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