Polytope of Type {8,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20,6}*1920a
Also Known As : {{8,20|2},{20,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,148893)
Rank : 4
Schlafli Type : {8,20,6}
Number of vertices, edges, etc : 8, 80, 60, 6
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 : {4,20,6}*960, {8,10,6}*960
   3-fold quotients : {8,20,2}*640a
   4-fold quotients : {2,20,6}*480a, {4,10,6}*480
   5-fold quotients : {8,4,6}*384a
   6-fold quotients : {4,20,2}*320, {8,10,2}*320
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {4,4,6}*192, {8,2,6}*192
   12-fold quotients : {2,20,2}*160, {4,10,2}*160
   15-fold quotients : {8,4,2}*128a
   20-fold quotients : {8,2,3}*96, {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,4,2}*64, {8,2,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,5,2}*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)( 31,511)( 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 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)
( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 91,106)
( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)(123,124)
(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)
(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)
(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)(190,202)
(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)(213,229)
(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)(221,236)
(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)(244,273)
(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)(252,285)
(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)(268,299)
(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)(306,351)
(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)(314,358)
(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)(322,340)
(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)(330,342)
(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)(368,399)
(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)(376,406)
(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)(384,413)
(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)(422,470)
(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)(430,472)
(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)(438,454)
(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)(446,461)
(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)(484,543)
(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)(492,555)
(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)(500,557)
(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)(508,569)
(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)(516,576)
(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)(524,583)
(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)
(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)
(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)(608,669)
(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)(616,676)
(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)(624,683)
(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)(632,695)
(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)(640,697)
(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)(648,709)
(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)(656,716)
(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)(724,813)
(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)(732,825)
(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)(740,827)
(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)(748,839)
(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)(756,786)
(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)(764,793)
(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)(772,805)
(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)(780,807)
(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)(848,939)
(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)(856,946)
(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)(864,953)
(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)(872,905)
(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)(880,907)
(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)(888,919)
(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)(896,926)
(897,930)(898,929)(899,928)(900,927);;
s2 := (  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,372)(  7,371)(  8,375)
(  9,374)( 10,373)( 11,367)( 12,366)( 13,370)( 14,369)( 15,368)( 16,377)
( 17,376)( 18,380)( 19,379)( 20,378)( 21,387)( 22,386)( 23,390)( 24,389)
( 25,388)( 26,382)( 27,381)( 28,385)( 29,384)( 30,383)( 31,392)( 32,391)
( 33,395)( 34,394)( 35,393)( 36,402)( 37,401)( 38,405)( 39,404)( 40,403)
( 41,397)( 42,396)( 43,400)( 44,399)( 45,398)( 46,407)( 47,406)( 48,410)
( 49,409)( 50,408)( 51,417)( 52,416)( 53,420)( 54,419)( 55,418)( 56,412)
( 57,411)( 58,415)( 59,414)( 60,413)( 61,422)( 62,421)( 63,425)( 64,424)
( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)( 72,426)
( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)( 80,438)
( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)( 88,445)
( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)( 96,462)
( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)(104,459)
(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)(112,476)
(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)(120,473)
(121,242)(122,241)(123,245)(124,244)(125,243)(126,252)(127,251)(128,255)
(129,254)(130,253)(131,247)(132,246)(133,250)(134,249)(135,248)(136,257)
(137,256)(138,260)(139,259)(140,258)(141,267)(142,266)(143,270)(144,269)
(145,268)(146,262)(147,261)(148,265)(149,264)(150,263)(151,272)(152,271)
(153,275)(154,274)(155,273)(156,282)(157,281)(158,285)(159,284)(160,283)
(161,277)(162,276)(163,280)(164,279)(165,278)(166,287)(167,286)(168,290)
(169,289)(170,288)(171,297)(172,296)(173,300)(174,299)(175,298)(176,292)
(177,291)(178,295)(179,294)(180,293)(181,302)(182,301)(183,305)(184,304)
(185,303)(186,312)(187,311)(188,315)(189,314)(190,313)(191,307)(192,306)
(193,310)(194,309)(195,308)(196,317)(197,316)(198,320)(199,319)(200,318)
(201,327)(202,326)(203,330)(204,329)(205,328)(206,322)(207,321)(208,325)
(209,324)(210,323)(211,332)(212,331)(213,335)(214,334)(215,333)(216,342)
(217,341)(218,345)(219,344)(220,343)(221,337)(222,336)(223,340)(224,339)
(225,338)(226,347)(227,346)(228,350)(229,349)(230,348)(231,357)(232,356)
(233,360)(234,359)(235,358)(236,352)(237,351)(238,355)(239,354)(240,353)
(481,842)(482,841)(483,845)(484,844)(485,843)(486,852)(487,851)(488,855)
(489,854)(490,853)(491,847)(492,846)(493,850)(494,849)(495,848)(496,857)
(497,856)(498,860)(499,859)(500,858)(501,867)(502,866)(503,870)(504,869)
(505,868)(506,862)(507,861)(508,865)(509,864)(510,863)(511,872)(512,871)
(513,875)(514,874)(515,873)(516,882)(517,881)(518,885)(519,884)(520,883)
(521,877)(522,876)(523,880)(524,879)(525,878)(526,887)(527,886)(528,890)
(529,889)(530,888)(531,897)(532,896)(533,900)(534,899)(535,898)(536,892)
(537,891)(538,895)(539,894)(540,893)(541,902)(542,901)(543,905)(544,904)
(545,903)(546,912)(547,911)(548,915)(549,914)(550,913)(551,907)(552,906)
(553,910)(554,909)(555,908)(556,917)(557,916)(558,920)(559,919)(560,918)
(561,927)(562,926)(563,930)(564,929)(565,928)(566,922)(567,921)(568,925)
(569,924)(570,923)(571,932)(572,931)(573,935)(574,934)(575,933)(576,942)
(577,941)(578,945)(579,944)(580,943)(581,937)(582,936)(583,940)(584,939)
(585,938)(586,947)(587,946)(588,950)(589,949)(590,948)(591,957)(592,956)
(593,960)(594,959)(595,958)(596,952)(597,951)(598,955)(599,954)(600,953)
(601,722)(602,721)(603,725)(604,724)(605,723)(606,732)(607,731)(608,735)
(609,734)(610,733)(611,727)(612,726)(613,730)(614,729)(615,728)(616,737)
(617,736)(618,740)(619,739)(620,738)(621,747)(622,746)(623,750)(624,749)
(625,748)(626,742)(627,741)(628,745)(629,744)(630,743)(631,752)(632,751)
(633,755)(634,754)(635,753)(636,762)(637,761)(638,765)(639,764)(640,763)
(641,757)(642,756)(643,760)(644,759)(645,758)(646,767)(647,766)(648,770)
(649,769)(650,768)(651,777)(652,776)(653,780)(654,779)(655,778)(656,772)
(657,771)(658,775)(659,774)(660,773)(661,782)(662,781)(663,785)(664,784)
(665,783)(666,792)(667,791)(668,795)(669,794)(670,793)(671,787)(672,786)
(673,790)(674,789)(675,788)(676,797)(677,796)(678,800)(679,799)(680,798)
(681,807)(682,806)(683,810)(684,809)(685,808)(686,802)(687,801)(688,805)
(689,804)(690,803)(691,812)(692,811)(693,815)(694,814)(695,813)(696,822)
(697,821)(698,825)(699,824)(700,823)(701,817)(702,816)(703,820)(704,819)
(705,818)(706,827)(707,826)(708,830)(709,829)(710,828)(711,837)(712,836)
(713,840)(714,839)(715,838)(716,832)(717,831)(718,835)(719,834)(720,833);;
s3 := (  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)(  8,123)
(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)
( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)
(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)(248,363)
(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)
(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)
(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)
(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)(280,395)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)(288,413)
(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)(304,429)
(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)(320,445)
(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)(336,451)
(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)
(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480)
(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)
(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)
(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)
(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)
(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)
(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)
(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)
(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)
(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)
(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)
(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)
(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)
(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)
(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)
(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)
(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)(728,843)
(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)(736,861)
(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)(744,859)
(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)(752,877)
(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)(760,875)
(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)(768,893)
(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)(776,896)
(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)(784,909)
(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)(792,912)
(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)(800,925)
(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)(808,928)
(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)(816,931)
(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)(824,944)
(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)(832,947)
(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)(840,960);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)
( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)
( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)
( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)
(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)
(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)
(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)
(190,202)(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)
(213,229)(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)
(221,236)(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)
(244,273)(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)
(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)
(268,299)(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)
(314,358)(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)
(322,340)(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)
(330,342)(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)
(368,399)(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)
(376,406)(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)
(384,413)(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)
(422,470)(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)
(430,472)(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)
(438,454)(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)
(446,461)(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)
(484,543)(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)
(492,555)(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)
(500,557)(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)
(508,569)(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)
(516,576)(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)
(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)
(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)
(540,597)(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)
(608,669)(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)
(616,676)(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)
(624,683)(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)
(632,695)(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)
(640,697)(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)
(648,709)(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)
(656,716)(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)
(724,813)(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)
(732,825)(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)
(740,827)(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)
(748,839)(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)
(756,786)(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)
(764,793)(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)
(772,805)(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)
(780,807)(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)
(848,939)(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)
(856,946)(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)
(864,953)(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)
(872,905)(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)
(880,907)(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)
(888,919)(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)
(896,926)(897,930)(898,929)(899,928)(900,927);
s2 := Sym(960)!(  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,372)(  7,371)
(  8,375)(  9,374)( 10,373)( 11,367)( 12,366)( 13,370)( 14,369)( 15,368)
( 16,377)( 17,376)( 18,380)( 19,379)( 20,378)( 21,387)( 22,386)( 23,390)
( 24,389)( 25,388)( 26,382)( 27,381)( 28,385)( 29,384)( 30,383)( 31,392)
( 32,391)( 33,395)( 34,394)( 35,393)( 36,402)( 37,401)( 38,405)( 39,404)
( 40,403)( 41,397)( 42,396)( 43,400)( 44,399)( 45,398)( 46,407)( 47,406)
( 48,410)( 49,409)( 50,408)( 51,417)( 52,416)( 53,420)( 54,419)( 55,418)
( 56,412)( 57,411)( 58,415)( 59,414)( 60,413)( 61,422)( 62,421)( 63,425)
( 64,424)( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)
( 72,426)( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)
( 80,438)( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)
( 88,445)( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)
( 96,462)( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)
(104,459)(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)
(112,476)(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)
(120,473)(121,242)(122,241)(123,245)(124,244)(125,243)(126,252)(127,251)
(128,255)(129,254)(130,253)(131,247)(132,246)(133,250)(134,249)(135,248)
(136,257)(137,256)(138,260)(139,259)(140,258)(141,267)(142,266)(143,270)
(144,269)(145,268)(146,262)(147,261)(148,265)(149,264)(150,263)(151,272)
(152,271)(153,275)(154,274)(155,273)(156,282)(157,281)(158,285)(159,284)
(160,283)(161,277)(162,276)(163,280)(164,279)(165,278)(166,287)(167,286)
(168,290)(169,289)(170,288)(171,297)(172,296)(173,300)(174,299)(175,298)
(176,292)(177,291)(178,295)(179,294)(180,293)(181,302)(182,301)(183,305)
(184,304)(185,303)(186,312)(187,311)(188,315)(189,314)(190,313)(191,307)
(192,306)(193,310)(194,309)(195,308)(196,317)(197,316)(198,320)(199,319)
(200,318)(201,327)(202,326)(203,330)(204,329)(205,328)(206,322)(207,321)
(208,325)(209,324)(210,323)(211,332)(212,331)(213,335)(214,334)(215,333)
(216,342)(217,341)(218,345)(219,344)(220,343)(221,337)(222,336)(223,340)
(224,339)(225,338)(226,347)(227,346)(228,350)(229,349)(230,348)(231,357)
(232,356)(233,360)(234,359)(235,358)(236,352)(237,351)(238,355)(239,354)
(240,353)(481,842)(482,841)(483,845)(484,844)(485,843)(486,852)(487,851)
(488,855)(489,854)(490,853)(491,847)(492,846)(493,850)(494,849)(495,848)
(496,857)(497,856)(498,860)(499,859)(500,858)(501,867)(502,866)(503,870)
(504,869)(505,868)(506,862)(507,861)(508,865)(509,864)(510,863)(511,872)
(512,871)(513,875)(514,874)(515,873)(516,882)(517,881)(518,885)(519,884)
(520,883)(521,877)(522,876)(523,880)(524,879)(525,878)(526,887)(527,886)
(528,890)(529,889)(530,888)(531,897)(532,896)(533,900)(534,899)(535,898)
(536,892)(537,891)(538,895)(539,894)(540,893)(541,902)(542,901)(543,905)
(544,904)(545,903)(546,912)(547,911)(548,915)(549,914)(550,913)(551,907)
(552,906)(553,910)(554,909)(555,908)(556,917)(557,916)(558,920)(559,919)
(560,918)(561,927)(562,926)(563,930)(564,929)(565,928)(566,922)(567,921)
(568,925)(569,924)(570,923)(571,932)(572,931)(573,935)(574,934)(575,933)
(576,942)(577,941)(578,945)(579,944)(580,943)(581,937)(582,936)(583,940)
(584,939)(585,938)(586,947)(587,946)(588,950)(589,949)(590,948)(591,957)
(592,956)(593,960)(594,959)(595,958)(596,952)(597,951)(598,955)(599,954)
(600,953)(601,722)(602,721)(603,725)(604,724)(605,723)(606,732)(607,731)
(608,735)(609,734)(610,733)(611,727)(612,726)(613,730)(614,729)(615,728)
(616,737)(617,736)(618,740)(619,739)(620,738)(621,747)(622,746)(623,750)
(624,749)(625,748)(626,742)(627,741)(628,745)(629,744)(630,743)(631,752)
(632,751)(633,755)(634,754)(635,753)(636,762)(637,761)(638,765)(639,764)
(640,763)(641,757)(642,756)(643,760)(644,759)(645,758)(646,767)(647,766)
(648,770)(649,769)(650,768)(651,777)(652,776)(653,780)(654,779)(655,778)
(656,772)(657,771)(658,775)(659,774)(660,773)(661,782)(662,781)(663,785)
(664,784)(665,783)(666,792)(667,791)(668,795)(669,794)(670,793)(671,787)
(672,786)(673,790)(674,789)(675,788)(676,797)(677,796)(678,800)(679,799)
(680,798)(681,807)(682,806)(683,810)(684,809)(685,808)(686,802)(687,801)
(688,805)(689,804)(690,803)(691,812)(692,811)(693,815)(694,814)(695,813)
(696,822)(697,821)(698,825)(699,824)(700,823)(701,817)(702,816)(703,820)
(704,819)(705,818)(706,827)(707,826)(708,830)(709,829)(710,828)(711,837)
(712,836)(713,840)(714,839)(715,838)(716,832)(717,831)(718,835)(719,834)
(720,833);
s3 := Sym(960)!(  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)
(  8,123)(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)
( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)
(248,363)(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)
(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)
(272,397)(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)
(280,395)(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)
(288,413)(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)
(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)
(320,445)(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)
(336,451)(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)
(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)
(360,480)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)
(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)
(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)
(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)
(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)
(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)
(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)
(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)
(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)
(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)
(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)
(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)
(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)
(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)
(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)
(600,720)(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)
(728,843)(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)
(736,861)(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)
(744,859)(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)
(752,877)(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)
(760,875)(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)
(768,893)(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)
(776,896)(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)
(784,909)(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)
(792,912)(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)
(800,925)(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)
(808,928)(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)
(816,931)(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)
(824,944)(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)
(832,947)(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)
(840,960);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope