Polytope of Type {4,6,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,10,4}*1920a
Also Known As : {{4,6|2},{6,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,208117)
Rank : 5
Schlafli Type : {4,6,10,4}
Number of vertices, edges, etc : 4, 12, 30, 20, 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 : {2,6,10,4}*960, {4,6,10,2}*960a
3-fold quotients : {4,2,10,4}*640
4-fold quotients : {2,6,10,2}*480
5-fold quotients : {4,6,2,4}*384a
6-fold quotients : {2,2,10,4}*320, {4,2,10,2}*320
10-fold quotients : {2,6,2,4}*192, {4,6,2,2}*192a
12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
15-fold quotients : {4,2,2,4}*128
20-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,2,4}*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, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)( 8, 64)
( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 81)
( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)( 24, 78)
( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)( 32,100)
( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)
( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)( 48,114)
( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,116)
( 57,120)( 58,119)( 59,118)( 60,117)(121,186)(122,190)(123,189)(124,188)
(125,187)(126,181)(127,185)(128,184)(129,183)(130,182)(131,191)(132,195)
(133,194)(134,193)(135,192)(136,201)(137,205)(138,204)(139,203)(140,202)
(141,196)(142,200)(143,199)(144,198)(145,197)(146,206)(147,210)(148,209)
(149,208)(150,207)(151,216)(152,220)(153,219)(154,218)(155,217)(156,211)
(157,215)(158,214)(159,213)(160,212)(161,221)(162,225)(163,224)(164,223)
(165,222)(166,231)(167,235)(168,234)(169,233)(170,232)(171,226)(172,230)
(173,229)(174,228)(175,227)(176,236)(177,240)(178,239)(179,238)(180,237)
(241,306)(242,310)(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)
(249,303)(250,302)(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)
(257,325)(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)
(265,317)(266,326)(267,330)(268,329)(269,328)(270,327)(271,336)(272,340)
(273,339)(274,338)(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)
(281,341)(282,345)(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)
(289,353)(290,352)(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)
(297,360)(298,359)(299,358)(300,357)(361,426)(362,430)(363,429)(364,428)
(365,427)(366,421)(367,425)(368,424)(369,423)(370,422)(371,431)(372,435)
(373,434)(374,433)(375,432)(376,441)(377,445)(378,444)(379,443)(380,442)
(381,436)(382,440)(383,439)(384,438)(385,437)(386,446)(387,450)(388,449)
(389,448)(390,447)(391,456)(392,460)(393,459)(394,458)(395,457)(396,451)
(397,455)(398,454)(399,453)(400,452)(401,461)(402,465)(403,464)(404,463)
(405,462)(406,471)(407,475)(408,474)(409,473)(410,472)(411,466)(412,470)
(413,469)(414,468)(415,467)(416,476)(417,480)(418,479)(419,478)(420,477)
(481,546)(482,550)(483,549)(484,548)(485,547)(486,541)(487,545)(488,544)
(489,543)(490,542)(491,551)(492,555)(493,554)(494,553)(495,552)(496,561)
(497,565)(498,564)(499,563)(500,562)(501,556)(502,560)(503,559)(504,558)
(505,557)(506,566)(507,570)(508,569)(509,568)(510,567)(511,576)(512,580)
(513,579)(514,578)(515,577)(516,571)(517,575)(518,574)(519,573)(520,572)
(521,581)(522,585)(523,584)(524,583)(525,582)(526,591)(527,595)(528,594)
(529,593)(530,592)(531,586)(532,590)(533,589)(534,588)(535,587)(536,596)
(537,600)(538,599)(539,598)(540,597)(601,666)(602,670)(603,669)(604,668)
(605,667)(606,661)(607,665)(608,664)(609,663)(610,662)(611,671)(612,675)
(613,674)(614,673)(615,672)(616,681)(617,685)(618,684)(619,683)(620,682)
(621,676)(622,680)(623,679)(624,678)(625,677)(626,686)(627,690)(628,689)
(629,688)(630,687)(631,696)(632,700)(633,699)(634,698)(635,697)(636,691)
(637,695)(638,694)(639,693)(640,692)(641,701)(642,705)(643,704)(644,703)
(645,702)(646,711)(647,715)(648,714)(649,713)(650,712)(651,706)(652,710)
(653,709)(654,708)(655,707)(656,716)(657,720)(658,719)(659,718)(660,717)
(721,786)(722,790)(723,789)(724,788)(725,787)(726,781)(727,785)(728,784)
(729,783)(730,782)(731,791)(732,795)(733,794)(734,793)(735,792)(736,801)
(737,805)(738,804)(739,803)(740,802)(741,796)(742,800)(743,799)(744,798)
(745,797)(746,806)(747,810)(748,809)(749,808)(750,807)(751,816)(752,820)
(753,819)(754,818)(755,817)(756,811)(757,815)(758,814)(759,813)(760,812)
(761,821)(762,825)(763,824)(764,823)(765,822)(766,831)(767,835)(768,834)
(769,833)(770,832)(771,826)(772,830)(773,829)(774,828)(775,827)(776,836)
(777,840)(778,839)(779,838)(780,837)(841,906)(842,910)(843,909)(844,908)
(845,907)(846,901)(847,905)(848,904)(849,903)(850,902)(851,911)(852,915)
(853,914)(854,913)(855,912)(856,921)(857,925)(858,924)(859,923)(860,922)
(861,916)(862,920)(863,919)(864,918)(865,917)(866,926)(867,930)(868,929)
(869,928)(870,927)(871,936)(872,940)(873,939)(874,938)(875,937)(876,931)
(877,935)(878,934)(879,933)(880,932)(881,941)(882,945)(883,944)(884,943)
(885,942)(886,951)(887,955)(888,954)(889,953)(890,952)(891,946)(892,950)
(893,949)(894,948)(895,947)(896,956)(897,960)(898,959)(899,958)(900,957);;
s3 := ( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,187)( 7,186)( 8,190)
( 9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,197)
( 17,196)( 18,200)( 19,199)( 20,198)( 21,202)( 22,201)( 23,205)( 24,204)
( 25,203)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,212)( 32,211)
( 33,215)( 34,214)( 35,213)( 36,217)( 37,216)( 38,220)( 39,219)( 40,218)
( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)( 56,237)
( 57,236)( 58,240)( 59,239)( 60,238)( 61,122)( 62,121)( 63,125)( 64,124)
( 65,123)( 66,127)( 67,126)( 68,130)( 69,129)( 70,128)( 71,132)( 72,131)
( 73,135)( 74,134)( 75,133)( 76,137)( 77,136)( 78,140)( 79,139)( 80,138)
( 81,142)( 82,141)( 83,145)( 84,144)( 85,143)( 86,147)( 87,146)( 88,150)
( 89,149)( 90,148)( 91,152)( 92,151)( 93,155)( 94,154)( 95,153)( 96,157)
( 97,156)( 98,160)( 99,159)(100,158)(101,162)(102,161)(103,165)(104,164)
(105,163)(106,167)(107,166)(108,170)(109,169)(110,168)(111,172)(112,171)
(113,175)(114,174)(115,173)(116,177)(117,176)(118,180)(119,179)(120,178)
