Polytope of Type {30,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {30,4,4}
Number of vertices, edges, etc : 60, 120, 16, 4
Order of s0s1s2s3 : 60
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 : {15,4,4}*960b, {30,4,2}*960
4-fold quotients : {30,2,4}*480, {15,4,2}*480, {30,4,2}*480b, {30,4,2}*480c
5-fold quotients : {6,4,4}*384d
8-fold quotients : {15,2,4}*240, {15,4,2}*240, {30,2,2}*240
10-fold quotients : {3,4,4}*192b, {6,4,2}*192
12-fold quotients : {10,2,4}*160
16-fold quotients : {15,2,2}*120
20-fold quotients : {6,2,4}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
24-fold quotients : {5,2,4}*80, {10,2,2}*80
40-fold quotients : {3,2,4}*48, {3,4,2}*48, {6,2,2}*48
48-fold quotients : {5,2,2}*40
60-fold quotients : {2,2,4}*32
80-fold quotients : {3,2,2}*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):
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
4 facets:
4 of 2-fold non-regular quotient of {30,4}*480
40 vertex figures:
20 of {4,4}*32
20 of {2,4}*16
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)
( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467)(483,484)(485,497)(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(501,521)(502,522)(503,524)(504,523)(505,537)(506,538)(507,540)(508,539)(509,533)(510,534)(511,536)(512,535)(513,529)(514,530)(515,532)(516,531)(517,525)(518,526)(519,528)(520,527)(543,544)(545,557)(546,558)(547,560)(548,559)(549,553)(550,554)(551,556)(552,555)(561,581)(562,582)(563,584)(564,583)(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)(579,588)(580,587)(603,604)(605,617)(606,618)(607,620)(608,619)(609,613)(610,614)(611,616)(612,615)(621,641)(622,642)(623,644)(624,643)(625,657)(626,658)(627,660)(628,659)(629,653)(630,654)(631,656)(632,655)(633,649)(634,650)(635,652)(636,651)(637,645)(638,646)(639,648)(640,647)(663,664)(665,677)(666,678)(667,680)(668,679)(669,673)(670,674)(671,676)(672,675)(681,701)(682,702)(683,704)(684,703)(685,717)(686,718)(687,720)(688,719)(689,713)(690,714)(691,716)(692,715)(693,709)(694,710)(695,712)(696,711)(697,705)(698,706)(699,708)(700,707)(723,724)(725,737)(726,738)(727,740)(728,739)(729,733)(730,734)(731,736)(732,735)(741,761)(742,762)(743,764)(744,763)(745,777)(746,778)(747,780)(748,779)(749,773)(750,774)(751,776)(752,775)(753,769)(754,770)(755,772)(756,771)(757,765)(758,766)(759,768)(760,767)(783,784)(785,797)(786,798)(787,800)(788,799)(789,793)(790,794)(791,796)(792,795)(801,821)(802,822)(803,824)(804,823)(805,837)(806,838)(807,840)(808,839)(809,833)(810,834)(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)(818,826)(819,828)(820,827)(843,844)(845,857)(846,858)(847,860)(848,859)(849,853)(850,854)(851,856)(852,855)(861,881)(862,882)(863,884)(864,883)(865,897)(866,898)(867,900)(868,899)(869,893)(870,894)(871,896)(872,895)(873,889)(874,890)(875,892)(876,891)(877,885)(878,886)(879,888)(880,887)(903,904)(905,917)(906,918)(907,920)(908,919)(909,913)(910,914)(911,916)(912,915)(921,941)(922,942)(923,944)(924,943)(925,957)(926,958)(927,960)(928,959)(929,953)(930,954)(931,956)(932,955)(933,949)(934,950)(935,952)(936,951)(937,945)(938,946)(939,948)(940,947);;
s1 := ( 1,505)( 2,508)( 3,507)( 4,506)( 5,501)( 6,504)( 7,503)( 8,502)( 9,517)( 10,520)( 11,519)( 12,518)( 13,513)( 14,516)( 15,515)( 16,514)( 17,509)( 18,512)( 19,511)( 20,510)
( 21,485)( 22,488)( 23,487)( 24,486)( 25,481)( 26,484)( 27,483)( 28,482)( 29,497)( 30,500)( 31,499)( 32,498)( 33,493)( 34,496)( 35,495)( 36,494)( 37,489)( 38,492)( 39,491)( 40,490)( 41,525)( 42,528)( 43,527)( 44,526)( 45,521)( 46,524)( 47,523)( 48,522)( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)( 56,534)( 57,529)( 58,532)( 59,531)( 60,530)( 61,565)( 62,568)( 63,567)( 64,566)( 65,561)( 66,564)( 67,563)( 68,562)( 69,577)( 70,580)( 71,579)( 72,578)( 73,573)( 74,576)( 75,575)( 76,574)( 77,569)( 78,572)( 79,571)( 80,570)( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)( 88,542)( 89,557)( 90,560)( 91,559)( 92,558)( 93,553)( 94,556)( 95,555)( 96,554)( 97,549)( 98,552)( 99,551)(100,550)(101,585)(102,588)(103,587)(104,586)(105,581)(106,584)(107,583)(108,582)(109,597)(110,600)(111,599)(112,598)(113,593)(114,596)(115,595)(116,594)(117,589)(118,592)(119,591)(120,590)(121,625)(122,628)(123,627)(124,626)(125,621)(126,624)(127,623)(128,622)(129,637)(130,640)(131,639)(132,638)(133,633)(134,636)(135,635)(136,634)(137,629)(138,632)(139,631)(140,630)(141,605)(142,608)(143,607)(144,606)(145,601)(146,604)(147,603)(148,602)(149,617)(150,620)(151,619)(152,618)(153,613)(154,616)(155,615)(156,614)(157,609)(158,612)(159,611)(160,610)(161,645)(162,648)(163,647)(164,646)(165,641)(166,644)(167,643)(168,642)(169,657)(170,660)(171,659)(172,658)(173,653)(174,656)(175,655)(176,654)(177,649)(178,652)(179,651)(180,650)(181,685)(182,688)(183,687)(184,686)(185,681)(186,684)(187,683)(188,682)(189,697)(190,700)(191,699)(192,698)(193,693)(194,696)(195,695)(196,694)(197,689)(198,692)(199,691)(200,690)(201,665)(202,668)(203,667)(204,666)(205,661)(206,664)(207,663)(208,662)(209,677)(210,680)(211,679)(212,678)(213,673)(214,676)(215,675)(216,674)(217,669)(218,672)(219,671)(220,670)(221,705)(222,708)(223,707)(224,706)(225,701)(226,704)(227,703)(228,702)(229,717)(230,720)(231,719)(232,718)(233,713)(234,716)(235,715)(236,714)(237,709)(238,712)(239,711)(240,710)(241,745)(242,748)(243,747)(244,746)(245,741)(246,744)(247,743)(248,742)(249,757)(250,760)(251,759)(252,758)(253,753)(254,756)(255,755)(256,754)(257,749)(258,752)(259,751)(260,750)(261,725)(262,728)(263,727)(264,726)(265,721)(266,724)(267,723)(268,722)(269,737)(270,740)(271,739)(272,738)(273,733)(274,736)(275,735)(276,734)(277,729)(278,732)(279,731)(280,730)(281,765)(282,768)(283,767)(284,766)(285,761)(286,764)(287,763)(288,762)(289,777)(290,780)(291,779)(292,778)(293,773)(294,776)(295,775)(296,774)(297,769)(298,772)(299,771)(300,770)(301,805)(302,808)(303,807)(304,806)(305,801)(306,804)(307,803)(308,802)(309,817)(310,820)(311,819)(312,818)(313,813)(314,816)(315,815)(316,814)(317,809)(318,812)(319,811)(320,810)(321,785)(322,788)(323,787)(324,786)(325,781)(326,784)(327,783)(328,782)(329,797)(330,800)(331,799)(332,798)(333,793)(334,796)(335,795)(336,794)(337,789)(338,792)(339,791)(340,790)(341,825)(342,828)(343,827)(344,826)(345,821)(346,824)(347,823)(348,822)(349,837)(350,840)(351,839)(352,838)(353,833)(354,836)(355,835)(356,834)(357,829)(358,832)(359,831)(360,830)(361,865)(362,868)(363,867)(364,866)(365,861)(366,864)(367,863)(368,862)(369,877)(370,880)(371,879)(372,878)(373,873)(374,876)(375,875)(376,874)(377,869)(378,872)(379,871)(380,870)(381,845)(382,848)(383,847)(384,846)(385,841)(386,844)(387,843)(388,842)(389,857)(390,860)(391,859)(392,858)(393,853)(394,856)(395,855)(396,854)(397,849)(398,852)(399,851)(400,850)(401,885)(402,888)(403,887)(404,886)(405,881)(406,884)(407,883)(408,882)(409,897)(410,900)(411,899)(412,898)(413,893)(414,896)(415,895)(416,894)(417,889)(418,892)(419,891)(420,890)(421,925)(422,928)(423,927)(424,926)(425,921)(426,924)(427,923)(428,922)(429,937)(430,940)(431,939)(432,938)(433,933)(434,936)(435,935)(436,934)(437,929)(438,932)(439,931)(440,930)(441,905)(442,908)(443,907)(444,906)(445,901)(446,904)(447,903)(448,902)(449,917)(450,920)(451,919)(452,918)(453,913)(454,916)(455,915)(456,914)(457,909)(458,912)(459,911)(460,910)(461,945)(462,948)(463,947)(464,946)(465,941)(466,944)(467,943)(468,942)(469,957)(470,960)(471,959)(472,958)(473,953)(474,956)
(475,955)(476,954)(477,949)(478,952)(479,951)(480,950);;
s2 := ( 1,242)( 2,241)( 3,244)( 4,243)( 5,246)( 6,245)( 7,248)( 8,247)( 9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)
( 21,262)( 22,261)( 23,264)( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)(121,422)(122,421)(123,424)(124,423)(125,426)(126,425)(127,428)(128,427)(129,430)(130,429)(131,432)(132,431)(133,434)(134,433)(135,436)(136,435)(137,438)(138,437)(139,440)(140,439)(141,442)(142,441)(143,444)(144,443)(145,446)(146,445)(147,448)(148,447)(149,450)(150,449)(151,452)(152,451)(153,454)(154,453)(155,456)(156,455)(157,458)(158,457)(159,460)(160,459)(161,462)(162,461)(163,464)(164,463)(165,466)(166,465)(167,468)(168,467)(169,470)(170,469)(171,472)(172,471)(173,474)(174,473)(175,476)(176,475)(177,478)(178,477)(179,480)(180,479)(181,362)(182,361)(183,364)(184,363)(185,366)(186,365)(187,368)(188,367)(189,370)(190,369)(191,372)(192,371)(193,374)(194,373)(195,376)(196,375)(197,378)(198,377)(199,380)(200,379)(201,382)(202,381)(203,384)(204,383)(205,386)(206,385)(207,388)(208,387)(209,390)(210,389)(211,392)(212,391)(213,394)(214,393)(215,396)(216,395)(217,398)(218,397)(219,400)(220,399)(221,402)(222,401)(223,404)(224,403)(225,406)(226,405)(227,408)(228,407)(229,410)(230,409)(231,412)(232,411)(233,414)(234,413)(235,416)(236,415)(237,418)(238,417)(239,420)(240,419)(481,722)(482,721)(483,724)(484,723)(485,726)(486,725)(487,728)(488,727)(489,730)(490,729)(491,732)(492,731)(493,734)(494,733)(495,736)(496,735)(497,738)(498,737)(499,740)(500,739)(501,742)(502,741)(503,744)(504,743)(505,746)(506,745)(507,748)(508,747)(509,750)(510,749)(511,752)(512,751)(513,754)(514,753)(515,756)(516,755)(517,758)(518,757)(519,760)(520,759)(521,762)(522,761)(523,764)(524,763)(525,766)(526,765)(527,768)(528,767)(529,770)(530,769)(531,772)(532,771)(533,774)(534,773)(535,776)(536,775)(537,778)(538,777)(539,780)(540,779)(541,782)(542,781)(543,784)(544,783)(545,786)(546,785)(547,788)(548,787)(549,790)(550,789)(551,792)(552,791)(553,794)(554,793)(555,796)(556,795)(557,798)(558,797)(559,800)(560,799)(561,802)(562,801)(563,804)(564,803)(565,806)(566,805)(567,808)(568,807)(569,810)(570,809)(571,812)(572,811)(573,814)(574,813)(575,816)(576,815)(577,818)(578,817)(579,820)(580,819)(581,822)(582,821)(583,824)(584,823)(585,826)(586,825)(587,828)(588,827)(589,830)(590,829)(591,832)(592,831)(593,834)(594,833)(595,836)(596,835)(597,838)(598,837)(599,840)(600,839)(601,902)(602,901)(603,904)(604,903)(605,906)(606,905)(607,908)(608,907)(609,910)(610,909)(611,912)(612,911)(613,914)(614,913)(615,916)(616,915)(617,918)(618,917)(619,920)(620,919)(621,922)(622,921)(623,924)(624,923)(625,926)(626,925)(627,928)(628,927)(629,930)(630,929)(631,932)(632,931)(633,934)(634,933)(635,936)(636,935)(637,938)(638,937)(639,940)(640,939)(641,942)(642,941)(643,944)(644,943)(645,946)(646,945)(647,948)(648,947)(649,950)(650,949)(651,952)(652,951)(653,954)(654,953)(655,956)(656,955)(657,958)(658,957)(659,960)(660,959)(661,842)(662,841)(663,844)(664,843)(665,846)(666,845)(667,848)(668,847)(669,850)(670,849)(671,852)(672,851)(673,854)(674,853)(675,856)(676,855)(677,858)(678,857)(679,860)(680,859)(681,862)(682,861)(683,864)(684,863)(685,866)(686,865)(687,868)(688,867)(689,870)(690,869)(691,872)(692,871)(693,874)(694,873)(695,876)(696,875)(697,878)(698,877)(699,880)(700,879)(701,882)(702,881)(703,884)(704,883)(705,886)(706,885)(707,888)(708,887)(709,890)(710,889)(711,892)(712,891)(713,894)(714,893)
(715,896)(716,895)(717,898)(718,897)(719,900)(720,899);;
s3 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)
( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)(496,616)(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)(504,624)(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,631)(512,632)(513,633)(514,634)(515,635)(516,636)(517,637)(518,638)(519,639)(520,640)(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)(528,648)(529,649)(530,650)(531,651)(532,652)(533,653)(534,654)(535,655)(536,656)(537,657)(538,658)(539,659)(540,660)(541,661)(542,662)(543,663)(544,664)(545,665)(546,666)(547,667)(548,668)(549,669)(550,670)(551,671)(552,672)(553,673)(554,674)(555,675)(556,676)(557,677)(558,678)(559,679)(560,680)(561,681)(562,682)(563,683)(564,684)(565,685)(566,686)(567,687)(568,688)(569,689)(570,690)(571,691)(572,692)(573,693)(574,694)(575,695)(576,696)(577,697)(578,698)(579,699)(580,700)(581,701)(582,702)(583,703)(584,704)(585,705)(586,706)(587,707)(588,708)(589,709)(590,710)(591,711)(592,712)(593,713)(594,714)(595,715)(596,716)(597,717)(598,718)(599,719)(600,720)(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)(728,848)(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)(736,856)(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)(744,864)(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,871)(752,872)(753,873)(754,874)(755,875)(756,876)(757,877)(758,878)(759,879)(760,880)(761,881)(762,882)(763,883)(764,884)(765,885)(766,886)(767,887)(768,888)(769,889)(770,890)(771,891)(772,892)(773,893)(774,894)(775,895)(776,896)(777,897)(778,898)(779,899)(780,900)(781,901)(782,902)(783,903)(784,904)(785,905)(786,906)(787,907)(788,908)(789,909)(790,910)(791,911)(792,912)(793,913)(794,914)(795,915)(796,916)(797,917)(798,918)(799,919)(800,920)(801,921)(802,922)(803,923)(804,924)(805,925)(806,926)(807,927)(808,928)(809,929)(810,930)(811,931)(812,932)(813,933)(814,934)(815,935)(816,936)(817,937)(818,938)(819,939)(820,940)(821,941)(822,942)(823,943)(824,944)(825,945)(826,946)(827,947)(828,948)(829,949)(830,950)(831,951)(832,952)(833,953)(834,954)
(835,955)(836,956)(837,957)(838,958)(839,959)(840,960);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*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*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)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)
( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467)(483,484)(485,497)(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(501,521)(502,522)(503,524)(504,523)(505,537)(506,538)(507,540)(508,539)(509,533)(510,534)(511,536)(512,535)(513,529)(514,530)(515,532)(516,531)(517,525)(518,526)(519,528)(520,527)(543,544)(545,557)(546,558)(547,560)(548,559)(549,553)(550,554)(551,556)(552,555)(561,581)(562,582)(563,584)(564,583)(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)(571,596)(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)(579,588)(580,587)(603,604)(605,617)(606,618)(607,620)(608,619)(609,613)(610,614)(611,616)(612,615)(621,641)(622,642)(623,644)(624,643)(625,657)(626,658)(627,660)(628,659)(629,653)(630,654)(631,656)(632,655)(633,649)(634,650)(635,652)(636,651)(637,645)(638,646)(639,648)(640,647)(663,664)(665,677)(666,678)(667,680)(668,679)(669,673)(670,674)(671,676)(672,675)(681,701)(682,702)(683,704)(684,703)(685,717)(686,718)(687,720)(688,719)(689,713)(690,714)(691,716)(692,715)(693,709)(694,710)(695,712)(696,711)(697,705)(698,706)(699,708)(700,707)(723,724)(725,737)(726,738)(727,740)(728,739)(729,733)(730,734)(731,736)(732,735)(741,761)(742,762)(743,764)(744,763)(745,777)(746,778)(747,780)(748,779)(749,773)(750,774)(751,776)(752,775)(753,769)(754,770)(755,772)(756,771)(757,765)(758,766)(759,768)(760,767)(783,784)(785,797)(786,798)(787,800)(788,799)(789,793)(790,794)(791,796)(792,795)(801,821)(802,822)(803,824)(804,823)(805,837)(806,838)(807,840)(808,839)(809,833)(810,834)(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)(818,826)(819,828)(820,827)(843,844)(845,857)(846,858)(847,860)(848,859)(849,853)(850,854)(851,856)(852,855)(861,881)(862,882)(863,884)(864,883)(865,897)(866,898)(867,900)(868,899)(869,893)(870,894)(871,896)(872,895)(873,889)(874,890)(875,892)(876,891)(877,885)(878,886)(879,888)(880,887)(903,904)(905,917)(906,918)(907,920)(908,919)(909,913)(910,914)(911,916)(912,915)(921,941)(922,942)(923,944)(924,943)(925,957)(926,958)(927,960)(928,959)(929,953)(930,954)(931,956)(932,955)(933,949)(934,950)(935,952)(936,951)(937,945)(938,946)(939,948)(940,947);
s1 := Sym(960)!( 1,505)( 2,508)( 3,507)( 4,506)( 5,501)( 6,504)( 7,503)( 8,502)( 9,517)( 10,520)( 11,519)( 12,518)( 13,513)( 14,516)( 15,515)( 16,514)( 17,509)( 18,512)( 19,511)
( 20,510)( 21,485)( 22,488)( 23,487)( 24,486)( 25,481)( 26,484)( 27,483)( 28,482)( 29,497)( 30,500)( 31,499)( 32,498)( 33,493)( 34,496)( 35,495)( 36,494)( 37,489)( 38,492)( 39,491)( 40,490)( 41,525)( 42,528)( 43,527)( 44,526)( 45,521)( 46,524)( 47,523)( 48,522)( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)( 56,534)( 57,529)( 58,532)( 59,531)( 60,530)( 61,565)( 62,568)( 63,567)( 64,566)( 65,561)( 66,564)( 67,563)( 68,562)( 69,577)( 70,580)( 71,579)( 72,578)( 73,573)( 74,576)( 75,575)( 76,574)( 77,569)( 78,572)( 79,571)( 80,570)( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)( 88,542)( 89,557)( 90,560)( 91,559)( 92,558)( 93,553)( 94,556)( 95,555)( 96,554)( 97,549)( 98,552)( 99,551)(100,550)(101,585)(102,588)(103,587)(104,586)(105,581)(106,584)(107,583)(108,582)(109,597)(110,600)(111,599)(112,598)(113,593)(114,596)(115,595)(116,594)(117,589)(118,592)(119,591)(120,590)(121,625)(122,628)(123,627)(124,626)(125,621)(126,624)(127,623)(128,622)(129,637)(130,640)(131,639)(132,638)(133,633)(134,636)(135,635)(136,634)(137,629)(138,632)(139,631)(140,630)(141,605)(142,608)(143,607)(144,606)(145,601)(146,604)(147,603)(148,602)(149,617)(150,620)(151,619)(152,618)(153,613)(154,616)(155,615)(156,614)(157,609)(158,612)(159,611)(160,610)(161,645)(162,648)(163,647)(164,646)(165,641)(166,644)(167,643)(168,642)(169,657)(170,660)(171,659)(172,658)(173,653)(174,656)(175,655)(176,654)(177,649)(178,652)(179,651)(180,650)(181,685)(182,688)(183,687)(184,686)(185,681)(186,684)(187,683)(188,682)(189,697)(190,700)(191,699)(192,698)(193,693)(194,696)(195,695)(196,694)(197,689)(198,692)(199,691)(200,690)(201,665)(202,668)(203,667)(204,666)(205,661)(206,664)(207,663)(208,662)(209,677)(210,680)(211,679)(212,678)(213,673)(214,676)(215,675)(216,674)(217,669)(218,672)(219,671)(220,670)(221,705)(222,708)(223,707)(224,706)(225,701)(226,704)(227,703)(228,702)(229,717)(230,720)(231,719)(232,718)(233,713)(234,716)(235,715)(236,714)(237,709)(238,712)(239,711)(240,710)(241,745)(242,748)(243,747)(244,746)(245,741)(246,744)(247,743)(248,742)(249,757)(250,760)(251,759)(252,758)(253,753)(254,756)(255,755)(256,754)(257,749)(258,752)(259,751)(260,750)(261,725)(262,728)(263,727)(264,726)(265,721)(266,724)(267,723)(268,722)(269,737)(270,740)(271,739)(272,738)(273,733)(274,736)(275,735)(276,734)(277,729)(278,732)(279,731)(280,730)(281,765)(282,768)(283,767)(284,766)(285,761)(286,764)(287,763)(288,762)(289,777)(290,780)(291,779)(292,778)(293,773)(294,776)(295,775)(296,774)(297,769)(298,772)(299,771)(300,770)(301,805)(302,808)(303,807)(304,806)(305,801)(306,804)(307,803)(308,802)(309,817)(310,820)(311,819)(312,818)(313,813)(314,816)(315,815)(316,814)(317,809)(318,812)(319,811)(320,810)(321,785)(322,788)(323,787)(324,786)(325,781)(326,784)(327,783)(328,782)(329,797)(330,800)(331,799)(332,798)(333,793)(334,796)(335,795)(336,794)(337,789)(338,792)(339,791)(340,790)(341,825)(342,828)(343,827)(344,826)(345,821)(346,824)(347,823)(348,822)(349,837)(350,840)(351,839)(352,838)(353,833)(354,836)(355,835)(356,834)(357,829)(358,832)(359,831)(360,830)(361,865)(362,868)(363,867)(364,866)(365,861)(366,864)(367,863)(368,862)(369,877)(370,880)(371,879)(372,878)(373,873)(374,876)(375,875)(376,874)(377,869)(378,872)(379,871)(380,870)(381,845)(382,848)(383,847)(384,846)(385,841)(386,844)(387,843)(388,842)(389,857)(390,860)(391,859)(392,858)(393,853)(394,856)(395,855)(396,854)(397,849)(398,852)(399,851)(400,850)(401,885)(402,888)(403,887)(404,886)(405,881)(406,884)(407,883)(408,882)(409,897)(410,900)(411,899)(412,898)(413,893)(414,896)(415,895)(416,894)(417,889)(418,892)(419,891)(420,890)(421,925)(422,928)(423,927)(424,926)(425,921)(426,924)(427,923)(428,922)(429,937)(430,940)(431,939)(432,938)(433,933)(434,936)(435,935)(436,934)(437,929)(438,932)(439,931)(440,930)(441,905)(442,908)(443,907)(444,906)(445,901)(446,904)(447,903)(448,902)(449,917)(450,920)(451,919)(452,918)(453,913)(454,916)(455,915)(456,914)(457,909)(458,912)(459,911)(460,910)(461,945)(462,948)(463,947)(464,946)(465,941)(466,944)(467,943)(468,942)(469,957)(470,960)(471,959)(472,958)(473,953)
(474,956)(475,955)(476,954)(477,949)(478,952)(479,951)(480,950);
s2 := Sym(960)!( 1,242)( 2,241)( 3,244)( 4,243)( 5,246)( 6,245)( 7,248)( 8,247)( 9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)( 17,258)( 18,257)( 19,260)
( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)(121,422)(122,421)(123,424)(124,423)(125,426)(126,425)(127,428)(128,427)(129,430)(130,429)(131,432)(132,431)(133,434)(134,433)(135,436)(136,435)(137,438)(138,437)(139,440)(140,439)(141,442)(142,441)(143,444)(144,443)(145,446)(146,445)(147,448)(148,447)(149,450)(150,449)(151,452)(152,451)(153,454)(154,453)(155,456)(156,455)(157,458)(158,457)(159,460)(160,459)(161,462)(162,461)(163,464)(164,463)(165,466)(166,465)(167,468)(168,467)(169,470)(170,469)(171,472)(172,471)(173,474)(174,473)(175,476)(176,475)(177,478)(178,477)(179,480)(180,479)(181,362)(182,361)(183,364)(184,363)(185,366)(186,365)(187,368)(188,367)(189,370)(190,369)(191,372)(192,371)(193,374)(194,373)(195,376)(196,375)(197,378)(198,377)(199,380)(200,379)(201,382)(202,381)(203,384)(204,383)(205,386)(206,385)(207,388)(208,387)(209,390)(210,389)(211,392)(212,391)(213,394)(214,393)(215,396)(216,395)(217,398)(218,397)(219,400)(220,399)(221,402)(222,401)(223,404)(224,403)(225,406)(226,405)(227,408)(228,407)(229,410)(230,409)(231,412)(232,411)(233,414)(234,413)(235,416)(236,415)(237,418)(238,417)(239,420)(240,419)(481,722)(482,721)(483,724)(484,723)(485,726)(486,725)(487,728)(488,727)(489,730)(490,729)(491,732)(492,731)(493,734)(494,733)(495,736)(496,735)(497,738)(498,737)(499,740)(500,739)(501,742)(502,741)(503,744)(504,743)(505,746)(506,745)(507,748)(508,747)(509,750)(510,749)(511,752)(512,751)(513,754)(514,753)(515,756)(516,755)(517,758)(518,757)(519,760)(520,759)(521,762)(522,761)(523,764)(524,763)(525,766)(526,765)(527,768)(528,767)(529,770)(530,769)(531,772)(532,771)(533,774)(534,773)(535,776)(536,775)(537,778)(538,777)(539,780)(540,779)(541,782)(542,781)(543,784)(544,783)(545,786)(546,785)(547,788)(548,787)(549,790)(550,789)(551,792)(552,791)(553,794)(554,793)(555,796)(556,795)(557,798)(558,797)(559,800)(560,799)(561,802)(562,801)(563,804)(564,803)(565,806)(566,805)(567,808)(568,807)(569,810)(570,809)(571,812)(572,811)(573,814)(574,813)(575,816)(576,815)(577,818)(578,817)(579,820)(580,819)(581,822)(582,821)(583,824)(584,823)(585,826)(586,825)(587,828)(588,827)(589,830)(590,829)(591,832)(592,831)(593,834)(594,833)(595,836)(596,835)(597,838)(598,837)(599,840)(600,839)(601,902)(602,901)(603,904)(604,903)(605,906)(606,905)(607,908)(608,907)(609,910)(610,909)(611,912)(612,911)(613,914)(614,913)(615,916)(616,915)(617,918)(618,917)(619,920)(620,919)(621,922)(622,921)(623,924)(624,923)(625,926)(626,925)(627,928)(628,927)(629,930)(630,929)(631,932)(632,931)(633,934)(634,933)(635,936)(636,935)(637,938)(638,937)(639,940)(640,939)(641,942)(642,941)(643,944)(644,943)(645,946)(646,945)(647,948)(648,947)(649,950)(650,949)(651,952)(652,951)(653,954)(654,953)(655,956)(656,955)(657,958)(658,957)(659,960)(660,959)(661,842)(662,841)(663,844)(664,843)(665,846)(666,845)(667,848)(668,847)(669,850)(670,849)(671,852)(672,851)(673,854)(674,853)(675,856)(676,855)(677,858)(678,857)(679,860)(680,859)(681,862)(682,861)(683,864)(684,863)(685,866)(686,865)(687,868)(688,867)(689,870)(690,869)(691,872)(692,871)(693,874)(694,873)(695,876)(696,875)(697,878)(698,877)(699,880)(700,879)(701,882)(702,881)(703,884)(704,883)(705,886)(706,885)(707,888)(708,887)(709,890)(710,889)(711,892)(712,891)(713,894)
(714,893)(715,896)(716,895)(717,898)(718,897)(719,900)(720,899);
s3 := Sym(960)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)
( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)(496,616)(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)(504,624)(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,631)(512,632)(513,633)(514,634)(515,635)(516,636)(517,637)(518,638)(519,639)(520,640)(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)(528,648)(529,649)(530,650)(531,651)(532,652)(533,653)(534,654)(535,655)(536,656)(537,657)(538,658)(539,659)(540,660)(541,661)(542,662)(543,663)(544,664)(545,665)(546,666)(547,667)(548,668)(549,669)(550,670)(551,671)(552,672)(553,673)(554,674)(555,675)(556,676)(557,677)(558,678)(559,679)(560,680)(561,681)(562,682)(563,683)(564,684)(565,685)(566,686)(567,687)(568,688)(569,689)(570,690)(571,691)(572,692)(573,693)(574,694)(575,695)(576,696)(577,697)(578,698)(579,699)(580,700)(581,701)(582,702)(583,703)(584,704)(585,705)(586,706)(587,707)(588,708)(589,709)(590,710)(591,711)(592,712)(593,713)(594,714)(595,715)(596,716)(597,717)(598,718)(599,719)(600,720)(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)(728,848)(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)(736,856)(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)(744,864)(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,871)(752,872)(753,873)(754,874)(755,875)(756,876)(757,877)(758,878)(759,879)(760,880)(761,881)(762,882)(763,883)(764,884)(765,885)(766,886)(767,887)(768,888)(769,889)(770,890)(771,891)(772,892)(773,893)(774,894)(775,895)(776,896)(777,897)(778,898)(779,899)(780,900)(781,901)(782,902)(783,903)(784,904)(785,905)(786,906)(787,907)(788,908)(789,909)(790,910)(791,911)(792,912)(793,913)(794,914)(795,915)(796,916)(797,917)(798,918)(799,919)(800,920)(801,921)(802,922)(803,923)(804,924)(805,925)(806,926)(807,927)(808,928)(809,929)(810,930)(811,931)(812,932)(813,933)(814,934)(815,935)(816,936)(817,937)(818,938)(819,939)(820,940)(821,941)(822,942)(823,943)(824,944)(825,945)(826,946)(827,947)(828,948)(829,949)(830,950)(831,951)(832,952)(833,953)
(834,954)(835,955)(836,956)(837,957)(838,958)(839,959)(840,960);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*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*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