Polytope of Type {4,24,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150682)
Rank : 4
Schlafli Type : {4,24,10}
Number of vertices, edges, etc : 4, 48, 120, 10
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12,10}*960a
   3-fold quotients : {4,8,10}*640b
   4-fold quotients : {2,12,10}*480, {4,6,10}*480a
   5-fold quotients : {4,24,2}*384b
   6-fold quotients : {4,4,10}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {4,12,2}*192a
   12-fold quotients : {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {4,8,2}*128b
   20-fold quotients : {2,12,2}*96, {4,6,2}*96a
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,4,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*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 := (  1,241)(  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)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)( 72,327)
( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)( 80,305)
( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)( 96,351)
( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)(104,359)
(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)(120,345)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)(192,447)
(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)(216,471)
(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(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)(541,796)(542,797)(543,798)(544,799)
(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)(552,807)
(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)(560,785)
(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)(568,793)
(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)(576,831)
(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)(584,839)
(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)(592,817)
(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)(600,825)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)(672,927)
(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)(688,913)
(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)(696,951)
(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)(704,959)
(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)(712,937)
(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)(720,945);;
s1 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)
( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)
( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)
( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)
(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)
(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)
(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,206)(187,207)(188,208)(189,209)(190,210)
(191,201)(192,202)(193,203)(194,204)(195,205)(211,226)(212,227)(213,228)
(214,229)(215,230)(216,236)(217,237)(218,238)(219,239)(220,240)(221,231)
(222,232)(223,233)(224,234)(225,235)(241,271)(242,272)(243,273)(244,274)
(245,275)(246,281)(247,282)(248,283)(249,284)(250,285)(251,276)(252,277)
(253,278)(254,279)(255,280)(256,286)(257,287)(258,288)(259,289)(260,290)
(261,296)(262,297)(263,298)(264,299)(265,300)(266,291)(267,292)(268,293)
(269,294)(270,295)(301,346)(302,347)(303,348)(304,349)(305,350)(306,356)
(307,357)(308,358)(309,359)(310,360)(311,351)(312,352)(313,353)(314,354)
(315,355)(316,331)(317,332)(318,333)(319,334)(320,335)(321,341)(322,342)
(323,343)(324,344)(325,345)(326,336)(327,337)(328,338)(329,339)(330,340)
(361,391)(362,392)(363,393)(364,394)(365,395)(366,401)(367,402)(368,403)
(369,404)(370,405)(371,396)(372,397)(373,398)(374,399)(375,400)(376,406)
(377,407)(378,408)(379,409)(380,410)(381,416)(382,417)(383,418)(384,419)
(385,420)(386,411)(387,412)(388,413)(389,414)(390,415)(421,466)(422,467)
(423,468)(424,469)(425,470)(426,476)(427,477)(428,478)(429,479)(430,480)
(431,471)(432,472)(433,473)(434,474)(435,475)(436,451)(437,452)(438,453)
(439,454)(440,455)(441,461)(442,462)(443,463)(444,464)(445,465)(446,456)
(447,457)(448,458)(449,459)(450,460)(481,541)(482,542)(483,543)(484,544)
(485,545)(486,551)(487,552)(488,553)(489,554)(490,555)(491,546)(492,547)
(493,548)(494,549)(495,550)(496,556)(497,557)(498,558)(499,559)(500,560)
(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)(508,563)
(509,564)(510,565)(511,571)(512,572)(513,573)(514,574)(515,575)(516,581)
(517,582)(518,583)(519,584)(520,585)(521,576)(522,577)(523,578)(524,579)
(525,580)(526,586)(527,587)(528,588)(529,589)(530,590)(531,596)(532,597)
(533,598)(534,599)(535,600)(536,591)(537,592)(538,593)(539,594)(540,595)
(601,661)(602,662)(603,663)(604,664)(605,665)(606,671)(607,672)(608,673)
(609,674)(610,675)(611,666)(612,667)(613,668)(614,669)(615,670)(616,676)
(617,677)(618,678)(619,679)(620,680)(621,686)(622,687)(623,688)(624,689)
(625,690)(626,681)(627,682)(628,683)(629,684)(630,685)(631,691)(632,692)
(633,693)(634,694)(635,695)(636,701)(637,702)(638,703)(639,704)(640,705)
(641,696)(642,697)(643,698)(644,699)(645,700)(646,706)(647,707)(648,708)
(649,709)(650,710)(651,716)(652,717)(653,718)(654,719)(655,720)(656,711)
(657,712)(658,713)(659,714)(660,715)(721,826)(722,827)(723,828)(724,829)
(725,830)(726,836)(727,837)(728,838)(729,839)(730,840)(731,831)(732,832)
(733,833)(734,834)(735,835)(736,811)(737,812)(738,813)(739,814)(740,815)
(741,821)(742,822)(743,823)(744,824)(745,825)(746,816)(747,817)(748,818)
(749,819)(750,820)(751,796)(752,797)(753,798)(754,799)(755,800)(756,806)
(757,807)(758,808)(759,809)(760,810)(761,801)(762,802)(763,803)(764,804)
(765,805)(766,781)(767,782)(768,783)(769,784)(770,785)(771,791)(772,792)
(773,793)(774,794)(775,795)(776,786)(777,787)(778,788)(779,789)(780,790)
(841,946)(842,947)(843,948)(844,949)(845,950)(846,956)(847,957)(848,958)
(849,959)(850,960)(851,951)(852,952)(853,953)(854,954)(855,955)(856,931)
(857,932)(858,933)(859,934)(860,935)(861,941)(862,942)(863,943)(864,944)
(865,945)(866,936)(867,937)(868,938)(869,939)(870,940)(871,916)(872,917)
(873,918)(874,919)(875,920)(876,926)(877,927)(878,928)(879,929)(880,930)
(881,921)(882,922)(883,923)(884,924)(885,925)(886,901)(887,902)(888,903)
(889,904)(890,905)(891,911)(892,912)(893,913)(894,914)(895,915)(896,906)
(897,907)(898,908)(899,909)(900,910);;
s2 := (  1,606)(  2,610)(  3,609)(  4,608)(  5,607)(  6,601)(  7,605)(  8,604)
(  9,603)( 10,602)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)( 16,621)
( 17,625)( 18,624)( 19,623)( 20,622)( 21,616)( 22,620)( 23,619)( 24,618)
( 25,617)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,651)( 32,655)
( 33,654)( 34,653)( 35,652)( 36,646)( 37,650)( 38,649)( 39,648)( 40,647)
( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,636)( 47,640)( 48,639)
( 49,638)( 50,637)( 51,631)( 52,635)( 53,634)( 54,633)( 55,632)( 56,641)
( 57,645)( 58,644)( 59,643)( 60,642)( 61,681)( 62,685)( 63,684)( 64,683)
( 65,682)( 66,676)( 67,680)( 68,679)( 69,678)( 70,677)( 71,686)( 72,690)
( 73,689)( 74,688)( 75,687)( 76,666)( 77,670)( 78,669)( 79,668)( 80,667)
( 81,661)( 82,665)( 83,664)( 84,663)( 85,662)( 86,671)( 87,675)( 88,674)
( 89,673)( 90,672)( 91,696)( 92,700)( 93,699)( 94,698)( 95,697)( 96,691)
( 97,695)( 98,694)( 99,693)(100,692)(101,701)(102,705)(103,704)(104,703)
(105,702)(106,711)(107,715)(108,714)(109,713)(110,712)(111,706)(112,710)
(113,709)(114,708)(115,707)(116,716)(117,720)(118,719)(119,718)(120,717)
(121,486)(122,490)(123,489)(124,488)(125,487)(126,481)(127,485)(128,484)
(129,483)(130,482)(131,491)(132,495)(133,494)(134,493)(135,492)(136,501)
(137,505)(138,504)(139,503)(140,502)(141,496)(142,500)(143,499)(144,498)
(145,497)(146,506)(147,510)(148,509)(149,508)(150,507)(151,531)(152,535)
(153,534)(154,533)(155,532)(156,526)(157,530)(158,529)(159,528)(160,527)
(161,536)(162,540)(163,539)(164,538)(165,537)(166,516)(167,520)(168,519)
(169,518)(170,517)(171,511)(172,515)(173,514)(174,513)(175,512)(176,521)
(177,525)(178,524)(179,523)(180,522)(181,561)(182,565)(183,564)(184,563)
(185,562)(186,556)(187,560)(188,559)(189,558)(190,557)(191,566)(192,570)
(193,569)(194,568)(195,567)(196,546)(197,550)(198,549)(199,548)(200,547)
(201,541)(202,545)(203,544)(204,543)(205,542)(206,551)(207,555)(208,554)
(209,553)(210,552)(211,576)(212,580)(213,579)(214,578)(215,577)(216,571)
(217,575)(218,574)(219,573)(220,572)(221,581)(222,585)(223,584)(224,583)
(225,582)(226,591)(227,595)(228,594)(229,593)(230,592)(231,586)(232,590)
(233,589)(234,588)(235,587)(236,596)(237,600)(238,599)(239,598)(240,597)
(241,846)(242,850)(243,849)(244,848)(245,847)(246,841)(247,845)(248,844)
(249,843)(250,842)(251,851)(252,855)(253,854)(254,853)(255,852)(256,861)
(257,865)(258,864)(259,863)(260,862)(261,856)(262,860)(263,859)(264,858)
(265,857)(266,866)(267,870)(268,869)(269,868)(270,867)(271,891)(272,895)
(273,894)(274,893)(275,892)(276,886)(277,890)(278,889)(279,888)(280,887)
(281,896)(282,900)(283,899)(284,898)(285,897)(286,876)(287,880)(288,879)
(289,878)(290,877)(291,871)(292,875)(293,874)(294,873)(295,872)(296,881)
(297,885)(298,884)(299,883)(300,882)(301,921)(302,925)(303,924)(304,923)
(305,922)(306,916)(307,920)(308,919)(309,918)(310,917)(311,926)(312,930)
(313,929)(314,928)(315,927)(316,906)(317,910)(318,909)(319,908)(320,907)
(321,901)(322,905)(323,904)(324,903)(325,902)(326,911)(327,915)(328,914)
(329,913)(330,912)(331,936)(332,940)(333,939)(334,938)(335,937)(336,931)
(337,935)(338,934)(339,933)(340,932)(341,941)(342,945)(343,944)(344,943)
(345,942)(346,951)(347,955)(348,954)(349,953)(350,952)(351,946)(352,950)
(353,949)(354,948)(355,947)(356,956)(357,960)(358,959)(359,958)(360,957)
(361,726)(362,730)(363,729)(364,728)(365,727)(366,721)(367,725)(368,724)
(369,723)(370,722)(371,731)(372,735)(373,734)(374,733)(375,732)(376,741)
(377,745)(378,744)(379,743)(380,742)(381,736)(382,740)(383,739)(384,738)
(385,737)(386,746)(387,750)(388,749)(389,748)(390,747)(391,771)(392,775)
(393,774)(394,773)(395,772)(396,766)(397,770)(398,769)(399,768)(400,767)
(401,776)(402,780)(403,779)(404,778)(405,777)(406,756)(407,760)(408,759)
(409,758)(410,757)(411,751)(412,755)(413,754)(414,753)(415,752)(416,761)
(417,765)(418,764)(419,763)(420,762)(421,801)(422,805)(423,804)(424,803)
(425,802)(426,796)(427,800)(428,799)(429,798)(430,797)(431,806)(432,810)
(433,809)(434,808)(435,807)(436,786)(437,790)(438,789)(439,788)(440,787)
(441,781)(442,785)(443,784)(444,783)(445,782)(446,791)(447,795)(448,794)
(449,793)(450,792)(451,816)(452,820)(453,819)(454,818)(455,817)(456,811)
(457,815)(458,814)(459,813)(460,812)(461,821)(462,825)(463,824)(464,823)
(465,822)(466,831)(467,835)(468,834)(469,833)(470,832)(471,826)(472,830)
(473,829)(474,828)(475,827)(476,836)(477,840)(478,839)(479,838)(480,837);;
s3 := (  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)(  8,130)
(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)(280,398)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)(304,424)
(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)(320,438)
(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)(328,450)
(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)(336,457)
(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)(344,464)
(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)(352,471)
(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)(360,478)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)(576,697)
(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)(592,711)
(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)(728,850)
(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)(744,864)
(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)(760,878)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)(784,904)
(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)(792,911)
(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)(800,918)
(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)(808,930)
(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)(816,937)
(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)(824,944)
(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)(832,951)
(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)(840,958);;
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)
( 72,327)( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)
( 80,305)( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)
( 96,351)( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)
(104,359)(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)
(120,345)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)
(192,447)(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,471)(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)
(232,457)(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(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)(541,796)(542,797)(543,798)
(544,799)(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)
(552,807)(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)
(560,785)(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)
(568,793)(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)
(576,831)(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)
(584,839)(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)
(592,817)(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)
(600,825)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)
(672,927)(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)
(688,913)(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,951)(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)
(704,959)(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)
(712,937)(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)
(720,945);
s1 := Sym(960)!(  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)
( 64, 79)( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)
( 72, 82)( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)
( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)
(103,113)(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)
(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)
(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,206)(187,207)(188,208)(189,209)
(190,210)(191,201)(192,202)(193,203)(194,204)(195,205)(211,226)(212,227)
(213,228)(214,229)(215,230)(216,236)(217,237)(218,238)(219,239)(220,240)
(221,231)(222,232)(223,233)(224,234)(225,235)(241,271)(242,272)(243,273)
(244,274)(245,275)(246,281)(247,282)(248,283)(249,284)(250,285)(251,276)
(252,277)(253,278)(254,279)(255,280)(256,286)(257,287)(258,288)(259,289)
(260,290)(261,296)(262,297)(263,298)(264,299)(265,300)(266,291)(267,292)
(268,293)(269,294)(270,295)(301,346)(302,347)(303,348)(304,349)(305,350)
(306,356)(307,357)(308,358)(309,359)(310,360)(311,351)(312,352)(313,353)
(314,354)(315,355)(316,331)(317,332)(318,333)(319,334)(320,335)(321,341)
(322,342)(323,343)(324,344)(325,345)(326,336)(327,337)(328,338)(329,339)
(330,340)(361,391)(362,392)(363,393)(364,394)(365,395)(366,401)(367,402)
(368,403)(369,404)(370,405)(371,396)(372,397)(373,398)(374,399)(375,400)
(376,406)(377,407)(378,408)(379,409)(380,410)(381,416)(382,417)(383,418)
(384,419)(385,420)(386,411)(387,412)(388,413)(389,414)(390,415)(421,466)
(422,467)(423,468)(424,469)(425,470)(426,476)(427,477)(428,478)(429,479)
(430,480)(431,471)(432,472)(433,473)(434,474)(435,475)(436,451)(437,452)
(438,453)(439,454)(440,455)(441,461)(442,462)(443,463)(444,464)(445,465)
(446,456)(447,457)(448,458)(449,459)(450,460)(481,541)(482,542)(483,543)
(484,544)(485,545)(486,551)(487,552)(488,553)(489,554)(490,555)(491,546)
(492,547)(493,548)(494,549)(495,550)(496,556)(497,557)(498,558)(499,559)
(500,560)(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)
(508,563)(509,564)(510,565)(511,571)(512,572)(513,573)(514,574)(515,575)
(516,581)(517,582)(518,583)(519,584)(520,585)(521,576)(522,577)(523,578)
(524,579)(525,580)(526,586)(527,587)(528,588)(529,589)(530,590)(531,596)
(532,597)(533,598)(534,599)(535,600)(536,591)(537,592)(538,593)(539,594)
(540,595)(601,661)(602,662)(603,663)(604,664)(605,665)(606,671)(607,672)
(608,673)(609,674)(610,675)(611,666)(612,667)(613,668)(614,669)(615,670)
(616,676)(617,677)(618,678)(619,679)(620,680)(621,686)(622,687)(623,688)
(624,689)(625,690)(626,681)(627,682)(628,683)(629,684)(630,685)(631,691)
(632,692)(633,693)(634,694)(635,695)(636,701)(637,702)(638,703)(639,704)
(640,705)(641,696)(642,697)(643,698)(644,699)(645,700)(646,706)(647,707)
(648,708)(649,709)(650,710)(651,716)(652,717)(653,718)(654,719)(655,720)
(656,711)(657,712)(658,713)(659,714)(660,715)(721,826)(722,827)(723,828)
(724,829)(725,830)(726,836)(727,837)(728,838)(729,839)(730,840)(731,831)
(732,832)(733,833)(734,834)(735,835)(736,811)(737,812)(738,813)(739,814)
(740,815)(741,821)(742,822)(743,823)(744,824)(745,825)(746,816)(747,817)
(748,818)(749,819)(750,820)(751,796)(752,797)(753,798)(754,799)(755,800)
(756,806)(757,807)(758,808)(759,809)(760,810)(761,801)(762,802)(763,803)
(764,804)(765,805)(766,781)(767,782)(768,783)(769,784)(770,785)(771,791)
(772,792)(773,793)(774,794)(775,795)(776,786)(777,787)(778,788)(779,789)
(780,790)(841,946)(842,947)(843,948)(844,949)(845,950)(846,956)(847,957)
(848,958)(849,959)(850,960)(851,951)(852,952)(853,953)(854,954)(855,955)
(856,931)(857,932)(858,933)(859,934)(860,935)(861,941)(862,942)(863,943)
(864,944)(865,945)(866,936)(867,937)(868,938)(869,939)(870,940)(871,916)
(872,917)(873,918)(874,919)(875,920)(876,926)(877,927)(878,928)(879,929)
(880,930)(881,921)(882,922)(883,923)(884,924)(885,925)(886,901)(887,902)
(888,903)(889,904)(890,905)(891,911)(892,912)(893,913)(894,914)(895,915)
(896,906)(897,907)(898,908)(899,909)(900,910);
s2 := Sym(960)!(  1,606)(  2,610)(  3,609)(  4,608)(  5,607)(  6,601)(  7,605)
(  8,604)(  9,603)( 10,602)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)
( 16,621)( 17,625)( 18,624)( 19,623)( 20,622)( 21,616)( 22,620)( 23,619)
( 24,618)( 25,617)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,651)
( 32,655)( 33,654)( 34,653)( 35,652)( 36,646)( 37,650)( 38,649)( 39,648)
( 40,647)( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,636)( 47,640)
( 48,639)( 49,638)( 50,637)( 51,631)( 52,635)( 53,634)( 54,633)( 55,632)
( 56,641)( 57,645)( 58,644)( 59,643)( 60,642)( 61,681)( 62,685)( 63,684)
( 64,683)( 65,682)( 66,676)( 67,680)( 68,679)( 69,678)( 70,677)( 71,686)
( 72,690)( 73,689)( 74,688)( 75,687)( 76,666)( 77,670)( 78,669)( 79,668)
( 80,667)( 81,661)( 82,665)( 83,664)( 84,663)( 85,662)( 86,671)( 87,675)
( 88,674)( 89,673)( 90,672)( 91,696)( 92,700)( 93,699)( 94,698)( 95,697)
( 96,691)( 97,695)( 98,694)( 99,693)(100,692)(101,701)(102,705)(103,704)
(104,703)(105,702)(106,711)(107,715)(108,714)(109,713)(110,712)(111,706)
(112,710)(113,709)(114,708)(115,707)(116,716)(117,720)(118,719)(119,718)
(120,717)(121,486)(122,490)(123,489)(124,488)(125,487)(126,481)(127,485)
(128,484)(129,483)(130,482)(131,491)(132,495)(133,494)(134,493)(135,492)
(136,501)(137,505)(138,504)(139,503)(140,502)(141,496)(142,500)(143,499)
(144,498)(145,497)(146,506)(147,510)(148,509)(149,508)(150,507)(151,531)
(152,535)(153,534)(154,533)(155,532)(156,526)(157,530)(158,529)(159,528)
(160,527)(161,536)(162,540)(163,539)(164,538)(165,537)(166,516)(167,520)
(168,519)(169,518)(170,517)(171,511)(172,515)(173,514)(174,513)(175,512)
(176,521)(177,525)(178,524)(179,523)(180,522)(181,561)(182,565)(183,564)
(184,563)(185,562)(186,556)(187,560)(188,559)(189,558)(190,557)(191,566)
(192,570)(193,569)(194,568)(195,567)(196,546)(197,550)(198,549)(199,548)
(200,547)(201,541)(202,545)(203,544)(204,543)(205,542)(206,551)(207,555)
(208,554)(209,553)(210,552)(211,576)(212,580)(213,579)(214,578)(215,577)
(216,571)(217,575)(218,574)(219,573)(220,572)(221,581)(222,585)(223,584)
(224,583)(225,582)(226,591)(227,595)(228,594)(229,593)(230,592)(231,586)
(232,590)(233,589)(234,588)(235,587)(236,596)(237,600)(238,599)(239,598)
(240,597)(241,846)(242,850)(243,849)(244,848)(245,847)(246,841)(247,845)
(248,844)(249,843)(250,842)(251,851)(252,855)(253,854)(254,853)(255,852)
(256,861)(257,865)(258,864)(259,863)(260,862)(261,856)(262,860)(263,859)
(264,858)(265,857)(266,866)(267,870)(268,869)(269,868)(270,867)(271,891)
(272,895)(273,894)(274,893)(275,892)(276,886)(277,890)(278,889)(279,888)
(280,887)(281,896)(282,900)(283,899)(284,898)(285,897)(286,876)(287,880)
(288,879)(289,878)(290,877)(291,871)(292,875)(293,874)(294,873)(295,872)
(296,881)(297,885)(298,884)(299,883)(300,882)(301,921)(302,925)(303,924)
(304,923)(305,922)(306,916)(307,920)(308,919)(309,918)(310,917)(311,926)
(312,930)(313,929)(314,928)(315,927)(316,906)(317,910)(318,909)(319,908)
(320,907)(321,901)(322,905)(323,904)(324,903)(325,902)(326,911)(327,915)
(328,914)(329,913)(330,912)(331,936)(332,940)(333,939)(334,938)(335,937)
(336,931)(337,935)(338,934)(339,933)(340,932)(341,941)(342,945)(343,944)
(344,943)(345,942)(346,951)(347,955)(348,954)(349,953)(350,952)(351,946)
(352,950)(353,949)(354,948)(355,947)(356,956)(357,960)(358,959)(359,958)
(360,957)(361,726)(362,730)(363,729)(364,728)(365,727)(366,721)(367,725)
(368,724)(369,723)(370,722)(371,731)(372,735)(373,734)(374,733)(375,732)
(376,741)(377,745)(378,744)(379,743)(380,742)(381,736)(382,740)(383,739)
(384,738)(385,737)(386,746)(387,750)(388,749)(389,748)(390,747)(391,771)
(392,775)(393,774)(394,773)(395,772)(396,766)(397,770)(398,769)(399,768)
(400,767)(401,776)(402,780)(403,779)(404,778)(405,777)(406,756)(407,760)
(408,759)(409,758)(410,757)(411,751)(412,755)(413,754)(414,753)(415,752)
(416,761)(417,765)(418,764)(419,763)(420,762)(421,801)(422,805)(423,804)
(424,803)(425,802)(426,796)(427,800)(428,799)(429,798)(430,797)(431,806)
(432,810)(433,809)(434,808)(435,807)(436,786)(437,790)(438,789)(439,788)
(440,787)(441,781)(442,785)(443,784)(444,783)(445,782)(446,791)(447,795)
(448,794)(449,793)(450,792)(451,816)(452,820)(453,819)(454,818)(455,817)
(456,811)(457,815)(458,814)(459,813)(460,812)(461,821)(462,825)(463,824)
(464,823)(465,822)(466,831)(467,835)(468,834)(469,833)(470,832)(471,826)
(472,830)(473,829)(474,828)(475,827)(476,836)(477,840)(478,839)(479,838)
(480,837);
s3 := Sym(960)!(  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)
(  8,130)(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)
(280,398)(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)
(304,424)(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)
(320,438)(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)
(328,450)(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)
(336,457)(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)
(344,464)(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)
(352,471)(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)
(360,478)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,697)(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)
(592,711)(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)
(728,850)(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)
(744,864)(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)
(760,878)(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)
(784,904)(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)
(792,911)(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)
(800,918)(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)
(808,930)(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)
(816,937)(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)
(824,944)(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)
(832,951)(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)
(840,958);
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*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;

References : None.
to this polytope