(241,437)(242,436)(243,440)(244,439)(245,438)(246,442)(247,441)(248,445)
(249,444)(250,443)(251,447)(252,446)(253,450)(254,449)(255,448)(256,422)
(257,421)(258,425)(259,424)(260,423)(261,427)(262,426)(263,430)(264,429)
(265,428)(266,432)(267,431)(268,435)(269,434)(270,433)(271,467)(272,466)
(273,470)(274,469)(275,468)(276,472)(277,471)(278,475)(279,474)(280,473)
(281,477)(282,476)(283,480)(284,479)(285,478)(286,452)(287,451)(288,455)
(289,454)(290,453)(291,457)(292,456)(293,460)(294,459)(295,458)(296,462)
(297,461)(298,465)(299,464)(300,463)(301,377)(302,376)(303,380)(304,379)
(305,378)(306,382)(307,381)(308,385)(309,384)(310,383)(311,387)(312,386)
(313,390)(314,389)(315,388)(316,362)(317,361)(318,365)(319,364)(320,363)
(321,367)(322,366)(323,370)(324,369)(325,368)(326,372)(327,371)(328,375)
(329,374)(330,373)(331,407)(332,406)(333,410)(334,409)(335,408)(336,412)
(337,411)(338,415)(339,414)(340,413)(341,417)(342,416)(343,420)(344,419)
(345,418)(346,392)(347,391)(348,395)(349,394)(350,393)(351,397)(352,396)
(353,400)(354,399)(355,398)(356,402)(357,401)(358,405)(359,404)(360,403)
(481,692)(482,691)(483,695)(484,694)(485,693)(486,697)(487,696)(488,700)
(489,699)(490,698)(491,702)(492,701)(493,705)(494,704)(495,703)(496,707)
(497,706)(498,710)(499,709)(500,708)(501,712)(502,711)(503,715)(504,714)
(505,713)(506,717)(507,716)(508,720)(509,719)(510,718)(511,662)(512,661)
(513,665)(514,664)(515,663)(516,667)(517,666)(518,670)(519,669)(520,668)
(521,672)(522,671)(523,675)(524,674)(525,673)(526,677)(527,676)(528,680)
(529,679)(530,678)(531,682)(532,681)(533,685)(534,684)(535,683)(536,687)
(537,686)(538,690)(539,689)(540,688)(541,632)(542,631)(543,635)(544,634)
(545,633)(546,637)(547,636)(548,640)(549,639)(550,638)(551,642)(552,641)
(553,645)(554,644)(555,643)(556,647)(557,646)(558,650)(559,649)(560,648)
(561,652)(562,651)(563,655)(564,654)(565,653)(566,657)(567,656)(568,660)
(569,659)(570,658)(571,602)(572,601)(573,605)(574,604)(575,603)(576,607)
(577,606)(578,610)(579,609)(580,608)(581,612)(582,611)(583,615)(584,614)
(585,613)(586,617)(587,616)(588,620)(589,619)(590,618)(591,622)(592,621)
(593,625)(594,624)(595,623)(596,627)(597,626)(598,630)(599,629)(600,628)
(721,947)(722,946)(723,950)(724,949)(725,948)(726,952)(727,951)(728,955)
(729,954)(730,953)(731,957)(732,956)(733,960)(734,959)(735,958)(736,932)
(737,931)(738,935)(739,934)(740,933)(741,937)(742,936)(743,940)(744,939)
(745,938)(746,942)(747,941)(748,945)(749,944)(750,943)(751,917)(752,916)
(753,920)(754,919)(755,918)(756,922)(757,921)(758,925)(759,924)(760,923)
(761,927)(762,926)(763,930)(764,929)(765,928)(766,902)(767,901)(768,905)
(769,904)(770,903)(771,907)(772,906)(773,910)(774,909)(775,908)(776,912)
(777,911)(778,915)(779,914)(780,913)(781,887)(782,886)(783,890)(784,889)
(785,888)(786,892)(787,891)(788,895)(789,894)(790,893)(791,897)(792,896)
(793,900)(794,899)(795,898)(796,872)(797,871)(798,875)(799,874)(800,873)
(801,877)(802,876)(803,880)(804,879)(805,878)(806,882)(807,881)(808,885)
(809,884)(810,883)(811,857)(812,856)(813,860)(814,859)(815,858)(816,862)
(817,861)(818,865)(819,864)(820,863)(821,867)(822,866)(823,870)(824,869)
(825,868)(826,842)(827,841)(828,845)(829,844)(830,843)(831,847)(832,846)
(833,850)(834,849)(835,848)(836,852)(837,851)(838,855)(839,854)(840,853);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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, 66)( 2, 70)( 3, 69)( 4, 68)( 5, 67)( 6, 61)( 7, 65)
( 8, 64)( 9, 63)( 10, 62)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 81)( 17, 85)( 18, 84)( 19, 83)( 20, 82)( 21, 76)( 22, 80)( 23, 79)
( 24, 78)( 25, 77)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 96)
( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)
( 40, 92)( 41,101)( 42,105)( 43,104)( 44,103)( 45,102)( 46,111)( 47,115)
( 48,114)( 49,113)( 50,112)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)
( 56,116)( 57,120)( 58,119)( 59,118)( 60,117)(121,186)(122,190)(123,189)
(124,188)(125,187)(126,181)(127,185)(128,184)(129,183)(130,182)(131,191)
(132,195)(133,194)(134,193)(135,192)(136,201)(137,205)(138,204)(139,203)
(140,202)(141,196)(142,200)(143,199)(144,198)(145,197)(146,206)(147,210)
(148,209)(149,208)(150,207)(151,216)(152,220)(153,219)(154,218)(155,217)
(156,211)(157,215)(158,214)(159,213)(160,212)(161,221)(162,225)(163,224)
(164,223)(165,222)(166,231)(167,235)(168,234)(169,233)(170,232)(171,226)
(172,230)(173,229)(174,228)(175,227)(176,236)(177,240)(178,239)(179,238)
(180,237)(241,306)(242,310)(243,309)(244,308)(245,307)(246,301)(247,305)
(248,304)(249,303)(250,302)(251,311)(252,315)(253,314)(254,313)(255,312)
(256,321)(257,325)(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)
(264,318)(265,317)(266,326)(267,330)(268,329)(269,328)(270,327)(271,336)
(272,340)(273,339)(274,338)(275,337)(276,331)(277,335)(278,334)(279,333)
(280,332)(281,341)(282,345)(283,344)(284,343)(285,342)(286,351)(287,355)
(288,354)(289,353)(290,352)(291,346)(292,350)(293,349)(294,348)(295,347)
(296,356)(297,360)(298,359)(299,358)(300,357)(361,426)(362,430)(363,429)
(364,428)(365,427)(366,421)(367,425)(368,424)(369,423)(370,422)(371,431)
(372,435)(373,434)(374,433)(375,432)(376,441)(377,445)(378,444)(379,443)
(380,442)(381,436)(382,440)(383,439)(384,438)(385,437)(386,446)(387,450)
(388,449)(389,448)(390,447)(391,456)(392,460)(393,459)(394,458)(395,457)
(396,451)(397,455)(398,454)(399,453)(400,452)(401,461)(402,465)(403,464)
(404,463)(405,462)(406,471)(407,475)(408,474)(409,473)(410,472)(411,466)
(412,470)(413,469)(414,468)(415,467)(416,476)(417,480)(418,479)(419,478)
(420,477)(481,546)(482,550)(483,549)(484,548)(485,547)(486,541)(487,545)
(488,544)(489,543)(490,542)(491,551)(492,555)(493,554)(494,553)(495,552)
(496,561)(497,565)(498,564)(499,563)(500,562)(501,556)(502,560)(503,559)
(504,558)(505,557)(506,566)(507,570)(508,569)(509,568)(510,567)(511,576)
(512,580)(513,579)(514,578)(515,577)(516,571)(517,575)(518,574)(519,573)
(520,572)(521,581)(522,585)(523,584)(524,583)(525,582)(526,591)(527,595)
(528,594)(529,593)(530,592)(531,586)(532,590)(533,589)(534,588)(535,587)
(536,596)(537,600)(538,599)(539,598)(540,597)(601,666)(602,670)(603,669)
(604,668)(605,667)(606,661)(607,665)(608,664)(609,663)(610,662)(611,671)
(612,675)(613,674)(614,673)(615,672)(616,681)(617,685)(618,684)(619,683)
(620,682)(621,676)(622,680)(623,679)(624,678)(625,677)(626,686)(627,690)
(628,689)(629,688)(630,687)(631,696)(632,700)(633,699)(634,698)(635,697)
(636,691)(637,695)(638,694)(639,693)(640,692)(641,701)(642,705)(643,704)
(644,703)(645,702)(646,711)(647,715)(648,714)(649,713)(650,712)(651,706)
(652,710)(653,709)(654,708)(655,707)(656,716)(657,720)(658,719)(659,718)
(660,717)(721,786)(722,790)(723,789)(724,788)(725,787)(726,781)(727,785)
(728,784)(729,783)(730,782)(731,791)(732,795)(733,794)(734,793)(735,792)
(736,801)(737,805)(738,804)(739,803)(740,802)(741,796)(742,800)(743,799)
(744,798)(745,797)(746,806)(747,810)(748,809)(749,808)(750,807)(751,816)
(752,820)(753,819)(754,818)(755,817)(756,811)(757,815)(758,814)(759,813)
(760,812)(761,821)(762,825)(763,824)(764,823)(765,822)(766,831)(767,835)
(768,834)(769,833)(770,832)(771,826)(772,830)(773,829)(774,828)(775,827)
(776,836)(777,840)(778,839)(779,838)(780,837)(841,906)(842,910)(843,909)
(844,908)(845,907)(846,901)(847,905)(848,904)(849,903)(850,902)(851,911)
(852,915)(853,914)(854,913)(855,912)(856,921)(857,925)(858,924)(859,923)
(860,922)(861,916)(862,920)(863,919)(864,918)(865,917)(866,926)(867,930)
(868,929)(869,928)(870,927)(871,936)(872,940)(873,939)(874,938)(875,937)
(876,931)(877,935)(878,934)(879,933)(880,932)(881,941)(882,945)(883,944)
(884,943)(885,942)(886,951)(887,955)(888,954)(889,953)(890,952)(891,946)
(892,950)(893,949)(894,948)(895,947)(896,956)(897,960)(898,959)(899,958)
(900,957);
s3 := Sym(960)!( 1,182)( 2,181)( 3,185)( 4,184)( 5,183)( 6,187)( 7,186)
( 8,190)( 9,189)( 10,188)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)
( 16,197)( 17,196)( 18,200)( 19,199)( 20,198)( 21,202)( 22,201)( 23,205)
( 24,204)( 25,203)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,212)
( 32,211)( 33,215)( 34,214)( 35,213)( 36,217)( 37,216)( 38,220)( 39,219)
( 40,218)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,232)( 52,231)( 53,235)( 54,234)( 55,233)
( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,122)( 62,121)( 63,125)
( 64,124)( 65,123)( 66,127)( 67,126)( 68,130)( 69,129)( 70,128)( 71,132)
( 72,131)( 73,135)( 74,134)( 75,133)( 76,137)( 77,136)( 78,140)( 79,139)
( 80,138)( 81,142)( 82,141)( 83,145)( 84,144)( 85,143)( 86,147)( 87,146)
( 88,150)( 89,149)( 90,148)( 91,152)( 92,151)( 93,155)( 94,154)( 95,153)
( 96,157)( 97,156)( 98,160)( 99,159)(100,158)(101,162)(102,161)(103,165)
(104,164)(105,163)(106,167)(107,166)(108,170)(109,169)(110,168)(111,172)
(112,171)(113,175)(114,174)(115,173)(116,177)(117,176)(118,180)(119,179)
(120,178)(241,437)(242,436)(243,440)(244,439)(245,438)(246,442)(247,441)
(248,445)(249,444)(250,443)(251,447)(252,446)(253,450)(254,449)(255,448)
(256,422)(257,421)(258,425)(259,424)(260,423)(261,427)(262,426)(263,430)
(264,429)(265,428)(266,432)(267,431)(268,435)(269,434)(270,433)(271,467)
(272,466)(273,470)(274,469)(275,468)(276,472)(277,471)(278,475)(279,474)
(280,473)(281,477)(282,476)(283,480)(284,479)(285,478)(286,452)(287,451)
(288,455)(289,454)(290,453)(291,457)(292,456)(293,460)(294,459)(295,458)
(296,462)(297,461)(298,465)(299,464)(300,463)(301,377)(302,376)(303,380)
(304,379)(305,378)(306,382)(307,381)(308,385)(309,384)(310,383)(311,387)
(312,386)(313,390)(314,389)(315,388)(316,362)(317,361)(318,365)(319,364)
(320,363)(321,367)(322,366)(323,370)(324,369)(325,368)(326,372)(327,371)
(328,375)(329,374)(330,373)(331,407)(332,406)(333,410)(334,409)(335,408)
(336,412)(337,411)(338,415)(339,414)(340,413)(341,417)(342,416)(343,420)
(344,419)(345,418)(346,392)(347,391)(348,395)(349,394)(350,393)(351,397)
(352,396)(353,400)(354,399)(355,398)(356,402)(357,401)(358,405)(359,404)
(360,403)(481,692)(482,691)(483,695)(484,694)(485,693)(486,697)(487,696)
(488,700)(489,699)(490,698)(491,702)(492,701)(493,705)(494,704)(495,703)
(496,707)(497,706)(498,710)(499,709)(500,708)(501,712)(502,711)(503,715)
(504,714)(505,713)(506,717)(507,716)(508,720)(509,719)(510,718)(511,662)
(512,661)(513,665)(514,664)(515,663)(516,667)(517,666)(518,670)(519,669)
(520,668)(521,672)(522,671)(523,675)(524,674)(525,673)(526,677)(527,676)
(528,680)(529,679)(530,678)(531,682)(532,681)(533,685)(534,684)(535,683)
(536,687)(537,686)(538,690)(539,689)(540,688)(541,632)(542,631)(543,635)
(544,634)(545,633)(546,637)(547,636)(548,640)(549,639)(550,638)(551,642)
(552,641)(553,645)(554,644)(555,643)(556,647)(557,646)(558,650)(559,649)
(560,648)(561,652)(562,651)(563,655)(564,654)(565,653)(566,657)(567,656)
(568,660)(569,659)(570,658)(571,602)(572,601)(573,605)(574,604)(575,603)
(576,607)(577,606)(578,610)(579,609)(580,608)(581,612)(582,611)(583,615)
(584,614)(585,613)(586,617)(587,616)(588,620)(589,619)(590,618)(591,622)
(592,621)(593,625)(594,624)(595,623)(596,627)(597,626)(598,630)(599,629)
(600,628)(721,947)(722,946)(723,950)(724,949)(725,948)(726,952)(727,951)
(728,955)(729,954)(730,953)(731,957)(732,956)(733,960)(734,959)(735,958)
(736,932)(737,931)(738,935)(739,934)(740,933)(741,937)(742,936)(743,940)
(744,939)(745,938)(746,942)(747,941)(748,945)(749,944)(750,943)(751,917)
(752,916)(753,920)(754,919)(755,918)(756,922)(757,921)(758,925)(759,924)
(760,923)(761,927)(762,926)(763,930)(764,929)(765,928)(766,902)(767,901)
(768,905)(769,904)(770,903)(771,907)(772,906)(773,910)(774,909)(775,908)
(776,912)(777,911)(778,915)(779,914)(780,913)(781,887)(782,886)(783,890)
(784,889)(785,888)(786,892)(787,891)(788,895)(789,894)(790,893)(791,897)
(792,896)(793,900)(794,899)(795,898)(796,872)(797,871)(798,875)(799,874)
(800,873)(801,877)(802,876)(803,880)(804,879)(805,878)(806,882)(807,881)
(808,885)(809,884)(810,883)(811,857)(812,856)(813,860)(814,859)(815,858)
(816,862)(817,861)(818,865)(819,864)(820,863)(821,867)(822,866)(823,870)
(824,869)(825,868)(826,842)(827,841)(828,845)(829,844)(830,843)(831,847)
(832,846)(833,850)(834,849)(835,848)(836,852)(837,851)(838,855)(839,854)
(840,853);
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope