Polytope of Type {8,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,30}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150654)
Rank : 4
Schlafli Type : {8,4,30}
Number of vertices, edges, etc : 8, 16, 60, 30
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 : {4,4,30}*960
   3-fold quotients : {8,4,10}*640b
   4-fold quotients : {2,4,30}*480a, {4,2,30}*480
   5-fold quotients : {8,4,6}*384b
   6-fold quotients : {4,4,10}*320
   8-fold quotients : {4,2,15}*240, {2,2,30}*240
   10-fold quotients : {4,4,6}*192
   12-fold quotients : {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {8,4,2}*128b
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,4,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope