Polytope of Type {8,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12,10}*1920a
Also Known As : {{8,12|2},{12,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,148891)
Rank : 4
Schlafli Type : {8,12,10}
Number of vertices, edges, etc : 8, 48, 60, 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, {8,6,10}*960
   3-fold quotients : {8,4,10}*640a
   4-fold quotients : {2,12,10}*480, {4,6,10}*480a
   5-fold quotients : {8,12,2}*384a
   6-fold quotients : {4,4,10}*320, {8,2,10}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {4,12,2}*192a, {8,6,2}*192
   12-fold quotients : {8,2,5}*160, {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {8,4,2}*128a
   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, {8,2,2}*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 := (  1,481)(  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)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(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)(151,631)(152,632)
(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)(160,640)
(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)(168,648)
(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)(176,656)
(177,657)(178,658)(179,659)(180,660)(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)(211,706)(212,707)(213,708)(214,709)(215,710)(216,711)
(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)(224,719)
(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)(232,697)
(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)(240,705)
(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)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(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)(391,871)(392,872)
(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)(400,880)
(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)(408,888)
(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)(416,896)
(417,897)(418,898)(419,899)(420,900)(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)(451,946)(452,947)(453,948)(454,949)(455,950)(456,951)
(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)(464,959)
(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)(472,937)
(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)(480,945);;
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)(721,811)(722,812)(723,813)(724,814)
(725,815)(726,821)(727,822)(728,823)(729,824)(730,825)(731,816)(732,817)
(733,818)(734,819)(735,820)(736,826)(737,827)(738,828)(739,829)(740,830)
(741,836)(742,837)(743,838)(744,839)(745,840)(746,831)(747,832)(748,833)
(749,834)(750,835)(751,781)(752,782)(753,783)(754,784)(755,785)(756,791)
(757,792)(758,793)(759,794)(760,795)(761,786)(762,787)(763,788)(764,789)
(765,790)(766,796)(767,797)(768,798)(769,799)(770,800)(771,806)(772,807)
(773,808)(774,809)(775,810)(776,801)(777,802)(778,803)(779,804)(780,805)
(841,931)(842,932)(843,933)(844,934)(845,935)(846,941)(847,942)(848,943)
(849,944)(850,945)(851,936)(852,937)(853,938)(854,939)(855,940)(856,946)
(857,947)(858,948)(859,949)(860,950)(861,956)(862,957)(863,958)(864,959)
(865,960)(866,951)(867,952)(868,953)(869,954)(870,955)(871,901)(872,902)
(873,903)(874,904)(875,905)(876,911)(877,912)(878,913)(879,914)(880,915)
(881,906)(882,907)(883,908)(884,909)(885,910)(886,916)(887,917)(888,918)
(889,919)(890,920)(891,926)(892,927)(893,928)(894,929)(895,930)(896,921)
(897,922)(898,923)(899,924)(900,925);;
s2 := (  1,366)(  2,370)(  3,369)(  4,368)(  5,367)(  6,361)(  7,365)(  8,364)
(  9,363)( 10,362)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)( 16,381)
( 17,385)( 18,384)( 19,383)( 20,382)( 21,376)( 22,380)( 23,379)( 24,378)
( 25,377)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,396)( 32,400)
( 33,399)( 34,398)( 35,397)( 36,391)( 37,395)( 38,394)( 39,393)( 40,392)
( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,411)( 47,415)( 48,414)
( 49,413)( 50,412)( 51,406)( 52,410)( 53,409)( 54,408)( 55,407)( 56,416)
( 57,420)( 58,419)( 59,418)( 60,417)( 61,426)( 62,430)( 63,429)( 64,428)
( 65,427)( 66,421)( 67,425)( 68,424)( 69,423)( 70,422)( 71,431)( 72,435)
( 73,434)( 74,433)( 75,432)( 76,441)( 77,445)( 78,444)( 79,443)( 80,442)
( 81,436)( 82,440)( 83,439)( 84,438)( 85,437)( 86,446)( 87,450)( 88,449)
( 89,448)( 90,447)( 91,456)( 92,460)( 93,459)( 94,458)( 95,457)( 96,451)
( 97,455)( 98,454)( 99,453)(100,452)(101,461)(102,465)(103,464)(104,463)
(105,462)(106,471)(107,475)(108,474)(109,473)(110,472)(111,466)(112,470)
(113,469)(114,468)(115,467)(116,476)(117,480)(118,479)(119,478)(120,477)
(121,246)(122,250)(123,249)(124,248)(125,247)(126,241)(127,245)(128,244)
(129,243)(130,242)(131,251)(132,255)(133,254)(134,253)(135,252)(136,261)
(137,265)(138,264)(139,263)(140,262)(141,256)(142,260)(143,259)(144,258)
(145,257)(146,266)(147,270)(148,269)(149,268)(150,267)(151,276)(152,280)
(153,279)(154,278)(155,277)(156,271)(157,275)(158,274)(159,273)(160,272)
(161,281)(162,285)(163,284)(164,283)(165,282)(166,291)(167,295)(168,294)
(169,293)(170,292)(171,286)(172,290)(173,289)(174,288)(175,287)(176,296)
(177,300)(178,299)(179,298)(180,297)(181,306)(182,310)(183,309)(184,308)
(185,307)(186,301)(187,305)(188,304)(189,303)(190,302)(191,311)(192,315)
(193,314)(194,313)(195,312)(196,321)(197,325)(198,324)(199,323)(200,322)
(201,316)(202,320)(203,319)(204,318)(205,317)(206,326)(207,330)(208,329)
(209,328)(210,327)(211,336)(212,340)(213,339)(214,338)(215,337)(216,331)
(217,335)(218,334)(219,333)(220,332)(221,341)(222,345)(223,344)(224,343)
(225,342)(226,351)(227,355)(228,354)(229,353)(230,352)(231,346)(232,350)
(233,349)(234,348)(235,347)(236,356)(237,360)(238,359)(239,358)(240,357)
(481,846)(482,850)(483,849)(484,848)(485,847)(486,841)(487,845)(488,844)
(489,843)(490,842)(491,851)(492,855)(493,854)(494,853)(495,852)(496,861)
(497,865)(498,864)(499,863)(500,862)(501,856)(502,860)(503,859)(504,858)
(505,857)(506,866)(507,870)(508,869)(509,868)(510,867)(511,876)(512,880)
(513,879)(514,878)(515,877)(516,871)(517,875)(518,874)(519,873)(520,872)
(521,881)(522,885)(523,884)(524,883)(525,882)(526,891)(527,895)(528,894)
(529,893)(530,892)(531,886)(532,890)(533,889)(534,888)(535,887)(536,896)
(537,900)(538,899)(539,898)(540,897)(541,906)(542,910)(543,909)(544,908)
(545,907)(546,901)(547,905)(548,904)(549,903)(550,902)(551,911)(552,915)
(553,914)(554,913)(555,912)(556,921)(557,925)(558,924)(559,923)(560,922)
(561,916)(562,920)(563,919)(564,918)(565,917)(566,926)(567,930)(568,929)
(569,928)(570,927)(571,936)(572,940)(573,939)(574,938)(575,937)(576,931)
(577,935)(578,934)(579,933)(580,932)(581,941)(582,945)(583,944)(584,943)
(585,942)(586,951)(587,955)(588,954)(589,953)(590,952)(591,946)(592,950)
(593,949)(594,948)(595,947)(596,956)(597,960)(598,959)(599,958)(600,957)
(601,726)(602,730)(603,729)(604,728)(605,727)(606,721)(607,725)(608,724)
(609,723)(610,722)(611,731)(612,735)(613,734)(614,733)(615,732)(616,741)
(617,745)(618,744)(619,743)(620,742)(621,736)(622,740)(623,739)(624,738)
(625,737)(626,746)(627,750)(628,749)(629,748)(630,747)(631,756)(632,760)
(633,759)(634,758)(635,757)(636,751)(637,755)(638,754)(639,753)(640,752)
(641,761)(642,765)(643,764)(644,763)(645,762)(646,771)(647,775)(648,774)
(649,773)(650,772)(651,766)(652,770)(653,769)(654,768)(655,767)(656,776)
(657,780)(658,779)(659,778)(660,777)(661,786)(662,790)(663,789)(664,788)
(665,787)(666,781)(667,785)(668,784)(669,783)(670,782)(671,791)(672,795)
(673,794)(674,793)(675,792)(676,801)(677,805)(678,804)(679,803)(680,802)
(681,796)(682,800)(683,799)(684,798)(685,797)(686,806)(687,810)(688,809)
(689,808)(690,807)(691,816)(692,820)(693,819)(694,818)(695,817)(696,811)
(697,815)(698,814)(699,813)(700,812)(701,821)(702,825)(703,824)(704,823)
(705,822)(706,831)(707,835)(708,834)(709,833)(710,832)(711,826)(712,830)
(713,829)(714,828)(715,827)(716,836)(717,840)(718,839)(719,838)(720,837);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,481)(  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)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(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)(151,631)
(152,632)(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)
(160,640)(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)
(168,648)(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)
(176,656)(177,657)(178,658)(179,659)(180,660)(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)(211,706)(212,707)(213,708)(214,709)(215,710)
(216,711)(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)
(224,719)(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)
(232,697)(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)
(240,705)(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)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(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)(391,871)
(392,872)(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)
(400,880)(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)
(408,888)(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)
(416,896)(417,897)(418,898)(419,899)(420,900)(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)(451,946)(452,947)(453,948)(454,949)(455,950)
(456,951)(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)
(464,959)(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)
(472,937)(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)
(480,945);
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)(721,811)(722,812)(723,813)
(724,814)(725,815)(726,821)(727,822)(728,823)(729,824)(730,825)(731,816)
(732,817)(733,818)(734,819)(735,820)(736,826)(737,827)(738,828)(739,829)
(740,830)(741,836)(742,837)(743,838)(744,839)(745,840)(746,831)(747,832)
(748,833)(749,834)(750,835)(751,781)(752,782)(753,783)(754,784)(755,785)
(756,791)(757,792)(758,793)(759,794)(760,795)(761,786)(762,787)(763,788)
(764,789)(765,790)(766,796)(767,797)(768,798)(769,799)(770,800)(771,806)
(772,807)(773,808)(774,809)(775,810)(776,801)(777,802)(778,803)(779,804)
(780,805)(841,931)(842,932)(843,933)(844,934)(845,935)(846,941)(847,942)
(848,943)(849,944)(850,945)(851,936)(852,937)(853,938)(854,939)(855,940)
(856,946)(857,947)(858,948)(859,949)(860,950)(861,956)(862,957)(863,958)
(864,959)(865,960)(866,951)(867,952)(868,953)(869,954)(870,955)(871,901)
(872,902)(873,903)(874,904)(875,905)(876,911)(877,912)(878,913)(879,914)
(880,915)(881,906)(882,907)(883,908)(884,909)(885,910)(886,916)(887,917)
(888,918)(889,919)(890,920)(891,926)(892,927)(893,928)(894,929)(895,930)
(896,921)(897,922)(898,923)(899,924)(900,925);
s2 := Sym(960)!(  1,366)(  2,370)(  3,369)(  4,368)(  5,367)(  6,361)(  7,365)
(  8,364)(  9,363)( 10,362)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)
( 16,381)( 17,385)( 18,384)( 19,383)( 20,382)( 21,376)( 22,380)( 23,379)
( 24,378)( 25,377)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,396)
( 32,400)( 33,399)( 34,398)( 35,397)( 36,391)( 37,395)( 38,394)( 39,393)
( 40,392)( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,411)( 47,415)
( 48,414)( 49,413)( 50,412)( 51,406)( 52,410)( 53,409)( 54,408)( 55,407)
( 56,416)( 57,420)( 58,419)( 59,418)( 60,417)( 61,426)( 62,430)( 63,429)
( 64,428)( 65,427)( 66,421)( 67,425)( 68,424)( 69,423)( 70,422)( 71,431)
( 72,435)( 73,434)( 74,433)( 75,432)( 76,441)( 77,445)( 78,444)( 79,443)
