Polytope of Type {4,4,30}

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

Permutation Representation (Magma) :

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

References : None.
to this polytope