Polytope of Type {15,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 4
Schlafli Type : {15,4,4}
Number of vertices, edges, etc : 30, 120, 32, 8
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 4
Special Properties :
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 : {15,4,4}*960a
4-fold quotients : {15,4,2}*480
5-fold quotients : {3,4,4}*384b
8-fold quotients : {15,4,2}*240
10-fold quotients : {3,4,4}*192a
16-fold quotients : {15,2,2}*120
20-fold quotients : {3,4,2}*96
40-fold quotients : {3,4,2}*48
48-fold quotients : {5,2,2}*40
80-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s2*s3*s2*s3> of order 2.
4 facets:
4 of {15,4}*240
30 vertex figures:
20 of 2-fold non-regular quotient of {4,4}*64
10 of {4,4}*32
P/N, where N=<s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
4 facets:
4 of 2-fold non-regular quotient of {15,4}*240
20 vertex figures:
10 of 2-fold non-regular quotient of {4,4}*64
10 of {2,4}*16
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74)
( 31, 76)( 32, 75)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(247,248)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)(566,646)(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)(582,710)(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)(598,694)(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)(614,678)(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)(630,662)(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)(732,735)(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)(744,791)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)(760,775)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)(808,887)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)(824,951)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)(840,935)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)(856,919)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)(872,903)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);;
s1 := ( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)( 8,110)( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83)( 20, 82)
( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)(484,578)(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)(492,586)(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)(500,562)(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)(508,570)(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)(516,626)(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)(524,634)(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)(532,610)(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)(540,618)(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)(548,594)(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)(556,602)(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)(644,658)(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)(652,666)(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)(676,706)(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)(684,714)(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)(695,703)(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)(726,832)(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)(734,824)(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)(742,816)(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)(750,808)(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)(758,880)(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)(766,872)(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)(774,864)(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)(782,856)(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)(790,848)(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)(798,840)(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)(886,912)(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)(894,904)(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)(918,960)(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)(926,952)(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)(938,940);;
s2 := ( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)( 8,484)( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)( 16,492)( 17,501)( 18,502)( 19,503)( 20,504)
( 21,497)( 22,498)( 23,499)( 24,500)( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)( 32,508)( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)( 40,516)( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)( 48,524)( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)( 56,532)( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)( 64,540)( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)( 72,548)( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)( 80,556)( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)( 88,564)( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)( 96,572)( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)(104,580)(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)(112,588)(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)(120,596)(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)(128,604)(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)(136,612)(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)(144,620)(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)(152,628)(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)(160,636)(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)(168,644)(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)(176,652)(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)(184,660)(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)(192,668)(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)(200,676)(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)(208,684)(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)(216,692)(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)(224,700)(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)(232,708)(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)(240,716)(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)(248,724)(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)(256,732)(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)(264,740)(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)(272,748)(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)(280,756)(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)(288,764)(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)(296,772)(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)(304,780)(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)(312,788)(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)(320,796)(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)(328,804)(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)(336,812)(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)(344,820)(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)(352,828)(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)(360,836)(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)(368,844)(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)(376,852)(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)(384,860)(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)(392,868)(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)(400,876)(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)(408,884)(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)(416,892)(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)(424,900)(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)(432,908)(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)(440,916)(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)(448,924)(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)(456,932)(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)(464,940)(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)(472,948)(473,957)(474,958)
(475,959)(476,960)(477,953)(478,954)(479,955)(480,956);;
s3 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,246)( 6,245)( 7,248)( 8,247)( 9,251)( 10,252)( 11,249)( 12,250)( 13,256)( 14,255)( 15,254)( 16,253)( 17,257)( 18,258)( 19,259)( 20,260)
( 21,262)( 22,261)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)( 28,266)( 29,272)( 30,271)( 31,270)( 32,269)( 33,273)( 34,274)( 35,275)( 36,276)( 37,278)( 38,277)( 39,280)( 40,279)( 41,283)( 42,284)( 43,281)( 44,282)( 45,288)( 46,287)( 47,286)( 48,285)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)( 64,301)( 65,305)( 66,306)( 67,307)( 68,308)( 69,310)( 70,309)( 71,312)( 72,311)( 73,315)( 74,316)( 75,313)( 76,314)( 77,320)( 78,319)( 79,318)( 80,317)( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)( 88,327)( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)( 97,337)( 98,338)( 99,339)(100,340)(101,342)(102,341)(103,344)(104,343)(105,347)(106,348)(107,345)(108,346)(109,352)(110,351)(111,350)(112,349)(113,353)(114,354)(115,355)(116,356)(117,358)(118,357)(119,360)(120,359)(121,363)(122,364)(123,361)(124,362)(125,368)(126,367)(127,366)(128,365)(129,369)(130,370)(131,371)(132,372)(133,374)(134,373)(135,376)(136,375)(137,379)(138,380)(139,377)(140,378)(141,384)(142,383)(143,382)(144,381)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)(160,397)(161,401)(162,402)(163,403)(164,404)(165,406)(166,405)(167,408)(168,407)(169,411)(170,412)(171,409)(172,410)(173,416)(174,415)(175,414)(176,413)(177,417)(178,418)(179,419)(180,420)(181,422)(182,421)(183,424)(184,423)(185,427)(186,428)(187,425)(188,426)(189,432)(190,431)(191,430)(192,429)(193,433)(194,434)(195,435)(196,436)(197,438)(198,437)(199,440)(200,439)(201,443)(202,444)(203,441)(204,442)(205,448)(206,447)(207,446)(208,445)(209,449)(210,450)(211,451)(212,452)(213,454)(214,453)(215,456)(216,455)(217,459)(218,460)(219,457)(220,458)(221,464)(222,463)(223,462)(224,461)(225,465)(226,466)(227,467)(228,468)(229,470)(230,469)(231,472)(232,471)(233,475)(234,476)(235,473)(236,474)(237,480)(238,479)(239,478)(240,477)(481,721)(482,722)(483,723)(484,724)(485,726)(486,725)(487,728)(488,727)(489,731)(490,732)(491,729)(492,730)(493,736)(494,735)(495,734)(496,733)(497,737)(498,738)(499,739)(500,740)(501,742)(502,741)(503,744)(504,743)(505,747)(506,748)(507,745)(508,746)(509,752)(510,751)(511,750)(512,749)(513,753)(514,754)(515,755)(516,756)(517,758)(518,757)(519,760)(520,759)(521,763)(522,764)(523,761)(524,762)(525,768)(526,767)(527,766)(528,765)(529,769)(530,770)(531,771)(532,772)(533,774)(534,773)(535,776)(536,775)(537,779)(538,780)(539,777)(540,778)(541,784)(542,783)(543,782)(544,781)(545,785)(546,786)(547,787)(548,788)(549,790)(550,789)(551,792)(552,791)(553,795)(554,796)(555,793)(556,794)(557,800)(558,799)(559,798)(560,797)(561,801)(562,802)(563,803)(564,804)(565,806)(566,805)(567,808)(568,807)(569,811)(570,812)(571,809)(572,810)(573,816)(574,815)(575,814)(576,813)(577,817)(578,818)(579,819)(580,820)(581,822)(582,821)(583,824)(584,823)(585,827)(586,828)(587,825)(588,826)(589,832)(590,831)(591,830)(592,829)(593,833)(594,834)(595,835)(596,836)(597,838)(598,837)(599,840)(600,839)(601,843)(602,844)(603,841)(604,842)(605,848)(606,847)(607,846)(608,845)(609,849)(610,850)(611,851)(612,852)(613,854)(614,853)(615,856)(616,855)(617,859)(618,860)(619,857)(620,858)(621,864)(622,863)(623,862)(624,861)(625,865)(626,866)(627,867)(628,868)(629,870)(630,869)(631,872)(632,871)(633,875)(634,876)(635,873)(636,874)(637,880)(638,879)(639,878)(640,877)(641,881)(642,882)(643,883)(644,884)(645,886)(646,885)(647,888)(648,887)(649,891)(650,892)(651,889)(652,890)(653,896)(654,895)(655,894)(656,893)(657,897)(658,898)(659,899)(660,900)(661,902)(662,901)(663,904)(664,903)(665,907)(666,908)(667,905)(668,906)(669,912)(670,911)(671,910)(672,909)(673,913)(674,914)(675,915)(676,916)(677,918)(678,917)(679,920)(680,919)(681,923)(682,924)(683,921)(684,922)(685,928)(686,927)(687,926)(688,925)(689,929)(690,930)(691,931)(692,932)(693,934)(694,933)(695,936)(696,935)(697,939)(698,940)(699,937)(700,938)(701,944)(702,943)(703,942)(704,941)(705,945)(706,946)(707,947)(708,948)(709,950)(710,949)(711,952)(712,951)(713,955)(714,956)
(715,953)(716,954)(717,960)(718,959)(719,958)(720,957);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)( 26, 78)( 27, 80)( 28, 79)( 29, 73)
( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(247,248)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)(566,646)(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)(582,710)(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)(598,694)(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)(614,678)(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)(630,662)(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)(732,735)(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)(744,791)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)(760,775)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)(808,887)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)(824,951)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)(840,935)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)(856,919)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)(872,903)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);
s1 := Sym(960)!( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)( 8,110)( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83)
( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)(484,578)(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)(492,586)(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)(500,562)(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)(508,570)(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)(516,626)(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)(524,634)(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)(532,610)(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)(540,618)(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)(548,594)(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)(556,602)(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)(644,658)(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)(652,666)(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)(676,706)(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)(684,714)(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)(695,703)(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)(726,832)(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)(734,824)(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)(742,816)(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)(750,808)(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)(758,880)(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)(766,872)(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)(774,864)(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)(782,856)(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)(790,848)(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)(798,840)(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)(886,912)(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)(894,904)(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)(918,960)(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)(926,952)(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)(938,940);
s2 := Sym(960)!( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)( 8,484)( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)( 16,492)( 17,501)( 18,502)( 19,503)
( 20,504)( 21,497)( 22,498)( 23,499)( 24,500)( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)( 32,508)( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)( 40,516)( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)( 48,524)( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)( 56,532)( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)( 64,540)( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)( 72,548)( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)( 80,556)( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)( 88,564)( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)( 96,572)( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)(104,580)(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)(112,588)(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)(120,596)(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)(128,604)(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)(136,612)(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)(144,620)(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)(152,628)(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)(160,636)(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)(168,644)(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)(176,652)(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)(184,660)(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)(192,668)(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)(200,676)(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)(208,684)(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)(216,692)(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)(224,700)(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)(232,708)(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)(240,716)(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)(248,724)(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)(256,732)(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)(264,740)(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)(272,748)(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)(280,756)(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)(288,764)(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)(296,772)(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)(304,780)(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)(312,788)(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)(320,796)(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)(328,804)(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)(336,812)(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)(344,820)(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)(352,828)(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)(360,836)(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)(368,844)(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)(376,852)(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)(384,860)(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)(392,868)(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)(400,876)(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)(408,884)(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)(416,892)(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)(424,900)(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)(432,908)(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)(440,916)(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)(448,924)(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)(456,932)(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)(464,940)(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)(472,948)(473,957)
(474,958)(475,959)(476,960)(477,953)(478,954)(479,955)(480,956);
s3 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,246)( 6,245)( 7,248)( 8,247)( 9,251)( 10,252)( 11,249)( 12,250)( 13,256)( 14,255)( 15,254)( 16,253)( 17,257)( 18,258)( 19,259)
( 20,260)( 21,262)( 22,261)( 23,264)( 24,263)( 25,267)( 26,268)( 27,265)( 28,266)( 29,272)( 30,271)( 31,270)( 32,269)( 33,273)( 34,274)( 35,275)( 36,276)( 37,278)( 38,277)( 39,280)( 40,279)( 41,283)( 42,284)( 43,281)( 44,282)( 45,288)( 46,287)( 47,286)( 48,285)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)( 64,301)( 65,305)( 66,306)( 67,307)( 68,308)( 69,310)( 70,309)( 71,312)( 72,311)( 73,315)( 74,316)( 75,313)( 76,314)( 77,320)( 78,319)( 79,318)( 80,317)( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)( 88,327)( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)( 97,337)( 98,338)( 99,339)(100,340)(101,342)(102,341)(103,344)(104,343)(105,347)(106,348)(107,345)(108,346)(109,352)(110,351)(111,350)(112,349)(113,353)(114,354)(115,355)(116,356)(117,358)(118,357)(119,360)(120,359)(121,363)(122,364)(123,361)(124,362)(125,368)(126,367)(127,366)(128,365)(129,369)(130,370)(131,371)(132,372)(133,374)(134,373)(135,376)(136,375)(137,379)(138,380)(139,377)(140,378)(141,384)(142,383)(143,382)(144,381)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)(160,397)(161,401)(162,402)(163,403)(164,404)(165,406)(166,405)(167,408)(168,407)(169,411)(170,412)(171,409)(172,410)(173,416)(174,415)(175,414)(176,413)(177,417)(178,418)(179,419)(180,420)(181,422)(182,421)(183,424)(184,423)(185,427)(186,428)(187,425)(188,426)(189,432)(190,431)(191,430)(192,429)(193,433)(194,434)(195,435)(196,436)(197,438)(198,437)(199,440)(200,439)(201,443)(202,444)(203,441)(204,442)(205,448)(206,447)(207,446)(208,445)(209,449)(210,450)(211,451)(212,452)(213,454)(214,453)(215,456)(216,455)(217,459)(218,460)(219,457)(220,458)(221,464)(222,463)(223,462)(224,461)(225,465)(226,466)(227,467)(228,468)(229,470)(230,469)(231,472)(232,471)(233,475)(234,476)(235,473)(236,474)(237,480)(238,479)(239,478)(240,477)(481,721)(482,722)(483,723)(484,724)(485,726)(486,725)(487,728)(488,727)(489,731)(490,732)(491,729)(492,730)(493,736)(494,735)(495,734)(496,733)(497,737)(498,738)(499,739)(500,740)(501,742)(502,741)(503,744)(504,743)(505,747)(506,748)(507,745)(508,746)(509,752)(510,751)(511,750)(512,749)(513,753)(514,754)(515,755)(516,756)(517,758)(518,757)(519,760)(520,759)(521,763)(522,764)(523,761)(524,762)(525,768)(526,767)(527,766)(528,765)(529,769)(530,770)(531,771)(532,772)(533,774)(534,773)(535,776)(536,775)(537,779)(538,780)(539,777)(540,778)(541,784)(542,783)(543,782)(544,781)(545,785)(546,786)(547,787)(548,788)(549,790)(550,789)(551,792)(552,791)(553,795)(554,796)(555,793)(556,794)(557,800)(558,799)(559,798)(560,797)(561,801)(562,802)(563,803)(564,804)(565,806)(566,805)(567,808)(568,807)(569,811)(570,812)(571,809)(572,810)(573,816)(574,815)(575,814)(576,813)(577,817)(578,818)(579,819)(580,820)(581,822)(582,821)(583,824)(584,823)(585,827)(586,828)(587,825)(588,826)(589,832)(590,831)(591,830)(592,829)(593,833)(594,834)(595,835)(596,836)(597,838)(598,837)(599,840)(600,839)(601,843)(602,844)(603,841)(604,842)(605,848)(606,847)(607,846)(608,845)(609,849)(610,850)(611,851)(612,852)(613,854)(614,853)(615,856)(616,855)(617,859)(618,860)(619,857)(620,858)(621,864)(622,863)(623,862)(624,861)(625,865)(626,866)(627,867)(628,868)(629,870)(630,869)(631,872)(632,871)(633,875)(634,876)(635,873)(636,874)(637,880)(638,879)(639,878)(640,877)(641,881)(642,882)(643,883)(644,884)(645,886)(646,885)(647,888)(648,887)(649,891)(650,892)(651,889)(652,890)(653,896)(654,895)(655,894)(656,893)(657,897)(658,898)(659,899)(660,900)(661,902)(662,901)(663,904)(664,903)(665,907)(666,908)(667,905)(668,906)(669,912)(670,911)(671,910)(672,909)(673,913)(674,914)(675,915)(676,916)(677,918)(678,917)(679,920)(680,919)(681,923)(682,924)(683,921)(684,922)(685,928)(686,927)(687,926)(688,925)(689,929)(690,930)(691,931)(692,932)(693,934)(694,933)(695,936)(696,935)(697,939)(698,940)(699,937)(700,938)(701,944)(702,943)(703,942)(704,941)(705,945)(706,946)(707,947)(708,948)(709,950)(710,949)(711,952)(712,951)(713,955)
(714,956)(715,953)(716,954)(717,960)(718,959)(719,958)(720,957);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope