(240,658)(241,782)(242,781)(243,785)(244,784)(245,783)(246,787)(247,786)
(248,790)(249,789)(250,788)(251,792)(252,791)(253,795)(254,794)(255,793)
(256,797)(257,796)(258,800)(259,799)(260,798)(261,802)(262,801)(263,805)
(264,804)(265,803)(266,807)(267,806)(268,810)(269,809)(270,808)(271,812)
(272,811)(273,815)(274,814)(275,813)(276,817)(277,816)(278,820)(279,819)
(280,818)(281,822)(282,821)(283,825)(284,824)(285,823)(286,827)(287,826)
(288,830)(289,829)(290,828)(291,832)(292,831)(293,835)(294,834)(295,833)
(296,837)(297,836)(298,840)(299,839)(300,838)(301,722)(302,721)(303,725)
(304,724)(305,723)(306,727)(307,726)(308,730)(309,729)(310,728)(311,732)
(312,731)(313,735)(314,734)(315,733)(316,737)(317,736)(318,740)(319,739)
(320,738)(321,742)(322,741)(323,745)(324,744)(325,743)(326,747)(327,746)
(328,750)(329,749)(330,748)(331,752)(332,751)(333,755)(334,754)(335,753)
(336,757)(337,756)(338,760)(339,759)(340,758)(341,762)(342,761)(343,765)
(344,764)(345,763)(346,767)(347,766)(348,770)(349,769)(350,768)(351,772)
(352,771)(353,775)(354,774)(355,773)(356,777)(357,776)(358,780)(359,779)
(360,778)(361,902)(362,901)(363,905)(364,904)(365,903)(366,907)(367,906)
(368,910)(369,909)(370,908)(371,912)(372,911)(373,915)(374,914)(375,913)
(376,917)(377,916)(378,920)(379,919)(380,918)(381,922)(382,921)(383,925)
(384,924)(385,923)(386,927)(387,926)(388,930)(389,929)(390,928)(391,932)
(392,931)(393,935)(394,934)(395,933)(396,937)(397,936)(398,940)(399,939)
(400,938)(401,942)(402,941)(403,945)(404,944)(405,943)(406,947)(407,946)
(408,950)(409,949)(410,948)(411,952)(412,951)(413,955)(414,954)(415,953)
(416,957)(417,956)(418,960)(419,959)(420,958)(421,842)(422,841)(423,845)
(424,844)(425,843)(426,847)(427,846)(428,850)(429,849)(430,848)(431,852)
(432,851)(433,855)(434,854)(435,853)(436,857)(437,856)(438,860)(439,859)
(440,858)(441,862)(442,861)(443,865)(444,864)(445,863)(446,867)(447,866)
(448,870)(449,869)(450,868)(451,872)(452,871)(453,875)(454,874)(455,873)
(456,877)(457,876)(458,880)(459,879)(460,878)(461,882)(462,881)(463,885)
(464,884)(465,883)(466,887)(467,886)(468,890)(469,889)(470,888)(471,892)
(472,891)(473,895)(474,894)(475,893)(476,897)(477,896)(478,900)(479,899)
(480,898);
s3 := Sym(960)!(241,256)(242,257)(243,258)(244,259)(245,260)(246,261)(247,262)
(248,263)(249,264)(250,265)(251,266)(252,267)(253,268)(254,269)(255,270)
(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)
(279,294)(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,316)
(302,317)(303,318)(304,319)(305,320)(306,321)(307,322)(308,323)(309,324)
(310,325)(311,326)(312,327)(313,328)(314,329)(315,330)(331,346)(332,347)
(333,348)(334,349)(335,350)(336,351)(337,352)(338,353)(339,354)(340,355)
(341,356)(342,357)(343,358)(344,359)(345,360)(361,376)(362,377)(363,378)
(364,379)(365,380)(366,381)(367,382)(368,383)(369,384)(370,385)(371,386)
(372,387)(373,388)(374,389)(375,390)(391,406)(392,407)(393,408)(394,409)
(395,410)(396,411)(397,412)(398,413)(399,414)(400,415)(401,416)(402,417)
(403,418)(404,419)(405,420)(421,436)(422,437)(423,438)(424,439)(425,440)
(426,441)(427,442)(428,443)(429,444)(430,445)(431,446)(432,447)(433,448)
(434,449)(435,450)(451,466)(452,467)(453,468)(454,469)(455,470)(456,471)
(457,472)(458,473)(459,474)(460,475)(461,476)(462,477)(463,478)(464,479)
(465,480)(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)
(488,518)(489,519)(490,520)(491,521)(492,522)(493,523)(494,524)(495,525)
(496,526)(497,527)(498,528)(499,529)(500,530)(501,531)(502,532)(503,533)
(504,534)(505,535)(506,536)(507,537)(508,538)(509,539)(510,540)(541,571)
(542,572)(543,573)(544,574)(545,575)(546,576)(547,577)(548,578)(549,579)
(550,580)(551,581)(552,582)(553,583)(554,584)(555,585)(556,586)(557,587)
(558,588)(559,589)(560,590)(561,591)(562,592)(563,593)(564,594)(565,595)
(566,596)(567,597)(568,598)(569,599)(570,600)(601,631)(602,632)(603,633)
(604,634)(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,641)
(612,642)(613,643)(614,644)(615,645)(616,646)(617,647)(618,648)(619,649)
(620,650)(621,651)(622,652)(623,653)(624,654)(625,655)(626,656)(627,657)
(628,658)(629,659)(630,660)(661,691)(662,692)(663,693)(664,694)(665,695)
(666,696)(667,697)(668,698)(669,699)(670,700)(671,701)(672,702)(673,703)
(674,704)(675,705)(676,706)(677,707)(678,708)(679,709)(680,710)(681,711)
(682,712)(683,713)(684,714)(685,715)(686,716)(687,717)(688,718)(689,719)
(690,720)(721,766)(722,767)(723,768)(724,769)(725,770)(726,771)(727,772)
(728,773)(729,774)(730,775)(731,776)(732,777)(733,778)(734,779)(735,780)
(736,751)(737,752)(738,753)(739,754)(740,755)(741,756)(742,757)(743,758)
(744,759)(745,760)(746,761)(747,762)(748,763)(749,764)(750,765)(781,826)
(782,827)(783,828)(784,829)(785,830)(786,831)(787,832)(788,833)(789,834)
(790,835)(791,836)(792,837)(793,838)(794,839)(795,840)(796,811)(797,812)
(798,813)(799,814)(800,815)(801,816)(802,817)(803,818)(804,819)(805,820)
(806,821)(807,822)(808,823)(809,824)(810,825)(841,886)(842,887)(843,888)
(844,889)(845,890)(846,891)(847,892)(848,893)(849,894)(850,895)(851,896)
(852,897)(853,898)(854,899)(855,900)(856,871)(857,872)(858,873)(859,874)
(860,875)(861,876)(862,877)(863,878)(864,879)(865,880)(866,881)(867,882)
(868,883)(869,884)(870,885)(901,946)(902,947)(903,948)(904,949)(905,950)
(906,951)(907,952)(908,953)(909,954)(910,955)(911,956)(912,957)(913,958)
(914,959)(915,960)(916,931)(917,932)(918,933)(919,934)(920,935)(921,936)
(922,937)(923,938)(924,939)(925,940)(926,941)(927,942)(928,943)(929,944)
(930,945);
s4 := 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,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >; 
 
References : None.
to this polytope