Polytope of Type {4,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240412)
Rank : 4
Schlafli Type : {4,30,4}
Number of vertices, edges, etc : 8, 120, 120, 4
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,15,4}*960b, {4,30,4}*960d, {4,30,4}*960f
4-fold quotients : {2,30,4}*480b, {4,15,4}*480
5-fold quotients : {4,6,4}*384d
8-fold quotients : {2,15,4}*240
10-fold quotients : {4,3,4}*192b, {4,6,4}*192d, {4,6,4}*192f
20-fold quotients : {2,6,4}*96c, {4,3,4}*96
40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s1> of order 2.
4 facets:
4 of 2-fold non-regular quotient of {4,30}*480
4 vertex figures:
4 of {30,4}*240b
Permutation Representation (GAP) :
s0 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)( 17,505)( 18,506)( 19,507)( 20,508)
( 21,509)( 22,510)( 23,511)( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)(473,945)(474,946)
(475,947)(476,948)(477,949)(478,950)(479,951)(480,952);;
s1 := ( 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);;
s2 := ( 1,337)( 2,340)( 3,339)( 4,338)( 5,349)( 6,352)( 7,351)( 8,350)( 9,345)( 10,348)( 11,347)( 12,346)( 13,341)( 14,344)( 15,343)( 16,342)( 17,321)( 18,324)( 19,323)( 20,322)
( 21,333)( 22,336)( 23,335)( 24,334)( 25,329)( 26,332)( 27,331)( 28,330)( 29,325)( 30,328)( 31,327)( 32,326)( 33,385)( 34,388)( 35,387)( 36,386)( 37,397)( 38,400)( 39,399)( 40,398)( 41,393)( 42,396)( 43,395)( 44,394)( 45,389)( 46,392)( 47,391)( 48,390)( 49,369)( 50,372)( 51,371)( 52,370)( 53,381)( 54,384)( 55,383)( 56,382)( 57,377)( 58,380)( 59,379)( 60,378)( 61,373)( 62,376)( 63,375)( 64,374)( 65,353)( 66,356)( 67,355)( 68,354)( 69,365)( 70,368)( 71,367)( 72,366)( 73,361)( 74,364)( 75,363)( 76,362)( 77,357)( 78,360)( 79,359)( 80,358)( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)( 88,270)( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)( 96,262)( 97,241)( 98,244)( 99,243)(100,242)(101,253)(102,256)(103,255)(104,254)(105,249)(106,252)(107,251)(108,250)(109,245)(110,248)(111,247)(112,246)(113,305)(114,308)(115,307)(116,306)(117,317)(118,320)(119,319)(120,318)(121,313)(122,316)(123,315)(124,314)(125,309)(126,312)(127,311)(128,310)(129,289)(130,292)(131,291)(132,290)(133,301)(134,304)(135,303)(136,302)(137,297)(138,300)(139,299)(140,298)(141,293)(142,296)(143,295)(144,294)(145,273)(146,276)(147,275)(148,274)(149,285)(150,288)(151,287)(152,286)(153,281)(154,284)(155,283)(156,282)(157,277)(158,280)(159,279)(160,278)(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)(168,430)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)(184,414)(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)(192,406)(193,465)(194,468)(195,467)(196,466)(197,477)(198,480)(199,479)(200,478)(201,473)(202,476)(203,475)(204,474)(205,469)(206,472)(207,471)(208,470)(209,449)(210,452)(211,451)(212,450)(213,461)(214,464)(215,463)(216,462)(217,457)(218,460)(219,459)(220,458)(221,453)(222,456)(223,455)(224,454)(225,433)(226,436)(227,435)(228,434)(229,445)(230,448)(231,447)(232,446)(233,441)(234,444)(235,443)(236,442)(237,437)(238,440)(239,439)(240,438)(481,817)(482,820)(483,819)(484,818)(485,829)(486,832)(487,831)(488,830)(489,825)(490,828)(491,827)(492,826)(493,821)(494,824)(495,823)(496,822)(497,801)(498,804)(499,803)(500,802)(501,813)(502,816)(503,815)(504,814)(505,809)(506,812)(507,811)(508,810)(509,805)(510,808)(511,807)(512,806)(513,865)(514,868)(515,867)(516,866)(517,877)(518,880)(519,879)(520,878)(521,873)(522,876)(523,875)(524,874)(525,869)(526,872)(527,871)(528,870)(529,849)(530,852)(531,851)(532,850)(533,861)(534,864)(535,863)(536,862)(537,857)(538,860)(539,859)(540,858)(541,853)(542,856)(543,855)(544,854)(545,833)(546,836)(547,835)(548,834)(549,845)(550,848)(551,847)(552,846)(553,841)(554,844)(555,843)(556,842)(557,837)(558,840)(559,839)(560,838)(561,737)(562,740)(563,739)(564,738)(565,749)(566,752)(567,751)(568,750)(569,745)(570,748)(571,747)(572,746)(573,741)(574,744)(575,743)(576,742)(577,721)(578,724)(579,723)(580,722)(581,733)(582,736)(583,735)(584,734)(585,729)(586,732)(587,731)(588,730)(589,725)(590,728)(591,727)(592,726)(593,785)(594,788)(595,787)(596,786)(597,797)(598,800)(599,799)(600,798)(601,793)(602,796)(603,795)(604,794)(605,789)(606,792)(607,791)(608,790)(609,769)(610,772)(611,771)(612,770)(613,781)(614,784)(615,783)(616,782)(617,777)(618,780)(619,779)(620,778)(621,773)(622,776)(623,775)(624,774)(625,753)(626,756)(627,755)(628,754)(629,765)(630,768)(631,767)(632,766)(633,761)(634,764)(635,763)(636,762)(637,757)(638,760)(639,759)(640,758)(641,897)(642,900)(643,899)(644,898)(645,909)(646,912)(647,911)(648,910)(649,905)(650,908)(651,907)(652,906)(653,901)(654,904)(655,903)(656,902)(657,881)(658,884)(659,883)(660,882)(661,893)(662,896)(663,895)(664,894)(665,889)(666,892)(667,891)(668,890)(669,885)(670,888)(671,887)(672,886)(673,945)(674,948)(675,947)(676,946)(677,957)(678,960)(679,959)(680,958)(681,953)(682,956)(683,955)(684,954)(685,949)(686,952)(687,951)(688,950)(689,929)(690,932)(691,931)(692,930)(693,941)(694,944)(695,943)(696,942)(697,937)(698,940)(699,939)(700,938)(701,933)(702,936)(703,935)(704,934)(705,913)(706,916)(707,915)(708,914)(709,925)(710,928)(711,927)(712,926)(713,921)(714,924)
(715,923)(716,922)(717,917)(718,920)(719,919)(720,918);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)
( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864)(865,866)(867,868)(869,870)(871,872)(873,874)(875,876)(877,878)(879,880)(881,882)(883,884)(885,886)(887,888)(889,890)(891,892)(893,894)(895,896)(897,898)(899,900)(901,902)(903,904)(905,906)(907,908)(909,910)(911,912)(913,914)(915,916)(917,918)(919,920)(921,922)(923,924)(925,926)(927,928)(929,930)(931,932)(933,934)(935,936)(937,938)(939,940)(941,942)(943,944)(945,946)(947,948)
(949,950)(951,952)(953,954)(955,956)(957,958)(959,960);;
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*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)( 17,505)( 18,506)( 19,507)
( 20,508)( 21,509)( 22,510)( 23,511)( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)(473,945)
(474,946)(475,947)(476,948)(477,949)(478,950)(479,951)(480,952);
s1 := 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);
s2 := Sym(960)!( 1,337)( 2,340)( 3,339)( 4,338)( 5,349)( 6,352)( 7,351)( 8,350)( 9,345)( 10,348)( 11,347)( 12,346)( 13,341)( 14,344)( 15,343)( 16,342)( 17,321)( 18,324)( 19,323)
( 20,322)( 21,333)( 22,336)( 23,335)( 24,334)( 25,329)( 26,332)( 27,331)( 28,330)( 29,325)( 30,328)( 31,327)( 32,326)( 33,385)( 34,388)( 35,387)( 36,386)( 37,397)( 38,400)( 39,399)( 40,398)( 41,393)( 42,396)( 43,395)( 44,394)( 45,389)( 46,392)( 47,391)( 48,390)( 49,369)( 50,372)( 51,371)( 52,370)( 53,381)( 54,384)( 55,383)( 56,382)( 57,377)( 58,380)( 59,379)( 60,378)( 61,373)( 62,376)( 63,375)( 64,374)( 65,353)( 66,356)( 67,355)( 68,354)( 69,365)( 70,368)( 71,367)( 72,366)( 73,361)( 74,364)( 75,363)( 76,362)( 77,357)( 78,360)( 79,359)( 80,358)( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)( 88,270)( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)( 96,262)( 97,241)( 98,244)( 99,243)(100,242)(101,253)(102,256)(103,255)(104,254)(105,249)(106,252)(107,251)(108,250)(109,245)(110,248)(111,247)(112,246)(113,305)(114,308)(115,307)(116,306)(117,317)(118,320)(119,319)(120,318)(121,313)(122,316)(123,315)(124,314)(125,309)(126,312)(127,311)(128,310)(129,289)(130,292)(131,291)(132,290)(133,301)(134,304)(135,303)(136,302)(137,297)(138,300)(139,299)(140,298)(141,293)(142,296)(143,295)(144,294)(145,273)(146,276)(147,275)(148,274)(149,285)(150,288)(151,287)(152,286)(153,281)(154,284)(155,283)(156,282)(157,277)(158,280)(159,279)(160,278)(161,417)(162,420)(163,419)(164,418)(165,429)(166,432)(167,431)(168,430)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)(177,401)(178,404)(179,403)(180,402)(181,413)(182,416)(183,415)(184,414)(185,409)(186,412)(187,411)(188,410)(189,405)(190,408)(191,407)(192,406)(193,465)(194,468)(195,467)(196,466)(197,477)(198,480)(199,479)(200,478)(201,473)(202,476)(203,475)(204,474)(205,469)(206,472)(207,471)(208,470)(209,449)(210,452)(211,451)(212,450)(213,461)(214,464)(215,463)(216,462)(217,457)(218,460)(219,459)(220,458)(221,453)(222,456)(223,455)(224,454)(225,433)(226,436)(227,435)(228,434)(229,445)(230,448)(231,447)(232,446)(233,441)(234,444)(235,443)(236,442)(237,437)(238,440)(239,439)(240,438)(481,817)(482,820)(483,819)(484,818)(485,829)(486,832)(487,831)(488,830)(489,825)(490,828)(491,827)(492,826)(493,821)(494,824)(495,823)(496,822)(497,801)(498,804)(499,803)(500,802)(501,813)(502,816)(503,815)(504,814)(505,809)(506,812)(507,811)(508,810)(509,805)(510,808)(511,807)(512,806)(513,865)(514,868)(515,867)(516,866)(517,877)(518,880)(519,879)(520,878)(521,873)(522,876)(523,875)(524,874)(525,869)(526,872)(527,871)(528,870)(529,849)(530,852)(531,851)(532,850)(533,861)(534,864)(535,863)(536,862)(537,857)(538,860)(539,859)(540,858)(541,853)(542,856)(543,855)(544,854)(545,833)(546,836)(547,835)(548,834)(549,845)(550,848)(551,847)(552,846)(553,841)(554,844)(555,843)(556,842)(557,837)(558,840)(559,839)(560,838)(561,737)(562,740)(563,739)(564,738)(565,749)(566,752)(567,751)(568,750)(569,745)(570,748)(571,747)(572,746)(573,741)(574,744)(575,743)(576,742)(577,721)(578,724)(579,723)(580,722)(581,733)(582,736)(583,735)(584,734)(585,729)(586,732)(587,731)(588,730)(589,725)(590,728)(591,727)(592,726)(593,785)(594,788)(595,787)(596,786)(597,797)(598,800)(599,799)(600,798)(601,793)(602,796)(603,795)(604,794)(605,789)(606,792)(607,791)(608,790)(609,769)(610,772)(611,771)(612,770)(613,781)(614,784)(615,783)(616,782)(617,777)(618,780)(619,779)(620,778)(621,773)(622,776)(623,775)(624,774)(625,753)(626,756)(627,755)(628,754)(629,765)(630,768)(631,767)(632,766)(633,761)(634,764)(635,763)(636,762)(637,757)(638,760)(639,759)(640,758)(641,897)(642,900)(643,899)(644,898)(645,909)(646,912)(647,911)(648,910)(649,905)(650,908)(651,907)(652,906)(653,901)(654,904)(655,903)(656,902)(657,881)(658,884)(659,883)(660,882)(661,893)(662,896)(663,895)(664,894)(665,889)(666,892)(667,891)(668,890)(669,885)(670,888)(671,887)(672,886)(673,945)(674,948)(675,947)(676,946)(677,957)(678,960)(679,959)(680,958)(681,953)(682,956)(683,955)(684,954)(685,949)(686,952)(687,951)(688,950)(689,929)(690,932)(691,931)(692,930)(693,941)(694,944)(695,943)(696,942)(697,937)(698,940)(699,939)(700,938)(701,933)(702,936)(703,935)(704,934)(705,913)(706,916)(707,915)(708,914)(709,925)(710,928)(711,927)(712,926)(713,921)
(714,924)(715,923)(716,922)(717,917)(718,920)(719,919)(720,918);
s3 := Sym(960)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)
( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864)(865,866)(867,868)(869,870)(871,872)(873,874)(875,876)(877,878)(879,880)(881,882)(883,884)(885,886)(887,888)(889,890)(891,892)(893,894)(895,896)(897,898)(899,900)(901,902)(903,904)(905,906)(907,908)(909,910)(911,912)(913,914)(915,916)(917,918)(919,920)(921,922)(923,924)(925,926)(927,928)(929,930)(931,932)(933,934)(935,936)(937,938)(939,940)(941,942)(943,944)(945,946)
(947,948)(949,950)(951,952)(953,954)(955,956)(957,958)(959,960);
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*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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