Polytope of Type {30,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {30,4,4}
Number of vertices, edges, etc : 60, 120, 16, 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 : {15,4,4}*960b, {30,4,2}*960
   4-fold quotients : {30,2,4}*480, {15,4,2}*480, {30,4,2}*480b, {30,4,2}*480c
   5-fold quotients : {6,4,4}*384d
   8-fold quotients : {15,2,4}*240, {15,4,2}*240, {30,2,2}*240
   10-fold quotients : {3,4,4}*192b, {6,4,2}*192
   12-fold quotients : {10,2,4}*160
   16-fold quotients : {15,2,2}*120
   20-fold quotients : {6,2,4}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   40-fold quotients : {3,2,4}*48, {3,4,2}*48, {6,2,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*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 := (  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);;
s1 := (  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);;
s2 := (  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)(  8,247)
(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)
( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)
( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)
( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)
( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)
( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)
( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)
( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)
( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)
( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)
(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)
(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)
(121,422)(122,421)(123,424)(124,423)(125,426)(126,425)(127,428)(128,427)
(129,430)(130,429)(131,432)(132,431)(133,434)(134,433)(135,436)(136,435)
(137,438)(138,437)(139,440)(140,439)(141,442)(142,441)(143,444)(144,443)
(145,446)(146,445)(147,448)(148,447)(149,450)(150,449)(151,452)(152,451)
(153,454)(154,453)(155,456)(156,455)(157,458)(158,457)(159,460)(160,459)
(161,462)(162,461)(163,464)(164,463)(165,466)(166,465)(167,468)(168,467)
(169,470)(170,469)(171,472)(172,471)(173,474)(174,473)(175,476)(176,475)
(177,478)(178,477)(179,480)(180,479)(181,362)(182,361)(183,364)(184,363)
(185,366)(186,365)(187,368)(188,367)(189,370)(190,369)(191,372)(192,371)
(193,374)(194,373)(195,376)(196,375)(197,378)(198,377)(199,380)(200,379)
(201,382)(202,381)(203,384)(204,383)(205,386)(206,385)(207,388)(208,387)
(209,390)(210,389)(211,392)(212,391)(213,394)(214,393)(215,396)(216,395)
(217,398)(218,397)(219,400)(220,399)(221,402)(222,401)(223,404)(224,403)
(225,406)(226,405)(227,408)(228,407)(229,410)(230,409)(231,412)(232,411)
(233,414)(234,413)(235,416)(236,415)(237,418)(238,417)(239,420)(240,419)
(481,722)(482,721)(483,724)(484,723)(485,726)(486,725)(487,728)(488,727)
(489,730)(490,729)(491,732)(492,731)(493,734)(494,733)(495,736)(496,735)
(497,738)(498,737)(499,740)(500,739)(501,742)(502,741)(503,744)(504,743)
(505,746)(506,745)(507,748)(508,747)(509,750)(510,749)(511,752)(512,751)
(513,754)(514,753)(515,756)(516,755)(517,758)(518,757)(519,760)(520,759)
(521,762)(522,761)(523,764)(524,763)(525,766)(526,765)(527,768)(528,767)
(529,770)(530,769)(531,772)(532,771)(533,774)(534,773)(535,776)(536,775)
(537,778)(538,777)(539,780)(540,779)(541,782)(542,781)(543,784)(544,783)
(545,786)(546,785)(547,788)(548,787)(549,790)(550,789)(551,792)(552,791)
(553,794)(554,793)(555,796)(556,795)(557,798)(558,797)(559,800)(560,799)
(561,802)(562,801)(563,804)(564,803)(565,806)(566,805)(567,808)(568,807)
(569,810)(570,809)(571,812)(572,811)(573,814)(574,813)(575,816)(576,815)
(577,818)(578,817)(579,820)(580,819)(581,822)(582,821)(583,824)(584,823)
(585,826)(586,825)(587,828)(588,827)(589,830)(590,829)(591,832)(592,831)
(593,834)(594,833)(595,836)(596,835)(597,838)(598,837)(599,840)(600,839)
(601,902)(602,901)(603,904)(604,903)(605,906)(606,905)(607,908)(608,907)
(609,910)(610,909)(611,912)(612,911)(613,914)(614,913)(615,916)(616,915)
(617,918)(618,917)(619,920)(620,919)(621,922)(622,921)(623,924)(624,923)
(625,926)(626,925)(627,928)(628,927)(629,930)(630,929)(631,932)(632,931)
(633,934)(634,933)(635,936)(636,935)(637,938)(638,937)(639,940)(640,939)
(641,942)(642,941)(643,944)(644,943)(645,946)(646,945)(647,948)(648,947)
(649,950)(650,949)(651,952)(652,951)(653,954)(654,953)(655,956)(656,955)
(657,958)(658,957)(659,960)(660,959)(661,842)(662,841)(663,844)(664,843)
(665,846)(666,845)(667,848)(668,847)(669,850)(670,849)(671,852)(672,851)
(673,854)(674,853)(675,856)(676,855)(677,858)(678,857)(679,860)(680,859)
(681,862)(682,861)(683,864)(684,863)(685,866)(686,865)(687,868)(688,867)
(689,870)(690,869)(691,872)(692,871)(693,874)(694,873)(695,876)(696,875)
(697,878)(698,877)(699,880)(700,879)(701,882)(702,881)(703,884)(704,883)
(705,886)(706,885)(707,888)(708,887)(709,890)(710,889)(711,892)(712,891)
(713,894)(714,893)(715,896)(716,895)(717,898)(718,897)(719,900)(720,899);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope