Polytope of Type {4,20,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20,12}*1920
Also Known As : {{4,20|2},{20,12|2}}. if this polytope has another name.
Group : SmallGroup(1920,58500)
Rank : 4
Schlafli Type : {4,20,12}
Number of vertices, edges, etc : 4, 40, 120, 12
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 : {4,20,6}*960, {4,10,12}*960, {2,20,12}*960
   3-fold quotients : {4,20,4}*640
   4-fold quotients : {2,10,12}*480, {2,20,6}*480a, {4,10,6}*480
   5-fold quotients : {4,4,12}*384
   6-fold quotients : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {4,4,4}*128
   20-fold quotients : {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {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.
Permutation Representation (GAP) : 
s0 := (  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);;
s1 := (  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,606)(  7,610)(  8,609)
(  9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)( 16,616)
( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)( 24,623)
( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,631)( 32,635)
( 33,634)( 34,633)( 35,632)( 36,636)( 37,640)( 38,639)( 39,638)( 40,637)
( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,646)( 47,650)( 48,649)
( 49,648)( 50,647)( 51,651)( 52,655)( 53,654)( 54,653)( 55,652)( 56,656)
( 57,660)( 58,659)( 59,658)( 60,657)( 61,661)( 62,665)( 63,664)( 64,663)
( 65,662)( 66,666)( 67,670)( 68,669)( 69,668)( 70,667)( 71,671)( 72,675)
( 73,674)( 74,673)( 75,672)( 76,676)( 77,680)( 78,679)( 79,678)( 80,677)
( 81,681)( 82,685)( 83,684)( 84,683)( 85,682)( 86,686)( 87,690)( 88,689)
( 89,688)( 90,687)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)( 96,696)
( 97,700)( 98,699)( 99,698)(100,697)(101,701)(102,705)(103,704)(104,703)
(105,702)(106,706)(107,710)(108,709)(109,708)(110,707)(111,711)(112,715)
(113,714)(114,713)(115,712)(116,716)(117,720)(118,719)(119,718)(120,717)
(121,541)(122,545)(123,544)(124,543)(125,542)(126,546)(127,550)(128,549)
(129,548)(130,547)(131,551)(132,555)(133,554)(134,553)(135,552)(136,556)
(137,560)(138,559)(139,558)(140,557)(141,561)(142,565)(143,564)(144,563)
(145,562)(146,566)(147,570)(148,569)(149,568)(150,567)(151,571)(152,575)
(153,574)(154,573)(155,572)(156,576)(157,580)(158,579)(159,578)(160,577)
(161,581)(162,585)(163,584)(164,583)(165,582)(166,586)(167,590)(168,589)
(169,588)(170,587)(171,591)(172,595)(173,594)(174,593)(175,592)(176,596)
(177,600)(178,599)(179,598)(180,597)(181,481)(182,485)(183,484)(184,483)
(185,482)(186,486)(187,490)(188,489)(189,488)(190,487)(191,491)(192,495)
(193,494)(194,493)(195,492)(196,496)(197,500)(198,499)(199,498)(200,497)
(201,501)(202,505)(203,504)(204,503)(205,502)(206,506)(207,510)(208,509)
(209,508)(210,507)(211,511)(212,515)(213,514)(214,513)(215,512)(216,516)
(217,520)(218,519)(219,518)(220,517)(221,521)(222,525)(223,524)(224,523)
(225,522)(226,526)(227,530)(228,529)(229,528)(230,527)(231,531)(232,535)
(233,534)(234,533)(235,532)(236,536)(237,540)(238,539)(239,538)(240,537)
(241,886)(242,890)(243,889)(244,888)(245,887)(246,891)(247,895)(248,894)
(249,893)(250,892)(251,896)(252,900)(253,899)(254,898)(255,897)(256,871)
(257,875)(258,874)(259,873)(260,872)(261,876)(262,880)(263,879)(264,878)
(265,877)(266,881)(267,885)(268,884)(269,883)(270,882)(271,856)(272,860)
(273,859)(274,858)(275,857)(276,861)(277,865)(278,864)(279,863)(280,862)
(281,866)(282,870)(283,869)(284,868)(285,867)(286,841)(287,845)(288,844)
(289,843)(290,842)(291,846)(292,850)(293,849)(294,848)(295,847)(296,851)
(297,855)(298,854)(299,853)(300,852)(301,946)(302,950)(303,949)(304,948)
(305,947)(306,951)(307,955)(308,954)(309,953)(310,952)(311,956)(312,960)
(313,959)(314,958)(315,957)(316,931)(317,935)(318,934)(319,933)(320,932)
(321,936)(322,940)(323,939)(324,938)(325,937)(326,941)(327,945)(328,944)
(329,943)(330,942)(331,916)(332,920)(333,919)(334,918)(335,917)(336,921)
(337,925)(338,924)(339,923)(340,922)(341,926)(342,930)(343,929)(344,928)
(345,927)(346,901)(347,905)(348,904)(349,903)(350,902)(351,906)(352,910)
(353,909)(354,908)(355,907)(356,911)(357,915)(358,914)(359,913)(360,912)
(361,826)(362,830)(363,829)(364,828)(365,827)(366,831)(367,835)(368,834)
(369,833)(370,832)(371,836)(372,840)(373,839)(374,838)(375,837)(376,811)
(377,815)(378,814)(379,813)(380,812)(381,816)(382,820)(383,819)(384,818)
(385,817)(386,821)(387,825)(388,824)(389,823)(390,822)(391,796)(392,800)
(393,799)(394,798)(395,797)(396,801)(397,805)(398,804)(399,803)(400,802)
(401,806)(402,810)(403,809)(404,808)(405,807)(406,781)(407,785)(408,784)
(409,783)(410,782)(411,786)(412,790)(413,789)(414,788)(415,787)(416,791)
(417,795)(418,794)(419,793)(420,792)(421,766)(422,770)(423,769)(424,768)
(425,767)(426,771)(427,775)(428,774)(429,773)(430,772)(431,776)(432,780)
(433,779)(434,778)(435,777)(436,751)(437,755)(438,754)(439,753)(440,752)
(441,756)(442,760)(443,759)(444,758)(445,757)(446,761)(447,765)(448,764)
(449,763)(450,762)(451,736)(452,740)(453,739)(454,738)(455,737)(456,741)
(457,745)(458,744)(459,743)(460,742)(461,746)(462,750)(463,749)(464,748)
(465,747)(466,721)(467,725)(468,724)(469,723)(470,722)(471,726)(472,730)
(473,729)(474,728)(475,727)(476,731)(477,735)(478,734)(479,733)(480,732);;
s2 := (  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,252)(  7,251)(  8,255)
(  9,254)( 10,253)( 11,247)( 12,246)( 13,250)( 14,249)( 15,248)( 16,257)
( 17,256)( 18,260)( 19,259)( 20,258)( 21,267)( 22,266)( 23,270)( 24,269)
( 25,268)( 26,262)( 27,261)( 28,265)( 29,264)( 30,263)( 31,272)( 32,271)
( 33,275)( 34,274)( 35,273)( 36,282)( 37,281)( 38,285)( 39,284)( 40,283)
( 41,277)( 42,276)( 43,280)( 44,279)( 45,278)( 46,287)( 47,286)( 48,290)
( 49,289)( 50,288)( 51,297)( 52,296)( 53,300)( 54,299)( 55,298)( 56,292)
( 57,291)( 58,295)( 59,294)( 60,293)( 61,302)( 62,301)( 63,305)( 64,304)
( 65,303)( 66,312)( 67,311)( 68,315)( 69,314)( 70,313)( 71,307)( 72,306)
( 73,310)( 74,309)( 75,308)( 76,317)( 77,316)( 78,320)( 79,319)( 80,318)
( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,322)( 87,321)( 88,325)
( 89,324)( 90,323)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)( 96,342)
( 97,341)( 98,345)( 99,344)(100,343)(101,337)(102,336)(103,340)(104,339)
(105,338)(106,347)(107,346)(108,350)(109,349)(110,348)(111,357)(112,356)
(113,360)(114,359)(115,358)(116,352)(117,351)(118,355)(119,354)(120,353)
(121,362)(122,361)(123,365)(124,364)(125,363)(126,372)(127,371)(128,375)
(129,374)(130,373)(131,367)(132,366)(133,370)(134,369)(135,368)(136,377)
(137,376)(138,380)(139,379)(140,378)(141,387)(142,386)(143,390)(144,389)
(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,392)(152,391)
(153,395)(154,394)(155,393)(156,402)(157,401)(158,405)(159,404)(160,403)
(161,397)(162,396)(163,400)(164,399)(165,398)(166,407)(167,406)(168,410)
(169,409)(170,408)(171,417)(172,416)(173,420)(174,419)(175,418)(176,412)
(177,411)(178,415)(179,414)(180,413)(181,422)(182,421)(183,425)(184,424)
(185,423)(186,432)(187,431)(188,435)(189,434)(190,433)(191,427)(192,426)
(193,430)(194,429)(195,428)(196,437)(197,436)(198,440)(199,439)(200,438)
(201,447)(202,446)(203,450)(204,449)(205,448)(206,442)(207,441)(208,445)
(209,444)(210,443)(211,452)(212,451)(213,455)(214,454)(215,453)(216,462)
(217,461)(218,465)(219,464)(220,463)(221,457)(222,456)(223,460)(224,459)
(225,458)(226,467)(227,466)(228,470)(229,469)(230,468)(231,477)(232,476)
(233,480)(234,479)(235,478)(236,472)(237,471)(238,475)(239,474)(240,473)
(481,722)(482,721)(483,725)(484,724)(485,723)(486,732)(487,731)(488,735)
(489,734)(490,733)(491,727)(492,726)(493,730)(494,729)(495,728)(496,737)
(497,736)(498,740)(499,739)(500,738)(501,747)(502,746)(503,750)(504,749)
(505,748)(506,742)(507,741)(508,745)(509,744)(510,743)(511,752)(512,751)
(513,755)(514,754)(515,753)(516,762)(517,761)(518,765)(519,764)(520,763)
(521,757)(522,756)(523,760)(524,759)(525,758)(526,767)(527,766)(528,770)
(529,769)(530,768)(531,777)(532,776)(533,780)(534,779)(535,778)(536,772)
(537,771)(538,775)(539,774)(540,773)(541,782)(542,781)(543,785)(544,784)
(545,783)(546,792)(547,791)(548,795)(549,794)(550,793)(551,787)(552,786)
(553,790)(554,789)(555,788)(556,797)(557,796)(558,800)(559,799)(560,798)
(561,807)(562,806)(563,810)(564,809)(565,808)(566,802)(567,801)(568,805)
(569,804)(570,803)(571,812)(572,811)(573,815)(574,814)(575,813)(576,822)
(577,821)(578,825)(579,824)(580,823)(581,817)(582,816)(583,820)(584,819)
(585,818)(586,827)(587,826)(588,830)(589,829)(590,828)(591,837)(592,836)
(593,840)(594,839)(595,838)(596,832)(597,831)(598,835)(599,834)(600,833)
(601,842)(602,841)(603,845)(604,844)(605,843)(606,852)(607,851)(608,855)
(609,854)(610,853)(611,847)(612,846)(613,850)(614,849)(615,848)(616,857)
(617,856)(618,860)(619,859)(620,858)(621,867)(622,866)(623,870)(624,869)
(625,868)(626,862)(627,861)(628,865)(629,864)(630,863)(631,872)(632,871)
(633,875)(634,874)(635,873)(636,882)(637,881)(638,885)(639,884)(640,883)
(641,877)(642,876)(643,880)(644,879)(645,878)(646,887)(647,886)(648,890)
(649,889)(650,888)(651,897)(652,896)(653,900)(654,899)(655,898)(656,892)
(657,891)(658,895)(659,894)(660,893)(661,902)(662,901)(663,905)(664,904)
(665,903)(666,912)(667,911)(668,915)(669,914)(670,913)(671,907)(672,906)
(673,910)(674,909)(675,908)(676,917)(677,916)(678,920)(679,919)(680,918)
(681,927)(682,926)(683,930)(684,929)(685,928)(686,922)(687,921)(688,925)
(689,924)(690,923)(691,932)(692,931)(693,935)(694,934)(695,933)(696,942)
(697,941)(698,945)(699,944)(700,943)(701,937)(702,936)(703,940)(704,939)
(705,938)(706,947)(707,946)(708,950)(709,949)(710,948)(711,957)(712,956)
(713,960)(714,959)(715,958)(716,952)(717,951)(718,955)(719,954)(720,953);;
s3 := (  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)(  8,603)
(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)( 16,621)
( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)( 24,619)
( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)( 32,637)
( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)( 40,635)
( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)( 48,653)
( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)( 56,656)
( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)( 64,669)
( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)( 72,672)
( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)( 80,685)
( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)( 88,688)
( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)( 96,691)
( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)(104,704)
(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)(112,707)
(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)(120,720)
(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)(128,483)
(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)(136,501)
(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)(144,499)
(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)(152,517)
(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)(160,515)
(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)(168,533)
(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)(176,536)
(177,537)(178,538)(179,539)(180,540)(181,546)(182,547)(183,548)(184,549)
(185,550)(186,541)(187,542)(188,543)(189,544)(190,545)(191,551)(192,552)
(193,553)(194,554)(195,555)(196,561)(197,562)(198,563)(199,564)(200,565)
(201,556)(202,557)(203,558)(204,559)(205,560)(206,566)(207,567)(208,568)
(209,569)(210,570)(211,576)(212,577)(213,578)(214,579)(215,580)(216,571)
(217,572)(218,573)(219,574)(220,575)(221,581)(222,582)(223,583)(224,584)
(225,585)(226,591)(227,592)(228,593)(229,594)(230,595)(231,586)(232,587)
(233,588)(234,589)(235,590)(236,596)(237,597)(238,598)(239,599)(240,600)
(241,861)(242,862)(243,863)(244,864)(245,865)(246,856)(247,857)(248,858)
(249,859)(250,860)(251,866)(252,867)(253,868)(254,869)(255,870)(256,846)
(257,847)(258,848)(259,849)(260,850)(261,841)(262,842)(263,843)(264,844)
(265,845)(266,851)(267,852)(268,853)(269,854)(270,855)(271,891)(272,892)
(273,893)(274,894)(275,895)(276,886)(277,887)(278,888)(279,889)(280,890)
(281,896)(282,897)(283,898)(284,899)(285,900)(286,876)(287,877)(288,878)
(289,879)(290,880)(291,871)(292,872)(293,873)(294,874)(295,875)(296,881)
(297,882)(298,883)(299,884)(300,885)(301,921)(302,922)(303,923)(304,924)
(305,925)(306,916)(307,917)(308,918)(309,919)(310,920)(311,926)(312,927)
(313,928)(314,929)(315,930)(316,906)(317,907)(318,908)(319,909)(320,910)
(321,901)(322,902)(323,903)(324,904)(325,905)(326,911)(327,912)(328,913)
(329,914)(330,915)(331,951)(332,952)(333,953)(334,954)(335,955)(336,946)
(337,947)(338,948)(339,949)(340,950)(341,956)(342,957)(343,958)(344,959)
(345,960)(346,936)(347,937)(348,938)(349,939)(350,940)(351,931)(352,932)
(353,933)(354,934)(355,935)(356,941)(357,942)(358,943)(359,944)(360,945)
(361,741)(362,742)(363,743)(364,744)(365,745)(366,736)(367,737)(368,738)
(369,739)(370,740)(371,746)(372,747)(373,748)(374,749)(375,750)(376,726)
(377,727)(378,728)(379,729)(380,730)(381,721)(382,722)(383,723)(384,724)
(385,725)(386,731)(387,732)(388,733)(389,734)(390,735)(391,771)(392,772)
(393,773)(394,774)(395,775)(396,766)(397,767)(398,768)(399,769)(400,770)
(401,776)(402,777)(403,778)(404,779)(405,780)(406,756)(407,757)(408,758)
(409,759)(410,760)(411,751)(412,752)(413,753)(414,754)(415,755)(416,761)
(417,762)(418,763)(419,764)(420,765)(421,801)(422,802)(423,803)(424,804)
(425,805)(426,796)(427,797)(428,798)(429,799)(430,800)(431,806)(432,807)
(433,808)(434,809)(435,810)(436,786)(437,787)(438,788)(439,789)(440,790)
(441,781)(442,782)(443,783)(444,784)(445,785)(446,791)(447,792)(448,793)
(449,794)(450,795)(451,831)(452,832)(453,833)(454,834)(455,835)(456,826)
(457,827)(458,828)(459,829)(460,830)(461,836)(462,837)(463,838)(464,839)
(465,840)(466,816)(467,817)(468,818)(469,819)(470,820)(471,811)(472,812)
(473,813)(474,814)(475,815)(476,821)(477,822)(478,823)(479,824)(480,825);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,121)(  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);
s1 := Sym(960)!(  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,606)(  7,610)
(  8,609)(  9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)
( 16,616)( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)
( 24,623)( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,631)
( 32,635)( 33,634)( 34,633)( 35,632)( 36,636)( 37,640)( 38,639)( 39,638)
( 40,637)( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,646)( 47,650)
( 48,649)( 49,648)( 50,647)( 51,651)( 52,655)( 53,654)( 54,653)( 55,652)
( 56,656)( 57,660)( 58,659)( 59,658)( 60,657)( 61,661)( 62,665)( 63,664)
( 64,663)( 65,662)( 66,666)( 67,670)( 68,669)( 69,668)( 70,667)( 71,671)
( 72,675)( 73,674)( 74,673)( 75,672)( 76,676)( 77,680)( 78,679)( 79,678)
( 80,677)( 81,681)( 82,685)( 83,684)( 84,683)( 85,682)( 86,686)( 87,690)
( 88,689)( 89,688)( 90,687)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)
( 96,696)( 97,700)( 98,699)( 99,698)(100,697)(101,701)(102,705)(103,704)
(104,703)(105,702)(106,706)(107,710)(108,709)(109,708)(110,707)(111,711)
(112,715)(113,714)(114,713)(115,712)(116,716)(117,720)(118,719)(119,718)
(120,717)(121,541)(122,545)(123,544)(124,543)(125,542)(126,546)(127,550)
(128,549)(129,548)(130,547)(131,551)(132,555)(133,554)(134,553)(135,552)
(136,556)(137,560)(138,559)(139,558)(140,557)(141,561)(142,565)(143,564)
(144,563)(145,562)(146,566)(147,570)(148,569)(149,568)(150,567)(151,571)
(152,575)(153,574)(154,573)(155,572)(156,576)(157,580)(158,579)(159,578)
(160,577)(161,581)(162,585)(163,584)(164,583)(165,582)(166,586)(167,590)
(168,589)(169,588)(170,587)(171,591)(172,595)(173,594)(174,593)(175,592)
(176,596)(177,600)(178,599)(179,598)(180,597)(181,481)(182,485)(183,484)
(184,483)(185,482)(186,486)(187,490)(188,489)(189,488)(190,487)(191,491)
(192,495)(193,494)(194,493)(195,492)(196,496)(197,500)(198,499)(199,498)
(200,497)(201,501)(202,505)(203,504)(204,503)(205,502)(206,506)(207,510)
(208,509)(209,508)(210,507)(211,511)(212,515)(213,514)(214,513)(215,512)
(216,516)(217,520)(218,519)(219,518)(220,517)(221,521)(222,525)(223,524)
(224,523)(225,522)(226,526)(227,530)(228,529)(229,528)(230,527)(231,531)
(232,535)(233,534)(234,533)(235,532)(236,536)(237,540)(238,539)(239,538)
(240,537)(241,886)(242,890)(243,889)(244,888)(245,887)(246,891)(247,895)
(248,894)(249,893)(250,892)(251,896)(252,900)(253,899)(254,898)(255,897)
(256,871)(257,875)(258,874)(259,873)(260,872)(261,876)(262,880)(263,879)
(264,878)(265,877)(266,881)(267,885)(268,884)(269,883)(270,882)(271,856)
(272,860)(273,859)(274,858)(275,857)(276,861)(277,865)(278,864)(279,863)
(280,862)(281,866)(282,870)(283,869)(284,868)(285,867)(286,841)(287,845)
(288,844)(289,843)(290,842)(291,846)(292,850)(293,849)(294,848)(295,847)
(296,851)(297,855)(298,854)(299,853)(300,852)(301,946)(302,950)(303,949)
(304,948)(305,947)(306,951)(307,955)(308,954)(309,953)(310,952)(311,956)
(312,960)(313,959)(314,958)(315,957)(316,931)(317,935)(318,934)(319,933)
(320,932)(321,936)(322,940)(323,939)(324,938)(325,937)(326,941)(327,945)
(328,944)(329,943)(330,942)(331,916)(332,920)(333,919)(334,918)(335,917)
(336,921)(337,925)(338,924)(339,923)(340,922)(341,926)(342,930)(343,929)
(344,928)(345,927)(346,901)(347,905)(348,904)(349,903)(350,902)(351,906)
(352,910)(353,909)(354,908)(355,907)(356,911)(357,915)(358,914)(359,913)
(360,912)(361,826)(362,830)(363,829)(364,828)(365,827)(366,831)(367,835)
(368,834)(369,833)(370,832)(371,836)(372,840)(373,839)(374,838)(375,837)
(376,811)(377,815)(378,814)(379,813)(380,812)(381,816)(382,820)(383,819)
(384,818)(385,817)(386,821)(387,825)(388,824)(389,823)(390,822)(391,796)
(392,800)(393,799)(394,798)(395,797)(396,801)(397,805)(398,804)(399,803)
(400,802)(401,806)(402,810)(403,809)(404,808)(405,807)(406,781)(407,785)
(408,784)(409,783)(410,782)(411,786)(412,790)(413,789)(414,788)(415,787)
(416,791)(417,795)(418,794)(419,793)(420,792)(421,766)(422,770)(423,769)
(424,768)(425,767)(426,771)(427,775)(428,774)(429,773)(430,772)(431,776)
(432,780)(433,779)(434,778)(435,777)(436,751)(437,755)(438,754)(439,753)
(440,752)(441,756)(442,760)(443,759)(444,758)(445,757)(446,761)(447,765)
(448,764)(449,763)(450,762)(451,736)(452,740)(453,739)(454,738)(455,737)
(456,741)(457,745)(458,744)(459,743)(460,742)(461,746)(462,750)(463,749)
(464,748)(465,747)(466,721)(467,725)(468,724)(469,723)(470,722)(471,726)
(472,730)(473,729)(474,728)(475,727)(476,731)(477,735)(478,734)(479,733)
(480,732);
s2 := Sym(960)!(  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,252)(  7,251)
(  8,255)(  9,254)( 10,253)( 11,247)( 12,246)( 13,250)( 14,249)( 15,248)
( 16,257)( 17,256)( 18,260)( 19,259)( 20,258)( 21,267)( 22,266)( 23,270)
( 24,269)( 25,268)( 26,262)( 27,261)( 28,265)( 29,264)( 30,263)( 31,272)
( 32,271)( 33,275)( 34,274)( 35,273)( 36,282)( 37,281)( 38,285)( 39,284)
( 40,283)( 41,277)( 42,276)( 43,280)( 44,279)( 45,278)( 46,287)( 47,286)
( 48,290)( 49,289)( 50,288)( 51,297)( 52,296)( 53,300)( 54,299)( 55,298)
( 56,292)( 57,291)( 58,295)( 59,294)( 60,293)( 61,302)( 62,301)( 63,305)
( 64,304)( 65,303)( 66,312)( 67,311)( 68,315)( 69,314)( 70,313)( 71,307)
( 72,306)( 73,310)( 74,309)( 75,308)( 76,317)( 77,316)( 78,320)( 79,319)
( 80,318)( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,322)( 87,321)
( 88,325)( 89,324)( 90,323)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)
( 96,342)( 97,341)( 98,345)( 99,344)(100,343)(101,337)(102,336)(103,340)
(104,339)(105,338)(106,347)(107,346)(108,350)(109,349)(110,348)(111,357)
(112,356)(113,360)(114,359)(115,358)(116,352)(117,351)(118,355)(119,354)
(120,353)(121,362)(122,361)(123,365)(124,364)(125,363)(126,372)(127,371)
(128,375)(129,374)(130,373)(131,367)(132,366)(133,370)(134,369)(135,368)
(136,377)(137,376)(138,380)(139,379)(140,378)(141,387)(142,386)(143,390)
(144,389)(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,392)
(152,391)(153,395)(154,394)(155,393)(156,402)(157,401)(158,405)(159,404)
(160,403)(161,397)(162,396)(163,400)(164,399)(165,398)(166,407)(167,406)
(168,410)(169,409)(170,408)(171,417)(172,416)(173,420)(174,419)(175,418)
(176,412)(177,411)(178,415)(179,414)(180,413)(181,422)(182,421)(183,425)
(184,424)(185,423)(186,432)(187,431)(188,435)(189,434)(190,433)(191,427)
(192,426)(193,430)(194,429)(195,428)(196,437)(197,436)(198,440)(199,439)
(200,438)(201,447)(202,446)(203,450)(204,449)(205,448)(206,442)(207,441)
(208,445)(209,444)(210,443)(211,452)(212,451)(213,455)(214,454)(215,453)
(216,462)(217,461)(218,465)(219,464)(220,463)(221,457)(222,456)(223,460)
(224,459)(225,458)(226,467)(227,466)(228,470)(229,469)(230,468)(231,477)
(232,476)(233,480)(234,479)(235,478)(236,472)(237,471)(238,475)(239,474)
(240,473)(481,722)(482,721)(483,725)(484,724)(485,723)(486,732)(487,731)
(488,735)(489,734)(490,733)(491,727)(492,726)(493,730)(494,729)(495,728)
(496,737)(497,736)(498,740)(499,739)(500,738)(501,747)(502,746)(503,750)
(504,749)(505,748)(506,742)(507,741)(508,745)(509,744)(510,743)(511,752)
(512,751)(513,755)(514,754)(515,753)(516,762)(517,761)(518,765)(519,764)
(520,763)(521,757)(522,756)(523,760)(524,759)(525,758)(526,767)(527,766)
(528,770)(529,769)(530,768)(531,777)(532,776)(533,780)(534,779)(535,778)
(536,772)(537,771)(538,775)(539,774)(540,773)(541,782)(542,781)(543,785)
(544,784)(545,783)(546,792)(547,791)(548,795)(549,794)(550,793)(551,787)
(552,786)(553,790)(554,789)(555,788)(556,797)(557,796)(558,800)(559,799)
(560,798)(561,807)(562,806)(563,810)(564,809)(565,808)(566,802)(567,801)
(568,805)(569,804)(570,803)(571,812)(572,811)(573,815)(574,814)(575,813)
(576,822)(577,821)(578,825)(579,824)(580,823)(581,817)(582,816)(583,820)
(584,819)(585,818)(586,827)(587,826)(588,830)(589,829)(590,828)(591,837)
(592,836)(593,840)(594,839)(595,838)(596,832)(597,831)(598,835)(599,834)
(600,833)(601,842)(602,841)(603,845)(604,844)(605,843)(606,852)(607,851)
(608,855)(609,854)(610,853)(611,847)(612,846)(613,850)(614,849)(615,848)
(616,857)(617,856)(618,860)(619,859)(620,858)(621,867)(622,866)(623,870)
(624,869)(625,868)(626,862)(627,861)(628,865)(629,864)(630,863)(631,872)
(632,871)(633,875)(634,874)(635,873)(636,882)(637,881)(638,885)(639,884)
(640,883)(641,877)(642,876)(643,880)(644,879)(645,878)(646,887)(647,886)
(648,890)(649,889)(650,888)(651,897)(652,896)(653,900)(654,899)(655,898)
(656,892)(657,891)(658,895)(659,894)(660,893)(661,902)(662,901)(663,905)
(664,904)(665,903)(666,912)(667,911)(668,915)(669,914)(670,913)(671,907)
(672,906)(673,910)(674,909)(675,908)(676,917)(677,916)(678,920)(679,919)
(680,918)(681,927)(682,926)(683,930)(684,929)(685,928)(686,922)(687,921)
(688,925)(689,924)(690,923)(691,932)(692,931)(693,935)(694,934)(695,933)
(696,942)(697,941)(698,945)(699,944)(700,943)(701,937)(702,936)(703,940)
(704,939)(705,938)(706,947)(707,946)(708,950)(709,949)(710,948)(711,957)
(712,956)(713,960)(714,959)(715,958)(716,952)(717,951)(718,955)(719,954)
(720,953);
s3 := Sym(960)!(  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)
(  8,603)(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)
( 16,621)( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)
( 24,619)( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)
( 32,637)( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)
( 40,635)( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)
( 48,653)( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)
( 56,656)( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)
( 64,669)( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)
( 72,672)( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)
( 80,685)( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)
( 88,688)( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)
( 96,691)( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)
(104,704)(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)
(112,707)(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)
(120,720)(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)
(128,483)(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)
(136,501)(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)
(144,499)(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)
(152,517)(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)
(160,515)(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)
(168,533)(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)
(176,536)(177,537)(178,538)(179,539)(180,540)(181,546)(182,547)(183,548)
(184,549)(185,550)(186,541)(187,542)(188,543)(189,544)(190,545)(191,551)
(192,552)(193,553)(194,554)(195,555)(196,561)(197,562)(198,563)(199,564)
(200,565)(201,556)(202,557)(203,558)(204,559)(205,560)(206,566)(207,567)
(208,568)(209,569)(210,570)(211,576)(212,577)(213,578)(214,579)(215,580)
(216,571)(217,572)(218,573)(219,574)(220,575)(221,581)(222,582)(223,583)
(224,584)(225,585)(226,591)(227,592)(228,593)(229,594)(230,595)(231,586)
(232,587)(233,588)(234,589)(235,590)(236,596)(237,597)(238,598)(239,599)
(240,600)(241,861)(242,862)(243,863)(244,864)(245,865)(246,856)(247,857)
(248,858)(249,859)(250,860)(251,866)(252,867)(253,868)(254,869)(255,870)
(256,846)(257,847)(258,848)(259,849)(260,850)(261,841)(262,842)(263,843)
(264,844)(265,845)(266,851)(267,852)(268,853)(269,854)(270,855)(271,891)
(272,892)(273,893)(274,894)(275,895)(276,886)(277,887)(278,888)(279,889)
(280,890)(281,896)(282,897)(283,898)(284,899)(285,900)(286,876)(287,877)
(288,878)(289,879)(290,880)(291,871)(292,872)(293,873)(294,874)(295,875)
(296,881)(297,882)(298,883)(299,884)(300,885)(301,921)(302,922)(303,923)
(304,924)(305,925)(306,916)(307,917)(308,918)(309,919)(310,920)(311,926)
(312,927)(313,928)(314,929)(315,930)(316,906)(317,907)(318,908)(319,909)
(320,910)(321,901)(322,902)(323,903)(324,904)(325,905)(326,911)(327,912)
(328,913)(329,914)(330,915)(331,951)(332,952)(333,953)(334,954)(335,955)
(336,946)(337,947)(338,948)(339,949)(340,950)(341,956)(342,957)(343,958)
(344,959)(345,960)(346,936)(347,937)(348,938)(349,939)(350,940)(351,931)
(352,932)(353,933)(354,934)(355,935)(356,941)(357,942)(358,943)(359,944)
(360,945)(361,741)(362,742)(363,743)(364,744)(365,745)(366,736)(367,737)
(368,738)(369,739)(370,740)(371,746)(372,747)(373,748)(374,749)(375,750)
(376,726)(377,727)(378,728)(379,729)(380,730)(381,721)(382,722)(383,723)
(384,724)(385,725)(386,731)(387,732)(388,733)(389,734)(390,735)(391,771)
(392,772)(393,773)(394,774)(395,775)(396,766)(397,767)(398,768)(399,769)
(400,770)(401,776)(402,777)(403,778)(404,779)(405,780)(406,756)(407,757)
(408,758)(409,759)(410,760)(411,751)(412,752)(413,753)(414,754)(415,755)
(416,761)(417,762)(418,763)(419,764)(420,765)(421,801)(422,802)(423,803)
(424,804)(425,805)(426,796)(427,797)(428,798)(429,799)(430,800)(431,806)
(432,807)(433,808)(434,809)(435,810)(436,786)(437,787)(438,788)(439,789)
(440,790)(441,781)(442,782)(443,783)(444,784)(445,785)(446,791)(447,792)
(448,793)(449,794)(450,795)(451,831)(452,832)(453,833)(454,834)(455,835)
(456,826)(457,827)(458,828)(459,829)(460,830)(461,836)(462,837)(463,838)
(464,839)(465,840)(466,816)(467,817)(468,818)(469,819)(470,820)(471,811)
(472,812)(473,813)(474,814)(475,815)(476,821)(477,822)(478,823)(479,824)
(480,825);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, 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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope