Polytope of Type {6,40,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40,4}*1920a
Also Known As : {{6,40|2},{40,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,148902)
Rank : 4
Schlafli Type : {6,40,4}
Number of vertices, edges, etc : 6, 120, 80, 4
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 : {6,20,4}*960, {6,40,2}*960
   3-fold quotients : {2,40,4}*640a
   4-fold quotients : {6,20,2}*480a, {6,10,4}*480
   5-fold quotients : {6,8,4}*384a
   6-fold quotients : {2,20,4}*320, {2,40,2}*320
   8-fold quotients : {6,10,2}*240
   10-fold quotients : {6,4,4}*192, {6,8,2}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160
   15-fold quotients : {2,8,4}*128a
   20-fold quotients : {6,2,4}*96, {6,4,2}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,4,4}*64, {2,8,2}*64
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {3,2,2}*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)(  6,131)(  7,132)(  8,133)
(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)( 24,149)
( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)( 72,187)
( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)( 88,203)
( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,221)
( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)(104,219)
(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)(248,373)
(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)(264,389)
(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)(280,405)
(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)(312,427)
(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)(328,443)
(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)(336,461)
(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)(344,459)
(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)(352,477)
(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)(360,475)
(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)
(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)
(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)
(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)(512,632)
(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)(520,645)
(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)(528,648)
(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)(536,651)
(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)(544,664)
(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)(552,667)
(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)(560,680)
(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)(568,683)
(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)(576,701)
(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)(584,699)
(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)(592,717)
(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)(600,715)
(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)
(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)
(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)
(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)(752,872)
(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)(760,885)
(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)(768,888)
(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)(776,891)
(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)(784,904)
(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)(792,907)
(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)(800,920)
(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)(808,923)
(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)(816,941)
(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)(824,939)
(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)(832,957)
(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)(840,955);;
s1 := (  1,606)(  2,610)(  3,609)(  4,608)(  5,607)(  6,601)(  7,605)(  8,604)
(  9,603)( 10,602)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)( 16,621)
( 17,625)( 18,624)( 19,623)( 20,622)( 21,616)( 22,620)( 23,619)( 24,618)
( 25,617)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,636)( 32,640)
( 33,639)( 34,638)( 35,637)( 36,631)( 37,635)( 38,634)( 39,633)( 40,632)
( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,651)( 47,655)( 48,654)
( 49,653)( 50,652)( 51,646)( 52,650)( 53,649)( 54,648)( 55,647)( 56,656)
( 57,660)( 58,659)( 59,658)( 60,657)( 61,681)( 62,685)( 63,684)( 64,683)
( 65,682)( 66,676)( 67,680)( 68,679)( 69,678)( 70,677)( 71,686)( 72,690)
( 73,689)( 74,688)( 75,687)( 76,666)( 77,670)( 78,669)( 79,668)( 80,667)
( 81,661)( 82,665)( 83,664)( 84,663)( 85,662)( 86,671)( 87,675)( 88,674)
( 89,673)( 90,672)( 91,711)( 92,715)( 93,714)( 94,713)( 95,712)( 96,706)
( 97,710)( 98,709)( 99,708)(100,707)(101,716)(102,720)(103,719)(104,718)
(105,717)(106,696)(107,700)(108,699)(109,698)(110,697)(111,691)(112,695)
(113,694)(114,693)(115,692)(116,701)(117,705)(118,704)(119,703)(120,702)
(121,486)(122,490)(123,489)(124,488)(125,487)(126,481)(127,485)(128,484)
(129,483)(130,482)(131,491)(132,495)(133,494)(134,493)(135,492)(136,501)
(137,505)(138,504)(139,503)(140,502)(141,496)(142,500)(143,499)(144,498)
(145,497)(146,506)(147,510)(148,509)(149,508)(150,507)(151,516)(152,520)
(153,519)(154,518)(155,517)(156,511)(157,515)(158,514)(159,513)(160,512)
(161,521)(162,525)(163,524)(164,523)(165,522)(166,531)(167,535)(168,534)
(169,533)(170,532)(171,526)(172,530)(173,529)(174,528)(175,527)(176,536)
(177,540)(178,539)(179,538)(180,537)(181,561)(182,565)(183,564)(184,563)
(185,562)(186,556)(187,560)(188,559)(189,558)(190,557)(191,566)(192,570)
(193,569)(194,568)(195,567)(196,546)(197,550)(198,549)(199,548)(200,547)
(201,541)(202,545)(203,544)(204,543)(205,542)(206,551)(207,555)(208,554)
(209,553)(210,552)(211,591)(212,595)(213,594)(214,593)(215,592)(216,586)
(217,590)(218,589)(219,588)(220,587)(221,596)(222,600)(223,599)(224,598)
(225,597)(226,576)(227,580)(228,579)(229,578)(230,577)(231,571)(232,575)
(233,574)(234,573)(235,572)(236,581)(237,585)(238,584)(239,583)(240,582)
(241,846)(242,850)(243,849)(244,848)(245,847)(246,841)(247,845)(248,844)
(249,843)(250,842)(251,851)(252,855)(253,854)(254,853)(255,852)(256,861)
(257,865)(258,864)(259,863)(260,862)(261,856)(262,860)(263,859)(264,858)
(265,857)(266,866)(267,870)(268,869)(269,868)(270,867)(271,876)(272,880)
(273,879)(274,878)(275,877)(276,871)(277,875)(278,874)(279,873)(280,872)
(281,881)(282,885)(283,884)(284,883)(285,882)(286,891)(287,895)(288,894)
(289,893)(290,892)(291,886)(292,890)(293,889)(294,888)(295,887)(296,896)
(297,900)(298,899)(299,898)(300,897)(301,921)(302,925)(303,924)(304,923)
(305,922)(306,916)(307,920)(308,919)(309,918)(310,917)(311,926)(312,930)
(313,929)(314,928)(315,927)(316,906)(317,910)(318,909)(319,908)(320,907)
(321,901)(322,905)(323,904)(324,903)(325,902)(326,911)(327,915)(328,914)
(329,913)(330,912)(331,951)(332,955)(333,954)(334,953)(335,952)(336,946)
(337,950)(338,949)(339,948)(340,947)(341,956)(342,960)(343,959)(344,958)
(345,957)(346,936)(347,940)(348,939)(349,938)(350,937)(351,931)(352,935)
(353,934)(354,933)(355,932)(356,941)(357,945)(358,944)(359,943)(360,942)
(361,726)(362,730)(363,729)(364,728)(365,727)(366,721)(367,725)(368,724)
(369,723)(370,722)(371,731)(372,735)(373,734)(374,733)(375,732)(376,741)
(377,745)(378,744)(379,743)(380,742)(381,736)(382,740)(383,739)(384,738)
(385,737)(386,746)(387,750)(388,749)(389,748)(390,747)(391,756)(392,760)
(393,759)(394,758)(395,757)(396,751)(397,755)(398,754)(399,753)(400,752)
(401,761)(402,765)(403,764)(404,763)(405,762)(406,771)(407,775)(408,774)
(409,773)(410,772)(411,766)(412,770)(413,769)(414,768)(415,767)(416,776)
(417,780)(418,779)(419,778)(420,777)(421,801)(422,805)(423,804)(424,803)
(425,802)(426,796)(427,800)(428,799)(429,798)(430,797)(431,806)(432,810)
(433,809)(434,808)(435,807)(436,786)(437,790)(438,789)(439,788)(440,787)
(441,781)(442,785)(443,784)(444,783)(445,782)(446,791)(447,795)(448,794)
(449,793)(450,792)(451,831)(452,835)(453,834)(454,833)(455,832)(456,826)
(457,830)(458,829)(459,828)(460,827)(461,836)(462,840)(463,839)(464,838)
(465,837)(466,816)(467,820)(468,819)(469,818)(470,817)(471,811)(472,815)
(473,814)(474,813)(475,812)(476,821)(477,825)(478,824)(479,823)(480,822);;
s2 := (  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);;
s3 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)(  6,131)(  7,132)
(  8,133)(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)
( 24,149)( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)
( 72,187)( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)
( 88,203)( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,221)( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)
(248,373)(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)
(264,389)(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)
(280,405)(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)
(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)
(328,443)(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,461)(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)
(344,459)(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)
(352,477)(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)
(360,475)(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)
(488,613)(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)
(496,616)(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)
(504,629)(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)
(512,632)(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)
(520,645)(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)
(528,648)(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)
(536,651)(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)
(544,664)(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)
(552,667)(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)
(560,680)(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)
(568,683)(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)
(576,701)(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)
(584,699)(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)
(592,717)(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)
(600,715)(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)
(728,853)(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)
(736,856)(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)
(744,869)(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)
(752,872)(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)
(760,885)(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)
(768,888)(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)
(776,891)(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)
(784,904)(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)
(792,907)(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)
(800,920)(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)
(808,923)(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)
(816,941)(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)
(824,939)(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)
(832,957)(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)
(840,955);
s1 := Sym(960)!(  1,606)(  2,610)(  3,609)(  4,608)(  5,607)(  6,601)(  7,605)
(  8,604)(  9,603)( 10,602)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)
( 16,621)( 17,625)( 18,624)( 19,623)( 20,622)( 21,616)( 22,620)( 23,619)
( 24,618)( 25,617)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,636)
( 32,640)( 33,639)( 34,638)( 35,637)( 36,631)( 37,635)( 38,634)( 39,633)
( 40,632)( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,651)( 47,655)
( 48,654)( 49,653)( 50,652)( 51,646)( 52,650)( 53,649)( 54,648)( 55,647)
( 56,656)( 57,660)( 58,659)( 59,658)( 60,657)( 61,681)( 62,685)( 63,684)
( 64,683)( 65,682)( 66,676)( 67,680)( 68,679)( 69,678)( 70,677)( 71,686)
( 72,690)( 73,689)( 74,688)( 75,687)( 76,666)( 77,670)( 78,669)( 79,668)
( 80,667)( 81,661)( 82,665)( 83,664)( 84,663)( 85,662)( 86,671)( 87,675)
( 88,674)( 89,673)( 90,672)( 91,711)( 92,715)( 93,714)( 94,713)( 95,712)
( 96,706)( 97,710)( 98,709)( 99,708)(100,707)(101,716)(102,720)(103,719)
(104,718)(105,717)(106,696)(107,700)(108,699)(109,698)(110,697)(111,691)
(112,695)(113,694)(114,693)(115,692)(116,701)(117,705)(118,704)(119,703)
(120,702)(121,486)(122,490)(123,489)(124,488)(125,487)(126,481)(127,485)
(128,484)(129,483)(130,482)(131,491)(132,495)(133,494)(134,493)(135,492)
(136,501)(137,505)(138,504)(139,503)(140,502)(141,496)(142,500)(143,499)
(144,498)(145,497)(146,506)(147,510)(148,509)(149,508)(150,507)(151,516)
(152,520)(153,519)(154,518)(155,517)(156,511)(157,515)(158,514)(159,513)
(160,512)(161,521)(162,525)(163,524)(164,523)(165,522)(166,531)(167,535)
(168,534)(169,533)(170,532)(171,526)(172,530)(173,529)(174,528)(175,527)
(176,536)(177,540)(178,539)(179,538)(180,537)(181,561)(182,565)(183,564)
(184,563)(185,562)(186,556)(187,560)(188,559)(189,558)(190,557)(191,566)
(192,570)(193,569)(194,568)(195,567)(196,546)(197,550)(198,549)(199,548)
(200,547)(201,541)(202,545)(203,544)(204,543)(205,542)(206,551)(207,555)
(208,554)(209,553)(210,552)(211,591)(212,595)(213,594)(214,593)(215,592)
(216,586)(217,590)(218,589)(219,588)(220,587)(221,596)(222,600)(223,599)
(224,598)(225,597)(226,576)(227,580)(228,579)(229,578)(230,577)(231,571)
(232,575)(233,574)(234,573)(235,572)(236,581)(237,585)(238,584)(239,583)
(240,582)(241,846)(242,850)(243,849)(244,848)(245,847)(246,841)(247,845)
(248,844)(249,843)(250,842)(251,851)(252,855)(253,854)(254,853)(255,852)
(256,861)(257,865)(258,864)(259,863)(260,862)(261,856)(262,860)(263,859)
(264,858)(265,857)(266,866)(267,870)(268,869)(269,868)(270,867)(271,876)
(272,880)(273,879)(274,878)(275,877)(276,871)(277,875)(278,874)(279,873)
(280,872)(281,881)(282,885)(283,884)(284,883)(285,882)(286,891)(287,895)
(288,894)(289,893)(290,892)(291,886)(292,890)(293,889)(294,888)(295,887)
(296,896)(297,900)(298,899)(299,898)(300,897)(301,921)(302,925)(303,924)
(304,923)(305,922)(306,916)(307,920)(308,919)(309,918)(310,917)(311,926)
(312,930)(313,929)(314,928)(315,927)(316,906)(317,910)(318,909)(319,908)
(320,907)(321,901)(322,905)(323,904)(324,903)(325,902)(326,911)(327,915)
(328,914)(329,913)(330,912)(331,951)(332,955)(333,954)(334,953)(335,952)
(336,946)(337,950)(338,949)(339,948)(340,947)(341,956)(342,960)(343,959)
(344,958)(345,957)(346,936)(347,940)(348,939)(349,938)(350,937)(351,931)
(352,935)(353,934)(354,933)(355,932)(356,941)(357,945)(358,944)(359,943)
(360,942)(361,726)(362,730)(363,729)(364,728)(365,727)(366,721)(367,725)
(368,724)(369,723)(370,722)(371,731)(372,735)(373,734)(374,733)(375,732)
(376,741)(377,745)(378,744)(379,743)(380,742)(381,736)(382,740)(383,739)
(384,738)(385,737)(386,746)(387,750)(388,749)(389,748)(390,747)(391,756)
(392,760)(393,759)(394,758)(395,757)(396,751)(397,755)(398,754)(399,753)
(400,752)(401,761)(402,765)(403,764)(404,763)(405,762)(406,771)(407,775)
(408,774)(409,773)(410,772)(411,766)(412,770)(413,769)(414,768)(415,767)
(416,776)(417,780)(418,779)(419,778)(420,777)(421,801)(422,805)(423,804)
(424,803)(425,802)(426,796)(427,800)(428,799)(429,798)(430,797)(431,806)
(432,810)(433,809)(434,808)(435,807)(436,786)(437,790)(438,789)(439,788)
(440,787)(441,781)(442,785)(443,784)(444,783)(445,782)(446,791)(447,795)
(448,794)(449,793)(450,792)(451,831)(452,835)(453,834)(454,833)(455,832)
(456,826)(457,830)(458,829)(459,828)(460,827)(461,836)(462,840)(463,839)
(464,838)(465,837)(466,816)(467,820)(468,819)(469,818)(470,817)(471,811)
(472,815)(473,814)(474,813)(475,812)(476,821)(477,825)(478,824)(479,823)
(480,822);
s2 := 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);
s3 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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