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