( 80,442)( 81,436)( 82,440)( 83,439)( 84,438)( 85,437)( 86,446)( 87,450)
( 88,449)( 89,448)( 90,447)( 91,456)( 92,460)( 93,459)( 94,458)( 95,457)
( 96,451)( 97,455)( 98,454)( 99,453)(100,452)(101,461)(102,465)(103,464)
(104,463)(105,462)(106,471)(107,475)(108,474)(109,473)(110,472)(111,466)
(112,470)(113,469)(114,468)(115,467)(116,476)(117,480)(118,479)(119,478)
(120,477)(121,246)(122,250)(123,249)(124,248)(125,247)(126,241)(127,245)
(128,244)(129,243)(130,242)(131,251)(132,255)(133,254)(134,253)(135,252)
(136,261)(137,265)(138,264)(139,263)(140,262)(141,256)(142,260)(143,259)
(144,258)(145,257)(146,266)(147,270)(148,269)(149,268)(150,267)(151,276)
(152,280)(153,279)(154,278)(155,277)(156,271)(157,275)(158,274)(159,273)
(160,272)(161,281)(162,285)(163,284)(164,283)(165,282)(166,291)(167,295)
(168,294)(169,293)(170,292)(171,286)(172,290)(173,289)(174,288)(175,287)
(176,296)(177,300)(178,299)(179,298)(180,297)(181,306)(182,310)(183,309)
(184,308)(185,307)(186,301)(187,305)(188,304)(189,303)(190,302)(191,311)
(192,315)(193,314)(194,313)(195,312)(196,321)(197,325)(198,324)(199,323)
(200,322)(201,316)(202,320)(203,319)(204,318)(205,317)(206,326)(207,330)
(208,329)(209,328)(210,327)(211,336)(212,340)(213,339)(214,338)(215,337)
(216,331)(217,335)(218,334)(219,333)(220,332)(221,341)(222,345)(223,344)
(224,343)(225,342)(226,351)(227,355)(228,354)(229,353)(230,352)(231,346)
(232,350)(233,349)(234,348)(235,347)(236,356)(237,360)(238,359)(239,358)
(240,357)(481,846)(482,850)(483,849)(484,848)(485,847)(486,841)(487,845)
(488,844)(489,843)(490,842)(491,851)(492,855)(493,854)(494,853)(495,852)
(496,861)(497,865)(498,864)(499,863)(500,862)(501,856)(502,860)(503,859)
(504,858)(505,857)(506,866)(507,870)(508,869)(509,868)(510,867)(511,876)
(512,880)(513,879)(514,878)(515,877)(516,871)(517,875)(518,874)(519,873)
(520,872)(521,881)(522,885)(523,884)(524,883)(525,882)(526,891)(527,895)
(528,894)(529,893)(530,892)(531,886)(532,890)(533,889)(534,888)(535,887)
(536,896)(537,900)(538,899)(539,898)(540,897)(541,906)(542,910)(543,909)
(544,908)(545,907)(546,901)(547,905)(548,904)(549,903)(550,902)(551,911)
(552,915)(553,914)(554,913)(555,912)(556,921)(557,925)(558,924)(559,923)
(560,922)(561,916)(562,920)(563,919)(564,918)(565,917)(566,926)(567,930)
(568,929)(569,928)(570,927)(571,936)(572,940)(573,939)(574,938)(575,937)
(576,931)(577,935)(578,934)(579,933)(580,932)(581,941)(582,945)(583,944)
(584,943)(585,942)(586,951)(587,955)(588,954)(589,953)(590,952)(591,946)
(592,950)(593,949)(594,948)(595,947)(596,956)(597,960)(598,959)(599,958)
(600,957)(601,726)(602,730)(603,729)(604,728)(605,727)(606,721)(607,725)
(608,724)(609,723)(610,722)(611,731)(612,735)(613,734)(614,733)(615,732)
(616,741)(617,745)(618,744)(619,743)(620,742)(621,736)(622,740)(623,739)
(624,738)(625,737)(626,746)(627,750)(628,749)(629,748)(630,747)(631,756)
(632,760)(633,759)(634,758)(635,757)(636,751)(637,755)(638,754)(639,753)
(640,752)(641,761)(642,765)(643,764)(644,763)(645,762)(646,771)(647,775)
(648,774)(649,773)(650,772)(651,766)(652,770)(653,769)(654,768)(655,767)
(656,776)(657,780)(658,779)(659,778)(660,777)(661,786)(662,790)(663,789)
(664,788)(665,787)(666,781)(667,785)(668,784)(669,783)(670,782)(671,791)
(672,795)(673,794)(674,793)(675,792)(676,801)(677,805)(678,804)(679,803)
(680,802)(681,796)(682,800)(683,799)(684,798)(685,797)(686,806)(687,810)
(688,809)(689,808)(690,807)(691,816)(692,820)(693,819)(694,818)(695,817)
(696,811)(697,815)(698,814)(699,813)(700,812)(701,821)(702,825)(703,824)
(704,823)(705,822)(706,831)(707,835)(708,834)(709,833)(710,832)(711,826)
(712,830)(713,829)(714,828)(715,827)(716,836)(717,840)(718,839)(719,838)
(720,837);
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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope