Polytope of Type {8,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30,4}*1920a
Also Known As : {{8,30|2},{30,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,182073)
Rank : 4
Schlafli Type : {8,30,4}
Number of vertices, edges, etc : 8, 120, 60, 4
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,30,4}*960a, {8,30,2}*960
3-fold quotients : {8,10,4}*640
4-fold quotients : {2,30,4}*480a, {4,30,2}*480a
5-fold quotients : {8,6,4}*384a
6-fold quotients : {4,10,4}*320, {8,10,2}*320
8-fold quotients : {2,30,2}*240
10-fold quotients : {4,6,4}*192a, {8,6,2}*192
12-fold quotients : {2,10,4}*160, {4,10,2}*160
15-fold quotients : {8,2,4}*128
16-fold quotients : {2,15,2}*120
20-fold quotients : {2,6,4}*96a, {4,6,2}*96a
24-fold quotients : {2,10,2}*80
30-fold quotients : {4,2,4}*64, {8,2,2}*64
40-fold quotients : {2,6,2}*48
48-fold quotients : {2,5,2}*40
60-fold quotients : {2,2,4}*32, {4,2,2}*32
80-fold quotients : {2,3,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)
( 21,501)( 22,502)( 23,503)( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)(128,668)(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)(136,676)(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)(144,684)(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)(152,692)(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)(160,700)(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)(168,708)(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)(176,716)(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)(192,612)(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)(216,636)(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)(224,644)(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)(232,652)(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)(240,660)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)(368,908)(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)(376,916)(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)(384,924)(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)(392,932)(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)(400,940)(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)(408,948)(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)(416,956)(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868)(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)(456,876)(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)(464,884)(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)(472,892)(473,893)(474,894)
(475,895)(476,896)(477,897)(478,898)(479,899)(480,900);;
s1 := ( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,131)( 7,135)( 8,134)( 9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)
( 21,146)( 22,150)( 23,149)( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,196)( 62,200)( 63,199)( 64,198)( 65,197)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,201)( 72,205)( 73,204)( 74,203)( 75,202)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)( 81,191)( 82,195)( 83,194)( 84,193)( 85,192)( 86,186)( 87,190)( 88,189)( 89,188)( 90,187)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)( 96,236)( 97,240)( 98,239)( 99,238)(100,237)(101,231)(102,235)(103,234)(104,233)(105,232)(106,211)(107,215)(108,214)(109,213)(110,212)(111,221)(112,225)(113,224)(114,223)(115,222)(116,216)(117,220)(118,219)(119,218)(120,217)(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)(248,374)(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)(256,376)(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)(264,388)(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)(272,395)(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)(280,402)(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)(288,409)(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)(297,415)(298,414)(299,413)(300,412)(301,436)(302,440)(303,439)(304,438)(305,437)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)(312,445)(313,444)(314,443)(315,442)(316,421)(317,425)(318,424)(319,423)(320,422)(321,431)(322,435)(323,434)(324,433)(325,432)(326,426)(327,430)(328,429)(329,428)(330,427)(331,466)(332,470)(333,469)(334,468)(335,467)(336,476)(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)(344,473)(345,472)(346,451)(347,455)(348,454)(349,453)(350,452)(351,461)(352,465)(353,464)(354,463)(355,462)(356,456)(357,460)(358,459)(359,458)(360,457)(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)(512,635)(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)(520,642)(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)(528,649)(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)(536,651)(537,655)(538,654)(539,653)(540,652)(541,676)(542,680)(543,679)(544,678)(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)(552,685)(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)(560,662)(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)(568,669)(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)(728,854)(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)(736,856)(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)(744,868)(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)(752,875)(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)(760,882)(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)(768,889)(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)(776,891)(777,895)(778,894)(779,893)(780,892)(781,916)(782,920)(783,919)(784,918)(785,917)(786,926)(787,930)(788,929)(789,928)(790,927)(791,921)(792,925)(793,924)(794,923)(795,922)(796,901)(797,905)(798,904)(799,903)(800,902)(801,911)(802,915)(803,914)(804,913)(805,912)(806,906)(807,910)(808,909)(809,908)(810,907)(811,946)(812,950)(813,949)(814,948)(815,947)(816,956)(817,960)(818,959)(819,958)(820,957)(821,951)(822,955)(823,954)(824,953)(825,952)(826,931)(827,935)(828,934)(829,933)(830,932)(831,941)(832,945)(833,944)(834,943)
(835,942)(836,936)(837,940)(838,939)(839,938)(840,937);;
s2 := ( 1,187)( 2,186)( 3,190)( 4,189)( 5,188)( 6,182)( 7,181)( 8,185)( 9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,202)( 17,201)( 18,205)( 19,204)( 20,203)
( 21,197)( 22,196)( 23,200)( 24,199)( 25,198)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,217)( 32,216)( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)( 40,213)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,232)( 47,231)( 48,235)( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,147)( 72,146)( 73,150)( 74,149)( 75,148)( 76,127)( 77,126)( 78,130)( 79,129)( 80,128)( 81,122)( 82,121)( 83,125)( 84,124)( 85,123)( 86,132)( 87,131)( 88,135)( 89,134)( 90,133)( 91,172)( 92,171)( 93,175)( 94,174)( 95,173)( 96,167)( 97,166)( 98,170)( 99,169)(100,168)(101,177)(102,176)(103,180)(104,179)(105,178)(106,157)(107,156)(108,160)(109,159)(110,158)(111,152)(112,151)(113,155)(114,154)(115,153)(116,162)(117,161)(118,165)(119,164)(120,163)(241,457)(242,456)(243,460)(244,459)(245,458)(246,452)(247,451)(248,455)(249,454)(250,453)(251,462)(252,461)(253,465)(254,464)(255,463)(256,472)(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)(264,469)(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,427)(272,426)(273,430)(274,429)(275,428)(276,422)(277,421)(278,425)(279,424)(280,423)(281,432)(282,431)(283,435)(284,434)(285,433)(286,442)(287,441)(288,445)(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)(296,447)(297,446)(298,450)(299,449)(300,448)(301,412)(302,411)(303,415)(304,414)(305,413)(306,407)(307,406)(308,410)(309,409)(310,408)(311,417)(312,416)(313,420)(314,419)(315,418)(316,397)(317,396)(318,400)(319,399)(320,398)(321,392)(322,391)(323,395)(324,394)(325,393)(326,402)(327,401)(328,405)(329,404)(330,403)(331,382)(332,381)(333,385)(334,384)(335,383)(336,377)(337,376)(338,380)(339,379)(340,378)(341,387)(342,386)(343,390)(344,389)(345,388)(346,367)(347,366)(348,370)(349,369)(350,368)(351,362)(352,361)(353,365)(354,364)(355,363)(356,372)(357,371)(358,375)(359,374)(360,373)(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)(512,636)(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)(600,718)(721,877)(722,876)(723,880)(724,879)(725,878)(726,872)(727,871)(728,875)(729,874)(730,873)(731,882)(732,881)(733,885)(734,884)(735,883)(736,892)(737,891)(738,895)(739,894)(740,893)(741,887)(742,886)(743,890)(744,889)(745,888)(746,897)(747,896)(748,900)(749,899)(750,898)(751,847)(752,846)(753,850)(754,849)(755,848)(756,842)(757,841)(758,845)(759,844)(760,843)(761,852)(762,851)(763,855)(764,854)(765,853)(766,862)(767,861)(768,865)(769,864)(770,863)(771,857)(772,856)(773,860)(774,859)(775,858)(776,867)(777,866)(778,870)(779,869)(780,868)(781,937)(782,936)(783,940)(784,939)(785,938)(786,932)(787,931)(788,935)(789,934)(790,933)(791,942)(792,941)(793,945)(794,944)(795,943)(796,952)(797,951)(798,955)(799,954)(800,953)(801,947)(802,946)(803,950)(804,949)(805,948)(806,957)(807,956)(808,960)(809,959)(810,958)(811,907)(812,906)(813,910)(814,909)(815,908)(816,902)(817,901)(818,905)(819,904)(820,903)(821,912)(822,911)(823,915)(824,914)(825,913)(826,922)(827,921)(828,925)(829,924)(830,923)(831,917)(832,916)(833,920)(834,919)
(835,918)(836,927)(837,926)(838,930)(839,929)(840,928);;
s3 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)
( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)(713,953)(714,954)
(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)( 17,497)( 18,498)( 19,499)
( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)(128,668)(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)(136,676)(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)(144,684)(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)(152,692)(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)(160,700)(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)(168,708)(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)(176,716)(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)(192,612)(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)(216,636)(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)(224,644)(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)(232,652)(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)(240,660)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)(368,908)(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)(376,916)(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)(384,924)(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)(392,932)(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)(400,940)(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)(408,948)(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)(416,956)(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868)(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)(456,876)(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)(464,884)(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)(472,892)(473,893)
(474,894)(475,895)(476,896)(477,897)(478,898)(479,899)(480,900);
s1 := Sym(960)!( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,131)( 7,135)( 8,134)( 9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)( 17,140)( 18,139)( 19,138)
( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,196)( 62,200)( 63,199)( 64,198)( 65,197)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,201)( 72,205)( 73,204)( 74,203)( 75,202)( 76,181)( 77,185)( 78,184)( 79,183)( 80,182)( 81,191)( 82,195)( 83,194)( 84,193)( 85,192)( 86,186)( 87,190)( 88,189)( 89,188)( 90,187)( 91,226)( 92,230)( 93,229)( 94,228)( 95,227)( 96,236)( 97,240)( 98,239)( 99,238)(100,237)(101,231)(102,235)(103,234)(104,233)(105,232)(106,211)(107,215)(108,214)(109,213)(110,212)(111,221)(112,225)(113,224)(114,223)(115,222)(116,216)(117,220)(118,219)(119,218)(120,217)(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)(248,374)(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)(256,376)(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)(264,388)(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)(272,395)(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)(280,402)(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)(288,409)(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)(297,415)(298,414)(299,413)(300,412)(301,436)(302,440)(303,439)(304,438)(305,437)(306,446)(307,450)(308,449)(309,448)(310,447)(311,441)(312,445)(313,444)(314,443)(315,442)(316,421)(317,425)(318,424)(319,423)(320,422)(321,431)(322,435)(323,434)(324,433)(325,432)(326,426)(327,430)(328,429)(329,428)(330,427)(331,466)(332,470)(333,469)(334,468)(335,467)(336,476)(337,480)(338,479)(339,478)(340,477)(341,471)(342,475)(343,474)(344,473)(345,472)(346,451)(347,455)(348,454)(349,453)(350,452)(351,461)(352,465)(353,464)(354,463)(355,462)(356,456)(357,460)(358,459)(359,458)(360,457)(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)(512,635)(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)(520,642)(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)(528,649)(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)(536,651)(537,655)(538,654)(539,653)(540,652)(541,676)(542,680)(543,679)(544,678)(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)(552,685)(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)(560,662)(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)(568,669)(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)(728,854)(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)(736,856)(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)(744,868)(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)(752,875)(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)(760,882)(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)(768,889)(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)(776,891)(777,895)(778,894)(779,893)(780,892)(781,916)(782,920)(783,919)(784,918)(785,917)(786,926)(787,930)(788,929)(789,928)(790,927)(791,921)(792,925)(793,924)(794,923)(795,922)(796,901)(797,905)(798,904)(799,903)(800,902)(801,911)(802,915)(803,914)(804,913)(805,912)(806,906)(807,910)(808,909)(809,908)(810,907)(811,946)(812,950)(813,949)(814,948)(815,947)(816,956)(817,960)(818,959)(819,958)(820,957)(821,951)(822,955)(823,954)(824,953)(825,952)(826,931)(827,935)(828,934)(829,933)(830,932)(831,941)(832,945)(833,944)
(834,943)(835,942)(836,936)(837,940)(838,939)(839,938)(840,937);
s2 := Sym(960)!( 1,187)( 2,186)( 3,190)( 4,189)( 5,188)( 6,182)( 7,181)( 8,185)( 9,184)( 10,183)( 11,192)( 12,191)( 13,195)( 14,194)( 15,193)( 16,202)( 17,201)( 18,205)( 19,204)
( 20,203)( 21,197)( 22,196)( 23,200)( 24,199)( 25,198)( 26,207)( 27,206)( 28,210)( 29,209)( 30,208)( 31,217)( 32,216)( 33,220)( 34,219)( 35,218)( 36,212)( 37,211)( 38,215)( 39,214)( 40,213)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,232)( 47,231)( 48,235)( 49,234)( 50,233)( 51,227)( 52,226)( 53,230)( 54,229)( 55,228)( 56,237)( 57,236)( 58,240)( 59,239)( 60,238)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,147)( 72,146)( 73,150)( 74,149)( 75,148)( 76,127)( 77,126)( 78,130)( 79,129)( 80,128)( 81,122)( 82,121)( 83,125)( 84,124)( 85,123)( 86,132)( 87,131)( 88,135)( 89,134)( 90,133)( 91,172)( 92,171)( 93,175)( 94,174)( 95,173)( 96,167)( 97,166)( 98,170)( 99,169)(100,168)(101,177)(102,176)(103,180)(104,179)(105,178)(106,157)(107,156)(108,160)(109,159)(110,158)(111,152)(112,151)(113,155)(114,154)(115,153)(116,162)(117,161)(118,165)(119,164)(120,163)(241,457)(242,456)(243,460)(244,459)(245,458)(246,452)(247,451)(248,455)(249,454)(250,453)(251,462)(252,461)(253,465)(254,464)(255,463)(256,472)(257,471)(258,475)(259,474)(260,473)(261,467)(262,466)(263,470)(264,469)(265,468)(266,477)(267,476)(268,480)(269,479)(270,478)(271,427)(272,426)(273,430)(274,429)(275,428)(276,422)(277,421)(278,425)(279,424)(280,423)(281,432)(282,431)(283,435)(284,434)(285,433)(286,442)(287,441)(288,445)(289,444)(290,443)(291,437)(292,436)(293,440)(294,439)(295,438)(296,447)(297,446)(298,450)(299,449)(300,448)(301,412)(302,411)(303,415)(304,414)(305,413)(306,407)(307,406)(308,410)(309,409)(310,408)(311,417)(312,416)(313,420)(314,419)(315,418)(316,397)(317,396)(318,400)(319,399)(320,398)(321,392)(322,391)(323,395)(324,394)(325,393)(326,402)(327,401)(328,405)(329,404)(330,403)(331,382)(332,381)(333,385)(334,384)(335,383)(336,377)(337,376)(338,380)(339,379)(340,378)(341,387)(342,386)(343,390)(344,389)(345,388)(346,367)(347,366)(348,370)(349,369)(350,368)(351,362)(352,361)(353,365)(354,364)(355,363)(356,372)(357,371)(358,375)(359,374)(360,373)(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)(512,636)(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)(600,718)(721,877)(722,876)(723,880)(724,879)(725,878)(726,872)(727,871)(728,875)(729,874)(730,873)(731,882)(732,881)(733,885)(734,884)(735,883)(736,892)(737,891)(738,895)(739,894)(740,893)(741,887)(742,886)(743,890)(744,889)(745,888)(746,897)(747,896)(748,900)(749,899)(750,898)(751,847)(752,846)(753,850)(754,849)(755,848)(756,842)(757,841)(758,845)(759,844)(760,843)(761,852)(762,851)(763,855)(764,854)(765,853)(766,862)(767,861)(768,865)(769,864)(770,863)(771,857)(772,856)(773,860)(774,859)(775,858)(776,867)(777,866)(778,870)(779,869)(780,868)(781,937)(782,936)(783,940)(784,939)(785,938)(786,932)(787,931)(788,935)(789,934)(790,933)(791,942)(792,941)(793,945)(794,944)(795,943)(796,952)(797,951)(798,955)(799,954)(800,953)(801,947)(802,946)(803,950)(804,949)(805,948)(806,957)(807,956)(808,960)(809,959)(810,958)(811,907)(812,906)(813,910)(814,909)(815,908)(816,902)(817,901)(818,905)(819,904)(820,903)(821,912)(822,911)(823,915)(824,914)(825,913)(826,922)(827,921)(828,925)(829,924)(830,923)(831,917)(832,916)(833,920)
(834,919)(835,918)(836,927)(837,926)(838,930)(839,929)(840,928);
s3 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)( 17,257)( 18,258)( 19,259)
( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)(713,953)
(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope