Polytope of Type {4,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {4,30,4}
Number of vertices, edges, etc : 8, 120, 120, 4
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 : {4,30,4}*960c, {4,30,2}*960
   4-fold quotients : {2,30,4}*480a, {4,15,2}*480, {4,30,2}*480b, {4,30,2}*480c
   5-fold quotients : {4,6,4}*384b
   8-fold quotients : {4,15,2}*240, {2,30,2}*240
   10-fold quotients : {4,6,4}*192c, {4,6,2}*192
   12-fold quotients : {2,10,4}*160
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,6,4}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {4,3,2}*48, {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope