Polytope of Type {4,6,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,10}*1920a
Also Known As : {{4,6|2},{6,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,208116)
Rank : 5
Schlafli Type : {4,6,4,10}
Number of vertices, edges, etc : 4, 12, 12, 20, 10
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 : {2,6,4,10}*960, {4,6,2,10}*960a
3-fold quotients : {4,2,4,10}*640
4-fold quotients : {4,6,2,5}*480a, {2,6,2,10}*480
5-fold quotients : {4,6,4,2}*384a
6-fold quotients : {2,2,4,10}*320, {4,2,2,10}*320
8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
10-fold quotients : {2,6,4,2}*192a, {4,6,2,2}*192a
12-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
15-fold quotients : {4,2,4,2}*128
16-fold quotients : {2,3,2,5}*120
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
40-fold quotients : {2,3,2,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,481)( 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)( 61,541)( 62,542)( 63,543)( 64,544)
( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)( 72,552)
( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)( 80,560)
( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)( 88,568)
( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)( 96,576)
( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)(112,592)
(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)(120,600)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)(184,694)
(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)(192,702)
(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)(200,710)
(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)(208,718)
(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)(216,666)
(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)(224,674)
(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)(232,682)
(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)(240,690)
(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)(301,781)(302,782)(303,783)(304,784)
(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)(312,792)
(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)(320,800)
(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)(328,808)
(329,809)(330,810)(331,811)(332,812)(333,813)(334,814)(335,815)(336,816)
(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)(344,824)
(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)(352,832)
(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)(360,840)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)(424,934)
(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)(432,942)
(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)(440,950)
(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)(448,958)
(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)(456,906)
(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)(464,914)
(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)(472,922)
(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)(480,930);;
s1 := ( 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);;
s2 := ( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)( 8,123)
( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)
( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)
(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)(248,378)
(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)(256,366)
(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)(264,364)
(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)(272,412)
(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)(280,410)
(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)(288,398)
(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)(296,401)
(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)(304,444)
(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)(312,447)
(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)(320,430)
(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)(328,433)
(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)(336,466)
(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)(344,479)
(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)(352,452)
(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)(360,465)
(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)(488,633)
(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)(496,651)
(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)(504,649)
(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)(512,607)
(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)(520,605)
(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)(528,623)
(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)(536,626)
(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)(544,699)
(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)(552,702)
(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)(560,715)
(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)(568,718)
(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)(576,661)
(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)(584,674)
(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)(592,677)
(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)(600,690)
(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)(728,888)
(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)(736,876)
(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)(744,874)
(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)(752,862)
(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)(760,860)
(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)(768,848)
(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)(776,851)
(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)(784,954)
(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)(792,957)
(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)(800,940)
(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)(808,943)
(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)(816,916)
(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)(824,929)
(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)(832,902)
(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)(840,915);;
s3 := ( 1,301)( 2,305)( 3,304)( 4,303)( 5,302)( 6,306)( 7,310)( 8,309)
( 9,308)( 10,307)( 11,311)( 12,315)( 13,314)( 14,313)( 15,312)( 16,316)
( 17,320)( 18,319)( 19,318)( 20,317)( 21,321)( 22,325)( 23,324)( 24,323)
( 25,322)( 26,326)( 27,330)( 28,329)( 29,328)( 30,327)( 31,331)( 32,335)
( 33,334)( 34,333)( 35,332)( 36,336)( 37,340)( 38,339)( 39,338)( 40,337)
( 41,341)( 42,345)( 43,344)( 44,343)( 45,342)( 46,346)( 47,350)( 48,349)
( 49,348)( 50,347)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)( 56,356)
( 57,360)( 58,359)( 59,358)( 60,357)( 61,241)( 62,245)( 63,244)( 64,243)
( 65,242)( 66,246)( 67,250)( 68,249)( 69,248)( 70,247)( 71,251)( 72,255)
( 73,254)( 74,253)( 75,252)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,261)( 82,265)( 83,264)( 84,263)( 85,262)( 86,266)( 87,270)( 88,269)
( 89,268)( 90,267)( 91,271)( 92,275)( 93,274)( 94,273)( 95,272)( 96,276)
( 97,280)( 98,279)( 99,278)(100,277)(101,281)(102,285)(103,284)(104,283)
(105,282)(106,286)(107,290)(108,289)(109,288)(110,287)(111,291)(112,295)
(113,294)(114,293)(115,292)(116,296)(117,300)(118,299)(119,298)(120,297)
(121,421)(122,425)(123,424)(124,423)(125,422)(126,426)(127,430)(128,429)
(129,428)(130,427)(131,431)(132,435)(133,434)(134,433)(135,432)(136,436)
(137,440)(138,439)(139,438)(140,437)(141,441)(142,445)(143,444)(144,443)
(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,451)(152,455)
(153,454)(154,453)(155,452)(156,456)(157,460)(158,459)(159,458)(160,457)
(161,461)(162,465)(163,464)(164,463)(165,462)(166,466)(167,470)(168,469)
(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)(176,476)
(177,480)(178,479)(179,478)(180,477)(181,361)(182,365)(183,364)(184,363)
(185,362)(186,366)(187,370)(188,369)(189,368)(190,367)(191,371)(192,375)
(193,374)(194,373)(195,372)(196,376)(197,380)(198,379)(199,378)(200,377)
(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)(208,389)
(209,388)(210,387)(211,391)(212,395)(213,394)(214,393)(215,392)(216,396)
(217,400)(218,399)(219,398)(220,397)(221,401)(222,405)(223,404)(224,403)
(225,402)(226,406)(227,410)(228,409)(229,408)(230,407)(231,411)(232,415)
(233,414)(234,413)(235,412)(236,416)(237,420)(238,419)(239,418)(240,417)
(481,781)(482,785)(483,784)(484,783)(485,782)(486,786)(487,790)(488,789)
(489,788)(490,787)(491,791)(492,795)(493,794)(494,793)(495,792)(496,796)
(497,800)(498,799)(499,798)(500,797)(501,801)(502,805)(503,804)(504,803)
(505,802)(506,806)(507,810)(508,809)(509,808)(510,807)(511,811)(512,815)
(513,814)(514,813)(515,812)(516,816)(517,820)(518,819)(519,818)(520,817)
(521,821)(522,825)(523,824)(524,823)(525,822)(526,826)(527,830)(528,829)
(529,828)(530,827)(531,831)(532,835)(533,834)(534,833)(535,832)(536,836)
(537,840)(538,839)(539,838)(540,837)(541,721)(542,725)(543,724)(544,723)
(545,722)(546,726)(547,730)(548,729)(549,728)(550,727)(551,731)(552,735)
(553,734)(554,733)(555,732)(556,736)(557,740)(558,739)(559,738)(560,737)
(561,741)(562,745)(563,744)(564,743)(565,742)(566,746)(567,750)(568,749)
(569,748)(570,747)(571,751)(572,755)(573,754)(574,753)(575,752)(576,756)
(577,760)(578,759)(579,758)(580,757)(581,761)(582,765)(583,764)(584,763)
(585,762)(586,766)(587,770)(588,769)(589,768)(590,767)(591,771)(592,775)
(593,774)(594,773)(595,772)(596,776)(597,780)(598,779)(599,778)(600,777)
(601,901)(602,905)(603,904)(604,903)(605,902)(606,906)(607,910)(608,909)
(609,908)(610,907)(611,911)(612,915)(613,914)(614,913)(615,912)(616,916)
(617,920)(618,919)(619,918)(620,917)(621,921)(622,925)(623,924)(624,923)
(625,922)(626,926)(627,930)(628,929)(629,928)(630,927)(631,931)(632,935)
(633,934)(634,933)(635,932)(636,936)(637,940)(638,939)(639,938)(640,937)
(641,941)(642,945)(643,944)(644,943)(645,942)(646,946)(647,950)(648,949)
(649,948)(650,947)(651,951)(652,955)(653,954)(654,953)(655,952)(656,956)
(657,960)(658,959)(659,958)(660,957)(661,841)(662,845)(663,844)(664,843)
(665,842)(666,846)(667,850)(668,849)(669,848)(670,847)(671,851)(672,855)
(673,854)(674,853)(675,852)(676,856)(677,860)(678,859)(679,858)(680,857)
(681,861)(682,865)(683,864)(684,863)(685,862)(686,866)(687,870)(688,869)
(689,868)(690,867)(691,871)(692,875)(693,874)(694,873)(695,872)(696,876)
(697,880)(698,879)(699,878)(700,877)(701,881)(702,885)(703,884)(704,883)
(705,882)(706,886)(707,890)(708,889)(709,888)(710,887)(711,891)(712,895)
(713,894)(714,893)(715,892)(716,896)(717,900)(718,899)(719,898)(720,897);;
s4 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)( 8, 70)
( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)
( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)( 32, 91)
( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)
( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)( 48,110)
( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)( 56,117)
( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)(124,184)
(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)(132,191)
(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)(140,198)
(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)(148,210)
(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)(156,217)
(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)(164,224)
(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)(172,231)
(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)(180,238)
(241,302)(242,301)(243,305)(244,304)(245,303)(246,307)(247,306)(248,310)
(249,309)(250,308)(251,312)(252,311)(253,315)(254,314)(255,313)(256,317)
(257,316)(258,320)(259,319)(260,318)(261,322)(262,321)(263,325)(264,324)
(265,323)(266,327)(267,326)(268,330)(269,329)(270,328)(271,332)(272,331)
(273,335)(274,334)(275,333)(276,337)(277,336)(278,340)(279,339)(280,338)
(281,342)(282,341)(283,345)(284,344)(285,343)(286,347)(287,346)(288,350)
(289,349)(290,348)(291,352)(292,351)(293,355)(294,354)(295,353)(296,357)
(297,356)(298,360)(299,359)(300,358)(361,422)(362,421)(363,425)(364,424)
(365,423)(366,427)(367,426)(368,430)(369,429)(370,428)(371,432)(372,431)
(373,435)(374,434)(375,433)(376,437)(377,436)(378,440)(379,439)(380,438)
(381,442)(382,441)(383,445)(384,444)(385,443)(386,447)(387,446)(388,450)
(389,449)(390,448)(391,452)(392,451)(393,455)(394,454)(395,453)(396,457)
(397,456)(398,460)(399,459)(400,458)(401,462)(402,461)(403,465)(404,464)
(405,463)(406,467)(407,466)(408,470)(409,469)(410,468)(411,472)(412,471)
(413,475)(414,474)(415,473)(416,477)(417,476)(418,480)(419,479)(420,478)
(481,542)(482,541)(483,545)(484,544)(485,543)(486,547)(487,546)(488,550)
(489,549)(490,548)(491,552)(492,551)(493,555)(494,554)(495,553)(496,557)
(497,556)(498,560)(499,559)(500,558)(501,562)(502,561)(503,565)(504,564)
(505,563)(506,567)(507,566)(508,570)(509,569)(510,568)(511,572)(512,571)
(513,575)(514,574)(515,573)(516,577)(517,576)(518,580)(519,579)(520,578)
(521,582)(522,581)(523,585)(524,584)(525,583)(526,587)(527,586)(528,590)
(529,589)(530,588)(531,592)(532,591)(533,595)(534,594)(535,593)(536,597)
(537,596)(538,600)(539,599)(540,598)(601,662)(602,661)(603,665)(604,664)
(605,663)(606,667)(607,666)(608,670)(609,669)(610,668)(611,672)(612,671)
(613,675)(614,674)(615,673)(616,677)(617,676)(618,680)(619,679)(620,678)
(621,682)(622,681)(623,685)(624,684)(625,683)(626,687)(627,686)(628,690)
(629,689)(630,688)(631,692)(632,691)(633,695)(634,694)(635,693)(636,697)
(637,696)(638,700)(639,699)(640,698)(641,702)(642,701)(643,705)(644,704)
(645,703)(646,707)(647,706)(648,710)(649,709)(650,708)(651,712)(652,711)
(653,715)(654,714)(655,713)(656,717)(657,716)(658,720)(659,719)(660,718)
(721,782)(722,781)(723,785)(724,784)(725,783)(726,787)(727,786)(728,790)
(729,789)(730,788)(731,792)(732,791)(733,795)(734,794)(735,793)(736,797)
(737,796)(738,800)(739,799)(740,798)(741,802)(742,801)(743,805)(744,804)
(745,803)(746,807)(747,806)(748,810)(749,809)(750,808)(751,812)(752,811)
(753,815)(754,814)(755,813)(756,817)(757,816)(758,820)(759,819)(760,818)
(761,822)(762,821)(763,825)(764,824)(765,823)(766,827)(767,826)(768,830)
(769,829)(770,828)(771,832)(772,831)(773,835)(774,834)(775,833)(776,837)
(777,836)(778,840)(779,839)(780,838)(841,902)(842,901)(843,905)(844,904)
(845,903)(846,907)(847,906)(848,910)(849,909)(850,908)(851,912)(852,911)
(853,915)(854,914)(855,913)(856,917)(857,916)(858,920)(859,919)(860,918)
(861,922)(862,921)(863,925)(864,924)(865,923)(866,927)(867,926)(868,930)
(869,929)(870,928)(871,932)(872,931)(873,935)(874,934)(875,933)(876,937)
(877,936)(878,940)(879,939)(880,938)(881,942)(882,941)(883,945)(884,944)
(885,943)(886,947)(887,946)(888,950)(889,949)(890,948)(891,952)(892,951)
(893,955)(894,954)(895,953)(896,957)(897,956)(898,960)(899,959)(900,958);;
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*s0*s1*s0*s1*s0*s1,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)( 61,541)( 62,542)( 63,543)
( 64,544)( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)
( 72,552)( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)
( 80,560)( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)
( 88,568)( 89,569)( 90,570)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)
( 96,576)( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)
(112,592)(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)
(120,600)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)
(184,694)(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)
(192,702)(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)
(200,710)(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)
(208,718)(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)
(216,666)(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)
(224,674)(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)
(232,682)(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)
(240,690)(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)(301,781)(302,782)(303,783)
(304,784)(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)
(312,792)(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)
(320,800)(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)
(328,808)(329,809)(330,810)(331,811)(332,812)(333,813)(334,814)(335,815)
(336,816)(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)
(344,824)(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)
(352,832)(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)
(360,840)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)
(424,934)(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)
(432,942)(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)
(440,950)(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)
(448,958)(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)
(456,906)(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)
(464,914)(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)
(472,922)(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)
(480,930);
s1 := 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);
s2 := Sym(960)!( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)
( 8,123)( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)
( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)
(248,378)(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)
(256,366)(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)
(264,364)(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)
(272,412)(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)
(280,410)(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)
(288,398)(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)
(296,401)(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)
(304,444)(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)
(312,447)(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)
(320,430)(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)
(328,433)(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)
(336,466)(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)
(344,479)(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)
(352,452)(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)
(360,465)(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)
(488,633)(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)
(496,651)(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)
(504,649)(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)
(512,607)(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)
(520,605)(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)
(528,623)(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,626)(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)
(544,699)(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)
(552,702)(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)
(560,715)(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)
(568,718)(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)
(576,661)(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)
(584,674)(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)
(592,677)(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)
(600,690)(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)
(728,888)(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)
(736,876)(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)
(744,874)(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)
(752,862)(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)
(760,860)(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)
(768,848)(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)
(776,851)(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)
(784,954)(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)
(792,957)(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)
(800,940)(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)
(808,943)(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)
(816,916)(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)
(824,929)(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)
(832,902)(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)
(840,915);
s3 := Sym(960)!( 1,301)( 2,305)( 3,304)( 4,303)( 5,302)( 6,306)( 7,310)
( 8,309)( 9,308)( 10,307)( 11,311)( 12,315)( 13,314)( 14,313)( 15,312)
( 16,316)( 17,320)( 18,319)( 19,318)( 20,317)( 21,321)( 22,325)( 23,324)
( 24,323)( 25,322)( 26,326)( 27,330)( 28,329)( 29,328)( 30,327)( 31,331)
( 32,335)( 33,334)( 34,333)( 35,332)( 36,336)( 37,340)( 38,339)( 39,338)
( 40,337)( 41,341)( 42,345)( 43,344)( 44,343)( 45,342)( 46,346)( 47,350)
( 48,349)( 49,348)( 50,347)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)
( 56,356)( 57,360)( 58,359)( 59,358)( 60,357)( 61,241)( 62,245)( 63,244)
( 64,243)( 65,242)( 66,246)( 67,250)( 68,249)( 69,248)( 70,247)( 71,251)
( 72,255)( 73,254)( 74,253)( 75,252)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,261)( 82,265)( 83,264)( 84,263)( 85,262)( 86,266)( 87,270)
( 88,269)( 89,268)( 90,267)( 91,271)( 92,275)( 93,274)( 94,273)( 95,272)
( 96,276)( 97,280)( 98,279)( 99,278)(100,277)(101,281)(102,285)(103,284)
(104,283)(105,282)(106,286)(107,290)(108,289)(109,288)(110,287)(111,291)
(112,295)(113,294)(114,293)(115,292)(116,296)(117,300)(118,299)(119,298)
(120,297)(121,421)(122,425)(123,424)(124,423)(125,422)(126,426)(127,430)
(128,429)(129,428)(130,427)(131,431)(132,435)(133,434)(134,433)(135,432)
(136,436)(137,440)(138,439)(139,438)(140,437)(141,441)(142,445)(143,444)
(144,443)(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,451)
(152,455)(153,454)(154,453)(155,452)(156,456)(157,460)(158,459)(159,458)
(160,457)(161,461)(162,465)(163,464)(164,463)(165,462)(166,466)(167,470)
(168,469)(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)
(176,476)(177,480)(178,479)(179,478)(180,477)(181,361)(182,365)(183,364)
(184,363)(185,362)(186,366)(187,370)(188,369)(189,368)(190,367)(191,371)
(192,375)(193,374)(194,373)(195,372)(196,376)(197,380)(198,379)(199,378)
(200,377)(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)
(208,389)(209,388)(210,387)(211,391)(212,395)(213,394)(214,393)(215,392)
(216,396)(217,400)(218,399)(219,398)(220,397)(221,401)(222,405)(223,404)
(224,403)(225,402)(226,406)(227,410)(228,409)(229,408)(230,407)(231,411)
(232,415)(233,414)(234,413)(235,412)(236,416)(237,420)(238,419)(239,418)
(240,417)(481,781)(482,785)(483,784)(484,783)(485,782)(486,786)(487,790)
(488,789)(489,788)(490,787)(491,791)(492,795)(493,794)(494,793)(495,792)
(496,796)(497,800)(498,799)(499,798)(500,797)(501,801)(502,805)(503,804)
(504,803)(505,802)(506,806)(507,810)(508,809)(509,808)(510,807)(511,811)
(512,815)(513,814)(514,813)(515,812)(516,816)(517,820)(518,819)(519,818)
(520,817)(521,821)(522,825)(523,824)(524,823)(525,822)(526,826)(527,830)
(528,829)(529,828)(530,827)(531,831)(532,835)(533,834)(534,833)(535,832)
(536,836)(537,840)(538,839)(539,838)(540,837)(541,721)(542,725)(543,724)
(544,723)(545,722)(546,726)(547,730)(548,729)(549,728)(550,727)(551,731)
(552,735)(553,734)(554,733)(555,732)(556,736)(557,740)(558,739)(559,738)
(560,737)(561,741)(562,745)(563,744)(564,743)(565,742)(566,746)(567,750)
(568,749)(569,748)(570,747)(571,751)(572,755)(573,754)(574,753)(575,752)
(576,756)(577,760)(578,759)(579,758)(580,757)(581,761)(582,765)(583,764)
(584,763)(585,762)(586,766)(587,770)(588,769)(589,768)(590,767)(591,771)
(592,775)(593,774)(594,773)(595,772)(596,776)(597,780)(598,779)(599,778)
(600,777)(601,901)(602,905)(603,904)(604,903)(605,902)(606,906)(607,910)
(608,909)(609,908)(610,907)(611,911)(612,915)(613,914)(614,913)(615,912)
(616,916)(617,920)(618,919)(619,918)(620,917)(621,921)(622,925)(623,924)
(624,923)(625,922)(626,926)(627,930)(628,929)(629,928)(630,927)(631,931)
(632,935)(633,934)(634,933)(635,932)(636,936)(637,940)(638,939)(639,938)
(640,937)(641,941)(642,945)(643,944)(644,943)(645,942)(646,946)(647,950)
(648,949)(649,948)(650,947)(651,951)(652,955)(653,954)(654,953)(655,952)
(656,956)(657,960)(658,959)(659,958)(660,957)(661,841)(662,845)(663,844)
(664,843)(665,842)(666,846)(667,850)(668,849)(669,848)(670,847)(671,851)
(672,855)(673,854)(674,853)(675,852)(676,856)(677,860)(678,859)(679,858)
(680,857)(681,861)(682,865)(683,864)(684,863)(685,862)(686,866)(687,870)
(688,869)(689,868)(690,867)(691,871)(692,875)(693,874)(694,873)(695,872)
(696,876)(697,880)(698,879)(699,878)(700,877)(701,881)(702,885)(703,884)
(704,883)(705,882)(706,886)(707,890)(708,889)(709,888)(710,887)(711,891)
(712,895)(713,894)(714,893)(715,892)(716,896)(717,900)(718,899)(719,898)
(720,897);
s4 := Sym(960)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)
( 8, 70)( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)
( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)
( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)
( 40, 98)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)
( 48,110)( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)
( 56,117)( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)
(124,184)(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)
(132,191)(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)
(140,198)(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)
(148,210)(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)
(156,217)(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)
(164,224)(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)
(172,231)(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)
(180,238)(241,302)(242,301)(243,305)(244,304)(245,303)(246,307)(247,306)
(248,310)(249,309)(250,308)(251,312)(252,311)(253,315)(254,314)(255,313)
(256,317)(257,316)(258,320)(259,319)(260,318)(261,322)(262,321)(263,325)
(264,324)(265,323)(266,327)(267,326)(268,330)(269,329)(270,328)(271,332)
(272,331)(273,335)(274,334)(275,333)(276,337)(277,336)(278,340)(279,339)
(280,338)(281,342)(282,341)(283,345)(284,344)(285,343)(286,347)(287,346)
(288,350)(289,349)(290,348)(291,352)(292,351)(293,355)(294,354)(295,353)
(296,357)(297,356)(298,360)(299,359)(300,358)(361,422)(362,421)(363,425)
(364,424)(365,423)(366,427)(367,426)(368,430)(369,429)(370,428)(371,432)
(372,431)(373,435)(374,434)(375,433)(376,437)(377,436)(378,440)(379,439)
(380,438)(381,442)(382,441)(383,445)(384,444)(385,443)(386,447)(387,446)
(388,450)(389,449)(390,448)(391,452)(392,451)(393,455)(394,454)(395,453)
(396,457)(397,456)(398,460)(399,459)(400,458)(401,462)(402,461)(403,465)
(404,464)(405,463)(406,467)(407,466)(408,470)(409,469)(410,468)(411,472)
(412,471)(413,475)(414,474)(415,473)(416,477)(417,476)(418,480)(419,479)
(420,478)(481,542)(482,541)(483,545)(484,544)(485,543)(486,547)(487,546)
(488,550)(489,549)(490,548)(491,552)(492,551)(493,555)(494,554)(495,553)
(496,557)(497,556)(498,560)(499,559)(500,558)(501,562)(502,561)(503,565)
(504,564)(505,563)(506,567)(507,566)(508,570)(509,569)(510,568)(511,572)
(512,571)(513,575)(514,574)(515,573)(516,577)(517,576)(518,580)(519,579)
(520,578)(521,582)(522,581)(523,585)(524,584)(525,583)(526,587)(527,586)
(528,590)(529,589)(530,588)(531,592)(532,591)(533,595)(534,594)(535,593)
(536,597)(537,596)(538,600)(539,599)(540,598)(601,662)(602,661)(603,665)
(604,664)(605,663)(606,667)(607,666)(608,670)(609,669)(610,668)(611,672)
(612,671)(613,675)(614,674)(615,673)(616,677)(617,676)(618,680)(619,679)
(620,678)(621,682)(622,681)(623,685)(624,684)(625,683)(626,687)(627,686)
(628,690)(629,689)(630,688)(631,692)(632,691)(633,695)(634,694)(635,693)
(636,697)(637,696)(638,700)(639,699)(640,698)(641,702)(642,701)(643,705)
(644,704)(645,703)(646,707)(647,706)(648,710)(649,709)(650,708)(651,712)
(652,711)(653,715)(654,714)(655,713)(656,717)(657,716)(658,720)(659,719)
(660,718)(721,782)(722,781)(723,785)(724,784)(725,783)(726,787)(727,786)
(728,790)(729,789)(730,788)(731,792)(732,791)(733,795)(734,794)(735,793)
(736,797)(737,796)(738,800)(739,799)(740,798)(741,802)(742,801)(743,805)
(744,804)(745,803)(746,807)(747,806)(748,810)(749,809)(750,808)(751,812)
(752,811)(753,815)(754,814)(755,813)(756,817)(757,816)(758,820)(759,819)
(760,818)(761,822)(762,821)(763,825)(764,824)(765,823)(766,827)(767,826)
(768,830)(769,829)(770,828)(771,832)(772,831)(773,835)(774,834)(775,833)
(776,837)(777,836)(778,840)(779,839)(780,838)(841,902)(842,901)(843,905)
(844,904)(845,903)(846,907)(847,906)(848,910)(849,909)(850,908)(851,912)
(852,911)(853,915)(854,914)(855,913)(856,917)(857,916)(858,920)(859,919)
(860,918)(861,922)(862,921)(863,925)(864,924)(865,923)(866,927)(867,926)
(868,930)(869,929)(870,928)(871,932)(872,931)(873,935)(874,934)(875,933)
(876,937)(877,936)(878,940)(879,939)(880,938)(881,942)(882,941)(883,945)
(884,944)(885,943)(886,947)(887,946)(888,950)(889,949)(890,948)(891,952)
(892,951)(893,955)(894,954)(895,953)(896,957)(897,956)(898,960)(899,959)
(900,958);
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*s0*s1*s0*s1*s0*s1,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope