Polytope of Type {20,8,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8,6}*1920a
Also Known As : {{20,8|2},{8,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,148893)
Rank : 4
Schlafli Type : {20,8,6}
Number of vertices, edges, etc : 20, 80, 24, 6
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,4,6}*960, {10,8,6}*960
3-fold quotients : {20,8,2}*640a
4-fold quotients : {20,2,6}*480, {10,4,6}*480
5-fold quotients : {4,8,6}*384a
6-fold quotients : {20,4,2}*320, {10,8,2}*320
8-fold quotients : {20,2,3}*240, {10,2,6}*240
10-fold quotients : {4,4,6}*192, {2,8,6}*192
12-fold quotients : {20,2,2}*160, {10,4,2}*160
15-fold quotients : {4,8,2}*128a
16-fold quotients : {5,2,6}*120, {10,2,3}*120
20-fold quotients : {2,4,6}*96a, {4,2,6}*96
24-fold quotients : {10,2,2}*80
30-fold quotients : {4,4,2}*64, {2,8,2}*64
32-fold quotients : {5,2,3}*60
40-fold quotients : {4,2,3}*48, {2,2,6}*48
48-fold quotients : {5,2,2}*40
60-fold quotients : {2,4,2}*32, {4,2,2}*32
80-fold quotients : {2,2,3}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)( 8,249)( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)
( 21,261)( 22,265)( 23,264)( 24,263)( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)( 32,275)( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)( 40,277)( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)( 48,289)( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)( 56,296)( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)( 64,303)( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)( 72,315)( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)(104,343)(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)(112,355)(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)(120,357)(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)(128,369)(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)(136,376)(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)(144,383)(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)(152,395)(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)(160,397)(161,401)(162,405)(163,404)(164,403)(165,402)(166,406)(167,410)(168,409)(169,408)(170,407)(171,411)(172,415)(173,414)(174,413)(175,412)(176,416)(177,420)(178,419)(179,418)(180,417)(181,421)(182,425)(183,424)(184,423)(185,422)(186,426)(187,430)(188,429)(189,428)(190,427)(191,431)(192,435)(193,434)(194,433)(195,432)(196,436)(197,440)(198,439)(199,438)(200,437)(201,441)(202,445)(203,444)(204,443)(205,442)(206,446)(207,450)(208,449)(209,448)(210,447)(211,451)(212,455)(213,454)(214,453)(215,452)(216,456)(217,460)(218,459)(219,458)(220,457)(221,461)(222,465)(223,464)(224,463)(225,462)(226,466)(227,470)(228,469)(229,468)(230,467)(231,471)(232,475)(233,474)(234,473)(235,472)(236,476)(237,480)(238,479)(239,478)(240,477)(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)(488,729)(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)(496,736)(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)(504,743)(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)(512,755)(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)(520,757)(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)(528,769)(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)(536,776)(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)(544,783)(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)(552,795)(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)(560,797)(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)(568,809)(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)(576,816)(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)(584,823)(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)(592,835)(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)(600,837)(601,841)(602,845)(603,844)(604,843)(605,842)(606,846)(607,850)(608,849)(609,848)(610,847)(611,851)(612,855)(613,854)(614,853)(615,852)(616,856)(617,860)(618,859)(619,858)(620,857)(621,861)(622,865)(623,864)(624,863)(625,862)(626,866)(627,870)(628,869)(629,868)(630,867)(631,871)(632,875)(633,874)(634,873)(635,872)(636,876)(637,880)(638,879)(639,878)(640,877)(641,881)(642,885)(643,884)(644,883)(645,882)(646,886)(647,890)(648,889)(649,888)(650,887)(651,891)(652,895)(653,894)(654,893)(655,892)(656,896)(657,900)(658,899)(659,898)(660,897)(661,901)(662,905)(663,904)(664,903)(665,902)(666,906)(667,910)(668,909)(669,908)(670,907)(671,911)(672,915)(673,914)(674,913)(675,912)(676,916)(677,920)(678,919)(679,918)(680,917)(681,921)(682,925)(683,924)(684,923)(685,922)(686,926)(687,930)(688,929)(689,928)(690,927)(691,931)(692,935)(693,934)(694,933)(695,932)(696,936)(697,940)(698,939)(699,938)(700,937)(701,941)(702,945)(703,944)(704,943)(705,942)(706,946)(707,950)(708,949)(709,948)(710,947)(711,951)(712,955)(713,954)(714,953)
(715,952)(716,956)(717,960)(718,959)(719,958)(720,957);;
s1 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)
( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 77)( 62, 76)( 63, 80)( 64, 79)( 65, 78)( 66, 82)( 67, 81)( 68, 85)( 69, 84)( 70, 83)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)( 99,114)(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,197)(182,196)(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)(213,230)(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)(221,237)(222,236)(223,240)(224,239)(225,238)(241,272)(242,271)(243,275)(244,274)(245,273)(246,277)(247,276)(248,280)(249,279)(250,278)(251,282)(252,281)(253,285)(254,284)(255,283)(256,287)(257,286)(258,290)(259,289)(260,288)(261,292)(262,291)(263,295)(264,294)(265,293)(266,297)(267,296)(268,300)(269,299)(270,298)(301,347)(302,346)(303,350)(304,349)(305,348)(306,352)(307,351)(308,355)(309,354)(310,353)(311,357)(312,356)(313,360)(314,359)(315,358)(316,332)(317,331)(318,335)(319,334)(320,333)(321,337)(322,336)(323,340)(324,339)(325,338)(326,342)(327,341)(328,345)(329,344)(330,343)(361,392)(362,391)(363,395)(364,394)(365,393)(366,397)(367,396)(368,400)(369,399)(370,398)(371,402)(372,401)(373,405)(374,404)(375,403)(376,407)(377,406)(378,410)(379,409)(380,408)(381,412)(382,411)(383,415)(384,414)(385,413)(386,417)(387,416)(388,420)(389,419)(390,418)(421,467)(422,466)(423,470)(424,469)(425,468)(426,472)(427,471)(428,475)(429,474)(430,473)(431,477)(432,476)(433,480)(434,479)(435,478)(436,452)(437,451)(438,455)(439,454)(440,453)(441,457)(442,456)(443,460)(444,459)(445,458)(446,462)(447,461)(448,465)(449,464)(450,463)(481,542)(482,541)(483,545)(484,544)(485,543)(486,547)(487,546)(488,550)(489,549)(490,548)(491,552)(492,551)(493,555)(494,554)(495,553)(496,557)(497,556)(498,560)(499,559)(500,558)(501,562)(502,561)(503,565)(504,564)(505,563)(506,567)(507,566)(508,570)(509,569)(510,568)(511,572)(512,571)(513,575)(514,574)(515,573)(516,577)(517,576)(518,580)(519,579)(520,578)(521,582)(522,581)(523,585)(524,584)(525,583)(526,587)(527,586)(528,590)(529,589)(530,588)(531,592)(532,591)(533,595)(534,594)(535,593)(536,597)(537,596)(538,600)(539,599)(540,598)(601,662)(602,661)(603,665)(604,664)(605,663)(606,667)(607,666)(608,670)(609,669)(610,668)(611,672)(612,671)(613,675)(614,674)(615,673)(616,677)(617,676)(618,680)(619,679)(620,678)(621,682)(622,681)(623,685)(624,684)(625,683)(626,687)(627,686)(628,690)(629,689)(630,688)(631,692)(632,691)(633,695)(634,694)(635,693)(636,697)(637,696)(638,700)(639,699)(640,698)(641,702)(642,701)(643,705)(644,704)(645,703)(646,707)(647,706)(648,710)(649,709)(650,708)(651,712)(652,711)(653,715)(654,714)(655,713)(656,717)(657,716)(658,720)(659,719)(660,718)(721,812)(722,811)(723,815)(724,814)(725,813)(726,817)(727,816)(728,820)(729,819)(730,818)(731,822)(732,821)(733,825)(734,824)(735,823)(736,827)(737,826)(738,830)(739,829)(740,828)(741,832)(742,831)(743,835)(744,834)(745,833)(746,837)(747,836)(748,840)(749,839)(750,838)(751,782)(752,781)(753,785)(754,784)(755,783)(756,787)(757,786)(758,790)(759,789)(760,788)(761,792)(762,791)(763,795)(764,794)(765,793)(766,797)(767,796)(768,800)(769,799)(770,798)(771,802)(772,801)(773,805)(774,804)(775,803)(776,807)(777,806)(778,810)(779,809)(780,808)(841,932)(842,931)(843,935)(844,934)(845,933)(846,937)(847,936)(848,940)(849,939)(850,938)(851,942)(852,941)(853,945)(854,944)(855,943)(856,947)(857,946)(858,950)(859,949)(860,948)(861,952)(862,951)(863,955)(864,954)(865,953)(866,957)(867,956)(868,960)(869,959)(870,958)(871,902)(872,901)(873,905)(874,904)(875,903)(876,907)(877,906)(878,910)(879,909)(880,908)(881,912)(882,911)(883,915)(884,914)(885,913)(886,917)(887,916)(888,920)(889,919)(890,918)(891,922)(892,921)(893,925)(894,924)(895,923)(896,927)(897,926)(898,930)(899,929)(900,928);;
s2 := ( 1,601)( 2,602)( 3,603)( 4,604)( 5,605)( 6,611)( 7,612)( 8,613)( 9,614)( 10,615)( 11,606)( 12,607)( 13,608)( 14,609)( 15,610)( 16,616)( 17,617)( 18,618)( 19,619)( 20,620)
( 21,626)( 22,627)( 23,628)( 24,629)( 25,630)( 26,621)( 27,622)( 28,623)( 29,624)( 30,625)( 31,631)( 32,632)( 33,633)( 34,634)( 35,635)( 36,641)( 37,642)( 38,643)( 39,644)( 40,645)( 41,636)( 42,637)( 43,638)( 44,639)( 45,640)( 46,646)( 47,647)( 48,648)( 49,649)( 50,650)( 51,656)( 52,657)( 53,658)( 54,659)( 55,660)( 56,651)( 57,652)( 58,653)( 59,654)( 60,655)( 61,676)( 62,677)( 63,678)( 64,679)( 65,680)( 66,686)( 67,687)( 68,688)( 69,689)( 70,690)( 71,681)( 72,682)( 73,683)( 74,684)( 75,685)( 76,661)( 77,662)( 78,663)( 79,664)( 80,665)( 81,671)( 82,672)( 83,673)( 84,674)( 85,675)( 86,666)( 87,667)( 88,668)( 89,669)( 90,670)( 91,706)( 92,707)( 93,708)( 94,709)( 95,710)( 96,716)( 97,717)( 98,718)( 99,719)(100,720)(101,711)(102,712)(103,713)(104,714)(105,715)(106,691)(107,692)(108,693)(109,694)(110,695)(111,701)(112,702)(113,703)(114,704)(115,705)(116,696)(117,697)(118,698)(119,699)(120,700)(121,481)(122,482)(123,483)(124,484)(125,485)(126,491)(127,492)(128,493)(129,494)(130,495)(131,486)(132,487)(133,488)(134,489)(135,490)(136,496)(137,497)(138,498)(139,499)(140,500)(141,506)(142,507)(143,508)(144,509)(145,510)(146,501)(147,502)(148,503)(149,504)(150,505)(151,511)(152,512)(153,513)(154,514)(155,515)(156,521)(157,522)(158,523)(159,524)(160,525)(161,516)(162,517)(163,518)(164,519)(165,520)(166,526)(167,527)(168,528)(169,529)(170,530)(171,536)(172,537)(173,538)(174,539)(175,540)(176,531)(177,532)(178,533)(179,534)(180,535)(181,556)(182,557)(183,558)(184,559)(185,560)(186,566)(187,567)(188,568)(189,569)(190,570)(191,561)(192,562)(193,563)(194,564)(195,565)(196,541)(197,542)(198,543)(199,544)(200,545)(201,551)(202,552)(203,553)(204,554)(205,555)(206,546)(207,547)(208,548)(209,549)(210,550)(211,586)(212,587)(213,588)(214,589)(215,590)(216,596)(217,597)(218,598)(219,599)(220,600)(221,591)(222,592)(223,593)(224,594)(225,595)(226,571)(227,572)(228,573)(229,574)(230,575)(231,581)(232,582)(233,583)(234,584)(235,585)(236,576)(237,577)(238,578)(239,579)(240,580)(241,841)(242,842)(243,843)(244,844)(245,845)(246,851)(247,852)(248,853)(249,854)(250,855)(251,846)(252,847)(253,848)(254,849)(255,850)(256,856)(257,857)(258,858)(259,859)(260,860)(261,866)(262,867)(263,868)(264,869)(265,870)(266,861)(267,862)(268,863)(269,864)(270,865)(271,871)(272,872)(273,873)(274,874)(275,875)(276,881)(277,882)(278,883)(279,884)(280,885)(281,876)(282,877)(283,878)(284,879)(285,880)(286,886)(287,887)(288,888)(289,889)(290,890)(291,896)(292,897)(293,898)(294,899)(295,900)(296,891)(297,892)(298,893)(299,894)(300,895)(301,916)(302,917)(303,918)(304,919)(305,920)(306,926)(307,927)(308,928)(309,929)(310,930)(311,921)(312,922)(313,923)(314,924)(315,925)(316,901)(317,902)(318,903)(319,904)(320,905)(321,911)(322,912)(323,913)(324,914)(325,915)(326,906)(327,907)(328,908)(329,909)(330,910)(331,946)(332,947)(333,948)(334,949)(335,950)(336,956)(337,957)(338,958)(339,959)(340,960)(341,951)(342,952)(343,953)(344,954)(345,955)(346,931)(347,932)(348,933)(349,934)(350,935)(351,941)(352,942)(353,943)(354,944)(355,945)(356,936)(357,937)(358,938)(359,939)(360,940)(361,721)(362,722)(363,723)(364,724)(365,725)(366,731)(367,732)(368,733)(369,734)(370,735)(371,726)(372,727)(373,728)(374,729)(375,730)(376,736)(377,737)(378,738)(379,739)(380,740)(381,746)(382,747)(383,748)(384,749)(385,750)(386,741)(387,742)(388,743)(389,744)(390,745)(391,751)(392,752)(393,753)(394,754)(395,755)(396,761)(397,762)(398,763)(399,764)(400,765)(401,756)(402,757)(403,758)(404,759)(405,760)(406,766)(407,767)(408,768)(409,769)(410,770)(411,776)(412,777)(413,778)(414,779)(415,780)(416,771)(417,772)(418,773)(419,774)(420,775)(421,796)(422,797)(423,798)(424,799)(425,800)(426,806)(427,807)(428,808)(429,809)(430,810)(431,801)(432,802)(433,803)(434,804)(435,805)(436,781)(437,782)(438,783)(439,784)(440,785)(441,791)(442,792)(443,793)(444,794)(445,795)(446,786)(447,787)(448,788)(449,789)(450,790)(451,826)(452,827)(453,828)(454,829)(455,830)(456,836)(457,837)(458,838)(459,839)(460,840)(461,831)(462,832)(463,833)(464,834)(465,835)(466,811)(467,812)(468,813)(469,814)(470,815)(471,821)(472,822)(473,823)(474,824)
(475,825)(476,816)(477,817)(478,818)(479,819)(480,820);;
s3 := ( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)( 8,123)( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)
( 21,136)( 22,137)( 23,138)( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)(248,363)(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)(280,395)(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)(288,413)(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)(296,416)(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)(320,445)(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)(328,448)(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)(336,451)(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)(344,464)(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)(728,843)(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)(736,861)(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)(744,859)(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)(752,877)(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)(760,875)(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)(768,893)(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)(776,896)(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)(784,909)(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)(792,912)(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)(800,925)(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)(808,928)(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)(816,931)(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)(824,944)(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)(832,947)(833,948)(834,949)
(835,950)(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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)( 8,249)( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,256)( 17,260)( 18,259)( 19,258)
( 20,257)( 21,261)( 22,265)( 23,264)( 24,263)( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)( 32,275)( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)( 40,277)( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)( 48,289)( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)( 56,296)( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)( 64,303)( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)( 72,315)( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)(104,343)(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)(112,355)(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)(120,357)(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)(128,369)(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)(136,376)(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)(144,383)(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)(152,395)(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)(160,397)(161,401)(162,405)(163,404)(164,403)(165,402)(166,406)(167,410)(168,409)(169,408)(170,407)(171,411)(172,415)(173,414)(174,413)(175,412)(176,416)(177,420)(178,419)(179,418)(180,417)(181,421)(182,425)(183,424)(184,423)(185,422)(186,426)(187,430)(188,429)(189,428)(190,427)(191,431)(192,435)(193,434)(194,433)(195,432)(196,436)(197,440)(198,439)(199,438)(200,437)(201,441)(202,445)(203,444)(204,443)(205,442)(206,446)(207,450)(208,449)(209,448)(210,447)(211,451)(212,455)(213,454)(214,453)(215,452)(216,456)(217,460)(218,459)(219,458)(220,457)(221,461)(222,465)(223,464)(224,463)(225,462)(226,466)(227,470)(228,469)(229,468)(230,467)(231,471)(232,475)(233,474)(234,473)(235,472)(236,476)(237,480)(238,479)(239,478)(240,477)(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)(488,729)(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)(496,736)(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)(504,743)(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)(512,755)(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)(520,757)(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)(528,769)(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)(536,776)(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)(544,783)(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)(552,795)(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)(560,797)(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)(568,809)(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)(576,816)(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)(584,823)(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)(592,835)(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)(600,837)(601,841)(602,845)(603,844)(604,843)(605,842)(606,846)(607,850)(608,849)(609,848)(610,847)(611,851)(612,855)(613,854)(614,853)(615,852)(616,856)(617,860)(618,859)(619,858)(620,857)(621,861)(622,865)(623,864)(624,863)(625,862)(626,866)(627,870)(628,869)(629,868)(630,867)(631,871)(632,875)(633,874)(634,873)(635,872)(636,876)(637,880)(638,879)(639,878)(640,877)(641,881)(642,885)(643,884)(644,883)(645,882)(646,886)(647,890)(648,889)(649,888)(650,887)(651,891)(652,895)(653,894)(654,893)(655,892)(656,896)(657,900)(658,899)(659,898)(660,897)(661,901)(662,905)(663,904)(664,903)(665,902)(666,906)(667,910)(668,909)(669,908)(670,907)(671,911)(672,915)(673,914)(674,913)(675,912)(676,916)(677,920)(678,919)(679,918)(680,917)(681,921)(682,925)(683,924)(684,923)(685,922)(686,926)(687,930)(688,929)(689,928)(690,927)(691,931)(692,935)(693,934)(694,933)(695,932)(696,936)(697,940)(698,939)(699,938)(700,937)(701,941)(702,945)(703,944)(704,943)(705,942)(706,946)(707,950)(708,949)(709,948)(710,947)(711,951)(712,955)(713,954)
(714,953)(715,952)(716,956)(717,960)(718,959)(719,958)(720,957);
s1 := Sym(960)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)( 41, 42)( 43, 45)( 46, 47)
( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)( 61, 77)( 62, 76)( 63, 80)( 64, 79)( 65, 78)( 66, 82)( 67, 81)( 68, 85)( 69, 84)( 70, 83)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)( 99,114)(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,197)(182,196)(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)(213,230)(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)(221,237)(222,236)(223,240)(224,239)(225,238)(241,272)(242,271)(243,275)(244,274)(245,273)(246,277)(247,276)(248,280)(249,279)(250,278)(251,282)(252,281)(253,285)(254,284)(255,283)(256,287)(257,286)(258,290)(259,289)(260,288)(261,292)(262,291)(263,295)(264,294)(265,293)(266,297)(267,296)(268,300)(269,299)(270,298)(301,347)(302,346)(303,350)(304,349)(305,348)(306,352)(307,351)(308,355)(309,354)(310,353)(311,357)(312,356)(313,360)(314,359)(315,358)(316,332)(317,331)(318,335)(319,334)(320,333)(321,337)(322,336)(323,340)(324,339)(325,338)(326,342)(327,341)(328,345)(329,344)(330,343)(361,392)(362,391)(363,395)(364,394)(365,393)(366,397)(367,396)(368,400)(369,399)(370,398)(371,402)(372,401)(373,405)(374,404)(375,403)(376,407)(377,406)(378,410)(379,409)(380,408)(381,412)(382,411)(383,415)(384,414)(385,413)(386,417)(387,416)(388,420)(389,419)(390,418)(421,467)(422,466)(423,470)(424,469)(425,468)(426,472)(427,471)(428,475)(429,474)(430,473)(431,477)(432,476)(433,480)(434,479)(435,478)(436,452)(437,451)(438,455)(439,454)(440,453)(441,457)(442,456)(443,460)(444,459)(445,458)(446,462)(447,461)(448,465)(449,464)(450,463)(481,542)(482,541)(483,545)(484,544)(485,543)(486,547)(487,546)(488,550)(489,549)(490,548)(491,552)(492,551)(493,555)(494,554)(495,553)(496,557)(497,556)(498,560)(499,559)(500,558)(501,562)(502,561)(503,565)(504,564)(505,563)(506,567)(507,566)(508,570)(509,569)(510,568)(511,572)(512,571)(513,575)(514,574)(515,573)(516,577)(517,576)(518,580)(519,579)(520,578)(521,582)(522,581)(523,585)(524,584)(525,583)(526,587)(527,586)(528,590)(529,589)(530,588)(531,592)(532,591)(533,595)(534,594)(535,593)(536,597)(537,596)(538,600)(539,599)(540,598)(601,662)(602,661)(603,665)(604,664)(605,663)(606,667)(607,666)(608,670)(609,669)(610,668)(611,672)(612,671)(613,675)(614,674)(615,673)(616,677)(617,676)(618,680)(619,679)(620,678)(621,682)(622,681)(623,685)(624,684)(625,683)(626,687)(627,686)(628,690)(629,689)(630,688)(631,692)(632,691)(633,695)(634,694)(635,693)(636,697)(637,696)(638,700)(639,699)(640,698)(641,702)(642,701)(643,705)(644,704)(645,703)(646,707)(647,706)(648,710)(649,709)(650,708)(651,712)(652,711)(653,715)(654,714)(655,713)(656,717)(657,716)(658,720)(659,719)(660,718)(721,812)(722,811)(723,815)(724,814)(725,813)(726,817)(727,816)(728,820)(729,819)(730,818)(731,822)(732,821)(733,825)(734,824)(735,823)(736,827)(737,826)(738,830)(739,829)(740,828)(741,832)(742,831)(743,835)(744,834)(745,833)(746,837)(747,836)(748,840)(749,839)(750,838)(751,782)(752,781)(753,785)(754,784)(755,783)(756,787)(757,786)(758,790)(759,789)(760,788)(761,792)(762,791)(763,795)(764,794)(765,793)(766,797)(767,796)(768,800)(769,799)(770,798)(771,802)(772,801)(773,805)(774,804)(775,803)(776,807)(777,806)(778,810)(779,809)(780,808)(841,932)(842,931)(843,935)(844,934)(845,933)(846,937)(847,936)(848,940)(849,939)(850,938)(851,942)(852,941)(853,945)(854,944)(855,943)(856,947)(857,946)(858,950)(859,949)(860,948)(861,952)(862,951)(863,955)(864,954)(865,953)(866,957)(867,956)(868,960)(869,959)(870,958)(871,902)(872,901)(873,905)(874,904)(875,903)(876,907)(877,906)(878,910)(879,909)(880,908)(881,912)(882,911)(883,915)(884,914)(885,913)(886,917)(887,916)(888,920)(889,919)(890,918)(891,922)(892,921)(893,925)(894,924)(895,923)(896,927)(897,926)(898,930)(899,929)(900,928);
s2 := Sym(960)!( 1,601)( 2,602)( 3,603)( 4,604)( 5,605)( 6,611)( 7,612)( 8,613)( 9,614)( 10,615)( 11,606)( 12,607)( 13,608)( 14,609)( 15,610)( 16,616)( 17,617)( 18,618)( 19,619)
( 20,620)( 21,626)( 22,627)( 23,628)( 24,629)( 25,630)( 26,621)( 27,622)( 28,623)( 29,624)( 30,625)( 31,631)( 32,632)( 33,633)( 34,634)( 35,635)( 36,641)( 37,642)( 38,643)( 39,644)( 40,645)( 41,636)( 42,637)( 43,638)( 44,639)( 45,640)( 46,646)( 47,647)( 48,648)( 49,649)( 50,650)( 51,656)( 52,657)( 53,658)( 54,659)( 55,660)( 56,651)( 57,652)( 58,653)( 59,654)( 60,655)( 61,676)( 62,677)( 63,678)( 64,679)( 65,680)( 66,686)( 67,687)( 68,688)( 69,689)( 70,690)( 71,681)( 72,682)( 73,683)( 74,684)( 75,685)( 76,661)( 77,662)( 78,663)( 79,664)( 80,665)( 81,671)( 82,672)( 83,673)( 84,674)( 85,675)( 86,666)( 87,667)( 88,668)( 89,669)( 90,670)( 91,706)( 92,707)( 93,708)( 94,709)( 95,710)( 96,716)( 97,717)( 98,718)( 99,719)(100,720)(101,711)(102,712)(103,713)(104,714)(105,715)(106,691)(107,692)(108,693)(109,694)(110,695)(111,701)(112,702)(113,703)(114,704)(115,705)(116,696)(117,697)(118,698)(119,699)(120,700)(121,481)(122,482)(123,483)(124,484)(125,485)(126,491)(127,492)(128,493)(129,494)(130,495)(131,486)(132,487)(133,488)(134,489)(135,490)(136,496)(137,497)(138,498)(139,499)(140,500)(141,506)(142,507)(143,508)(144,509)(145,510)(146,501)(147,502)(148,503)(149,504)(150,505)(151,511)(152,512)(153,513)(154,514)(155,515)(156,521)(157,522)(158,523)(159,524)(160,525)(161,516)(162,517)(163,518)(164,519)(165,520)(166,526)(167,527)(168,528)(169,529)(170,530)(171,536)(172,537)(173,538)(174,539)(175,540)(176,531)(177,532)(178,533)(179,534)(180,535)(181,556)(182,557)(183,558)(184,559)(185,560)(186,566)(187,567)(188,568)(189,569)(190,570)(191,561)(192,562)(193,563)(194,564)(195,565)(196,541)(197,542)(198,543)(199,544)(200,545)(201,551)(202,552)(203,553)(204,554)(205,555)(206,546)(207,547)(208,548)(209,549)(210,550)(211,586)(212,587)(213,588)(214,589)(215,590)(216,596)(217,597)(218,598)(219,599)(220,600)(221,591)(222,592)(223,593)(224,594)(225,595)(226,571)(227,572)(228,573)(229,574)(230,575)(231,581)(232,582)(233,583)(234,584)(235,585)(236,576)(237,577)(238,578)(239,579)(240,580)(241,841)(242,842)(243,843)(244,844)(245,845)(246,851)(247,852)(248,853)(249,854)(250,855)(251,846)(252,847)(253,848)(254,849)(255,850)(256,856)(257,857)(258,858)(259,859)(260,860)(261,866)(262,867)(263,868)(264,869)(265,870)(266,861)(267,862)(268,863)(269,864)(270,865)(271,871)(272,872)(273,873)(274,874)(275,875)(276,881)(277,882)(278,883)(279,884)(280,885)(281,876)(282,877)(283,878)(284,879)(285,880)(286,886)(287,887)(288,888)(289,889)(290,890)(291,896)(292,897)(293,898)(294,899)(295,900)(296,891)(297,892)(298,893)(299,894)(300,895)(301,916)(302,917)(303,918)(304,919)(305,920)(306,926)(307,927)(308,928)(309,929)(310,930)(311,921)(312,922)(313,923)(314,924)(315,925)(316,901)(317,902)(318,903)(319,904)(320,905)(321,911)(322,912)(323,913)(324,914)(325,915)(326,906)(327,907)(328,908)(329,909)(330,910)(331,946)(332,947)(333,948)(334,949)(335,950)(336,956)(337,957)(338,958)(339,959)(340,960)(341,951)(342,952)(343,953)(344,954)(345,955)(346,931)(347,932)(348,933)(349,934)(350,935)(351,941)(352,942)(353,943)(354,944)(355,945)(356,936)(357,937)(358,938)(359,939)(360,940)(361,721)(362,722)(363,723)(364,724)(365,725)(366,731)(367,732)(368,733)(369,734)(370,735)(371,726)(372,727)(373,728)(374,729)(375,730)(376,736)(377,737)(378,738)(379,739)(380,740)(381,746)(382,747)(383,748)(384,749)(385,750)(386,741)(387,742)(388,743)(389,744)(390,745)(391,751)(392,752)(393,753)(394,754)(395,755)(396,761)(397,762)(398,763)(399,764)(400,765)(401,756)(402,757)(403,758)(404,759)(405,760)(406,766)(407,767)(408,768)(409,769)(410,770)(411,776)(412,777)(413,778)(414,779)(415,780)(416,771)(417,772)(418,773)(419,774)(420,775)(421,796)(422,797)(423,798)(424,799)(425,800)(426,806)(427,807)(428,808)(429,809)(430,810)(431,801)(432,802)(433,803)(434,804)(435,805)(436,781)(437,782)(438,783)(439,784)(440,785)(441,791)(442,792)(443,793)(444,794)(445,795)(446,786)(447,787)(448,788)(449,789)(450,790)(451,826)(452,827)(453,828)(454,829)(455,830)(456,836)(457,837)(458,838)(459,839)(460,840)(461,831)(462,832)(463,833)(464,834)(465,835)(466,811)(467,812)(468,813)(469,814)(470,815)(471,821)(472,822)(473,823)
(474,824)(475,825)(476,816)(477,817)(478,818)(479,819)(480,820);
s3 := Sym(960)!( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)( 8,123)( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)( 17,142)( 18,143)( 19,144)
( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)(248,363)(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)(280,395)(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)(288,413)(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)(296,416)(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)(320,445)(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)(328,448)(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)(336,451)(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)(344,464)(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)(728,843)(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)(736,861)(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)(744,859)(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)(752,877)(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)(760,875)(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)(768,893)(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)(776,896)(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)(784,909)(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)(792,912)(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)(800,925)(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)(808,928)(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)(816,931)(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)(824,944)(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)(832,947)(833,948)
(834,949)(835,950)(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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope