Polytope of Type {6,4,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,40}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150684)
Rank : 4
Schlafli Type : {6,4,40}
Number of vertices, edges, etc : 6, 12, 80, 40
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 : {6,4,20}*960
3-fold quotients : {2,4,40}*640b
4-fold quotients : {6,2,20}*480, {6,4,10}*480
5-fold quotients : {6,4,8}*384b
6-fold quotients : {2,4,20}*320
8-fold quotients : {3,2,20}*240, {6,2,10}*240
10-fold quotients : {6,4,4}*192
12-fold quotients : {2,2,20}*160, {2,4,10}*160
15-fold quotients : {2,4,8}*128b
16-fold quotients : {3,2,10}*120, {6,2,5}*120
20-fold quotients : {6,2,4}*96, {6,4,2}*96a
24-fold quotients : {2,2,10}*80
30-fold quotients : {2,4,4}*64
32-fold quotients : {3,2,5}*60
40-fold quotients : {3,2,4}*48, {6,2,2}*48
48-fold quotients : {2,2,5}*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)( 2,367)( 3,368)( 4,369)( 5,370)( 6,361)( 7,362)( 8,363)
( 9,364)( 10,365)( 11,371)( 12,372)( 13,373)( 14,374)( 15,375)( 16,381)
( 17,382)( 18,383)( 19,384)( 20,385)( 21,376)( 22,377)( 23,378)( 24,379)
( 25,380)( 26,386)( 27,387)( 28,388)( 29,389)( 30,390)( 31,396)( 32,397)
( 33,398)( 34,399)( 35,400)( 36,391)( 37,392)( 38,393)( 39,394)( 40,395)
( 41,401)( 42,402)( 43,403)( 44,404)( 45,405)( 46,411)( 47,412)( 48,413)
( 49,414)( 50,415)( 51,406)( 52,407)( 53,408)( 54,409)( 55,410)( 56,416)
( 57,417)( 58,418)( 59,419)( 60,420)( 61,441)( 62,442)( 63,443)( 64,444)
( 65,445)( 66,436)( 67,437)( 68,438)( 69,439)( 70,440)( 71,446)( 72,447)
( 73,448)( 74,449)( 75,450)( 76,426)( 77,427)( 78,428)( 79,429)( 80,430)
( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,431)( 87,432)( 88,433)
( 89,434)( 90,435)( 91,471)( 92,472)( 93,473)( 94,474)( 95,475)( 96,466)
( 97,467)( 98,468)( 99,469)(100,470)(101,476)(102,477)(103,478)(104,479)
(105,480)(106,456)(107,457)(108,458)(109,459)(110,460)(111,451)(112,452)
(113,453)(114,454)(115,455)(116,461)(117,462)(118,463)(119,464)(120,465)
(121,246)(122,247)(123,248)(124,249)(125,250)(126,241)(127,242)(128,243)
(129,244)(130,245)(131,251)(132,252)(133,253)(134,254)(135,255)(136,261)
(137,262)(138,263)(139,264)(140,265)(141,256)(142,257)(143,258)(144,259)
(145,260)(146,266)(147,267)(148,268)(149,269)(150,270)(151,276)(152,277)
(153,278)(154,279)(155,280)(156,271)(157,272)(158,273)(159,274)(160,275)
(161,281)(162,282)(163,283)(164,284)(165,285)(166,291)(167,292)(168,293)
(169,294)(170,295)(171,286)(172,287)(173,288)(174,289)(175,290)(176,296)
(177,297)(178,298)(179,299)(180,300)(181,321)(182,322)(183,323)(184,324)
(185,325)(186,316)(187,317)(188,318)(189,319)(190,320)(191,326)(192,327)
(193,328)(194,329)(195,330)(196,306)(197,307)(198,308)(199,309)(200,310)
(201,301)(202,302)(203,303)(204,304)(205,305)(206,311)(207,312)(208,313)
(209,314)(210,315)(211,351)(212,352)(213,353)(214,354)(215,355)(216,346)
(217,347)(218,348)(219,349)(220,350)(221,356)(222,357)(223,358)(224,359)
(225,360)(226,336)(227,337)(228,338)(229,339)(230,340)(231,331)(232,332)
(233,333)(234,334)(235,335)(236,341)(237,342)(238,343)(239,344)(240,345)
(481,846)(482,847)(483,848)(484,849)(485,850)(486,841)(487,842)(488,843)
(489,844)(490,845)(491,851)(492,852)(493,853)(494,854)(495,855)(496,861)
(497,862)(498,863)(499,864)(500,865)(501,856)(502,857)(503,858)(504,859)
(505,860)(506,866)(507,867)(508,868)(509,869)(510,870)(511,876)(512,877)
(513,878)(514,879)(515,880)(516,871)(517,872)(518,873)(519,874)(520,875)
(521,881)(522,882)(523,883)(524,884)(525,885)(526,891)(527,892)(528,893)
(529,894)(530,895)(531,886)(532,887)(533,888)(534,889)(535,890)(536,896)
(537,897)(538,898)(539,899)(540,900)(541,921)(542,922)(543,923)(544,924)
(545,925)(546,916)(547,917)(548,918)(549,919)(550,920)(551,926)(552,927)
(553,928)(554,929)(555,930)(556,906)(557,907)(558,908)(559,909)(560,910)
(561,901)(562,902)(563,903)(564,904)(565,905)(566,911)(567,912)(568,913)
(569,914)(570,915)(571,951)(572,952)(573,953)(574,954)(575,955)(576,946)
(577,947)(578,948)(579,949)(580,950)(581,956)(582,957)(583,958)(584,959)
(585,960)(586,936)(587,937)(588,938)(589,939)(590,940)(591,931)(592,932)
(593,933)(594,934)(595,935)(596,941)(597,942)(598,943)(599,944)(600,945)
(601,726)(602,727)(603,728)(604,729)(605,730)(606,721)(607,722)(608,723)
(609,724)(610,725)(611,731)(612,732)(613,733)(614,734)(615,735)(616,741)
(617,742)(618,743)(619,744)(620,745)(621,736)(622,737)(623,738)(624,739)
(625,740)(626,746)(627,747)(628,748)(629,749)(630,750)(631,756)(632,757)
(633,758)(634,759)(635,760)(636,751)(637,752)(638,753)(639,754)(640,755)
(641,761)(642,762)(643,763)(644,764)(645,765)(646,771)(647,772)(648,773)
(649,774)(650,775)(651,766)(652,767)(653,768)(654,769)(655,770)(656,776)
(657,777)(658,778)(659,779)(660,780)(661,801)(662,802)(663,803)(664,804)
(665,805)(666,796)(667,797)(668,798)(669,799)(670,800)(671,806)(672,807)
(673,808)(674,809)(675,810)(676,786)(677,787)(678,788)(679,789)(680,790)
(681,781)(682,782)(683,783)(684,784)(685,785)(686,791)(687,792)(688,793)
(689,794)(690,795)(691,831)(692,832)(693,833)(694,834)(695,835)(696,826)
(697,827)(698,828)(699,829)(700,830)(701,836)(702,837)(703,838)(704,839)
(705,840)(706,816)(707,817)(708,818)(709,819)(710,820)(711,811)(712,812)
(713,813)(714,814)(715,815)(716,821)(717,822)(718,823)(719,824)(720,825);;
s2 := ( 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)(721,826)(722,830)(723,829)(724,828)
(725,827)(726,831)(727,835)(728,834)(729,833)(730,832)(731,836)(732,840)
(733,839)(734,838)(735,837)(736,811)(737,815)(738,814)(739,813)(740,812)
(741,816)(742,820)(743,819)(744,818)(745,817)(746,821)(747,825)(748,824)
(749,823)(750,822)(751,796)(752,800)(753,799)(754,798)(755,797)(756,801)
(757,805)(758,804)(759,803)(760,802)(761,806)(762,810)(763,809)(764,808)
(765,807)(766,781)(767,785)(768,784)(769,783)(770,782)(771,786)(772,790)
(773,789)(774,788)(775,787)(776,791)(777,795)(778,794)(779,793)(780,792)
(841,946)(842,950)(843,949)(844,948)(845,947)(846,951)(847,955)(848,954)
(849,953)(850,952)(851,956)(852,960)(853,959)(854,958)(855,957)(856,931)
(857,935)(858,934)(859,933)(860,932)(861,936)(862,940)(863,939)(864,938)
(865,937)(866,941)(867,945)(868,944)(869,943)(870,942)(871,916)(872,920)
(873,919)(874,918)(875,917)(876,921)(877,925)(878,924)(879,923)(880,922)
(881,926)(882,930)(883,929)(884,928)(885,927)(886,901)(887,905)(888,904)
(889,903)(890,902)(891,906)(892,910)(893,909)(894,908)(895,907)(896,911)
(897,915)(898,914)(899,913)(900,912);;
s3 := ( 1,482)( 2,481)( 3,485)( 4,484)( 5,483)( 6,487)( 7,486)( 8,490)
( 9,489)( 10,488)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)( 16,497)
( 17,496)( 18,500)( 19,499)( 20,498)( 21,502)( 22,501)( 23,505)( 24,504)
( 25,503)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,527)( 32,526)
( 33,530)( 34,529)( 35,528)( 36,532)( 37,531)( 38,535)( 39,534)( 40,533)
( 41,537)( 42,536)( 43,540)( 44,539)( 45,538)( 46,512)( 47,511)( 48,515)
( 49,514)( 50,513)( 51,517)( 52,516)( 53,520)( 54,519)( 55,518)( 56,522)
( 57,521)( 58,525)( 59,524)( 60,523)( 61,557)( 62,556)( 63,560)( 64,559)
( 65,558)( 66,562)( 67,561)( 68,565)( 69,564)( 70,563)( 71,567)( 72,566)
( 73,570)( 74,569)( 75,568)( 76,542)( 77,541)( 78,545)( 79,544)( 80,543)
( 81,547)( 82,546)( 83,550)( 84,549)( 85,548)( 86,552)( 87,551)( 88,555)
( 89,554)( 90,553)( 91,572)( 92,571)( 93,575)( 94,574)( 95,573)( 96,577)
( 97,576)( 98,580)( 99,579)(100,578)(101,582)(102,581)(103,585)(104,584)
(105,583)(106,587)(107,586)(108,590)(109,589)(110,588)(111,592)(112,591)
(113,595)(114,594)(115,593)(116,597)(117,596)(118,600)(119,599)(120,598)
(121,602)(122,601)(123,605)(124,604)(125,603)(126,607)(127,606)(128,610)
(129,609)(130,608)(131,612)(132,611)(133,615)(134,614)(135,613)(136,617)
(137,616)(138,620)(139,619)(140,618)(141,622)(142,621)(143,625)(144,624)
(145,623)(146,627)(147,626)(148,630)(149,629)(150,628)(151,647)(152,646)
(153,650)(154,649)(155,648)(156,652)(157,651)(158,655)(159,654)(160,653)
(161,657)(162,656)(163,660)(164,659)(165,658)(166,632)(167,631)(168,635)
(169,634)(170,633)(171,637)(172,636)(173,640)(174,639)(175,638)(176,642)
(177,641)(178,645)(179,644)(180,643)(181,677)(182,676)(183,680)(184,679)
(185,678)(186,682)(187,681)(188,685)(189,684)(190,683)(191,687)(192,686)
(193,690)(194,689)(195,688)(196,662)(197,661)(198,665)(199,664)(200,663)
(201,667)(202,666)(203,670)(204,669)(205,668)(206,672)(207,671)(208,675)
(209,674)(210,673)(211,692)(212,691)(213,695)(214,694)(215,693)(216,697)
(217,696)(218,700)(219,699)(220,698)(221,702)(222,701)(223,705)(224,704)
(225,703)(226,707)(227,706)(228,710)(229,709)(230,708)(231,712)(232,711)
(233,715)(234,714)(235,713)(236,717)(237,716)(238,720)(239,719)(240,718)
(241,722)(242,721)(243,725)(244,724)(245,723)(246,727)(247,726)(248,730)
(249,729)(250,728)(251,732)(252,731)(253,735)(254,734)(255,733)(256,737)
(257,736)(258,740)(259,739)(260,738)(261,742)(262,741)(263,745)(264,744)
(265,743)(266,747)(267,746)(268,750)(269,749)(270,748)(271,767)(272,766)
(273,770)(274,769)(275,768)(276,772)(277,771)(278,775)(279,774)(280,773)
(281,777)(282,776)(283,780)(284,779)(285,778)(286,752)(287,751)(288,755)
(289,754)(290,753)(291,757)(292,756)(293,760)(294,759)(295,758)(296,762)
(297,761)(298,765)(299,764)(300,763)(301,797)(302,796)(303,800)(304,799)
(305,798)(306,802)(307,801)(308,805)(309,804)(310,803)(311,807)(312,806)
(313,810)(314,809)(315,808)(316,782)(317,781)(318,785)(319,784)(320,783)
(321,787)(322,786)(323,790)(324,789)(325,788)(326,792)(327,791)(328,795)
(329,794)(330,793)(331,812)(332,811)(333,815)(334,814)(335,813)(336,817)
(337,816)(338,820)(339,819)(340,818)(341,822)(342,821)(343,825)(344,824)
(345,823)(346,827)(347,826)(348,830)(349,829)(350,828)(351,832)(352,831)
(353,835)(354,834)(355,833)(356,837)(357,836)(358,840)(359,839)(360,838)
(361,842)(362,841)(363,845)(364,844)(365,843)(366,847)(367,846)(368,850)
(369,849)(370,848)(371,852)(372,851)(373,855)(374,854)(375,853)(376,857)
(377,856)(378,860)(379,859)(380,858)(381,862)(382,861)(383,865)(384,864)
(385,863)(386,867)(387,866)(388,870)(389,869)(390,868)(391,887)(392,886)
(393,890)(394,889)(395,888)(396,892)(397,891)(398,895)(399,894)(400,893)
(401,897)(402,896)(403,900)(404,899)(405,898)(406,872)(407,871)(408,875)
(409,874)(410,873)(411,877)(412,876)(413,880)(414,879)(415,878)(416,882)
(417,881)(418,885)(419,884)(420,883)(421,917)(422,916)(423,920)(424,919)
(425,918)(426,922)(427,921)(428,925)(429,924)(430,923)(431,927)(432,926)
(433,930)(434,929)(435,928)(436,902)(437,901)(438,905)(439,904)(440,903)
(441,907)(442,906)(443,910)(444,909)(445,908)(446,912)(447,911)(448,915)
(449,914)(450,913)(451,932)(452,931)(453,935)(454,934)(455,933)(456,937)
(457,936)(458,940)(459,939)(460,938)(461,942)(462,941)(463,945)(464,944)
(465,943)(466,947)(467,946)(468,950)(469,949)(470,948)(471,952)(472,951)
(473,955)(474,954)(475,953)(476,957)(477,956)(478,960)(479,959)(480,958);;
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*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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)( 2,367)( 3,368)( 4,369)( 5,370)( 6,361)( 7,362)
( 8,363)( 9,364)( 10,365)( 11,371)( 12,372)( 13,373)( 14,374)( 15,375)
( 16,381)( 17,382)( 18,383)( 19,384)( 20,385)( 21,376)( 22,377)( 23,378)
( 24,379)( 25,380)( 26,386)( 27,387)( 28,388)( 29,389)( 30,390)( 31,396)
( 32,397)( 33,398)( 34,399)( 35,400)( 36,391)( 37,392)( 38,393)( 39,394)
( 40,395)( 41,401)( 42,402)( 43,403)( 44,404)( 45,405)( 46,411)( 47,412)
( 48,413)( 49,414)( 50,415)( 51,406)( 52,407)( 53,408)( 54,409)( 55,410)
( 56,416)( 57,417)( 58,418)( 59,419)( 60,420)( 61,441)( 62,442)( 63,443)
( 64,444)( 65,445)( 66,436)( 67,437)( 68,438)( 69,439)( 70,440)( 71,446)
( 72,447)( 73,448)( 74,449)( 75,450)( 76,426)( 77,427)( 78,428)( 79,429)
( 80,430)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,431)( 87,432)
( 88,433)( 89,434)( 90,435)( 91,471)( 92,472)( 93,473)( 94,474)( 95,475)
( 96,466)( 97,467)( 98,468)( 99,469)(100,470)(101,476)(102,477)(103,478)
(104,479)(105,480)(106,456)(107,457)(108,458)(109,459)(110,460)(111,451)
(112,452)(113,453)(114,454)(115,455)(116,461)(117,462)(118,463)(119,464)
(120,465)(121,246)(122,247)(123,248)(124,249)(125,250)(126,241)(127,242)
(128,243)(129,244)(130,245)(131,251)(132,252)(133,253)(134,254)(135,255)
(136,261)(137,262)(138,263)(139,264)(140,265)(141,256)(142,257)(143,258)
(144,259)(145,260)(146,266)(147,267)(148,268)(149,269)(150,270)(151,276)
(152,277)(153,278)(154,279)(155,280)(156,271)(157,272)(158,273)(159,274)
(160,275)(161,281)(162,282)(163,283)(164,284)(165,285)(166,291)(167,292)
(168,293)(169,294)(170,295)(171,286)(172,287)(173,288)(174,289)(175,290)
(176,296)(177,297)(178,298)(179,299)(180,300)(181,321)(182,322)(183,323)
(184,324)(185,325)(186,316)(187,317)(188,318)(189,319)(190,320)(191,326)
(192,327)(193,328)(194,329)(195,330)(196,306)(197,307)(198,308)(199,309)
(200,310)(201,301)(202,302)(203,303)(204,304)(205,305)(206,311)(207,312)
(208,313)(209,314)(210,315)(211,351)(212,352)(213,353)(214,354)(215,355)
(216,346)(217,347)(218,348)(219,349)(220,350)(221,356)(222,357)(223,358)
(224,359)(225,360)(226,336)(227,337)(228,338)(229,339)(230,340)(231,331)
(232,332)(233,333)(234,334)(235,335)(236,341)(237,342)(238,343)(239,344)
(240,345)(481,846)(482,847)(483,848)(484,849)(485,850)(486,841)(487,842)
(488,843)(489,844)(490,845)(491,851)(492,852)(493,853)(494,854)(495,855)
(496,861)(497,862)(498,863)(499,864)(500,865)(501,856)(502,857)(503,858)
(504,859)(505,860)(506,866)(507,867)(508,868)(509,869)(510,870)(511,876)
(512,877)(513,878)(514,879)(515,880)(516,871)(517,872)(518,873)(519,874)
(520,875)(521,881)(522,882)(523,883)(524,884)(525,885)(526,891)(527,892)
(528,893)(529,894)(530,895)(531,886)(532,887)(533,888)(534,889)(535,890)
(536,896)(537,897)(538,898)(539,899)(540,900)(541,921)(542,922)(543,923)
(544,924)(545,925)(546,916)(547,917)(548,918)(549,919)(550,920)(551,926)
(552,927)(553,928)(554,929)(555,930)(556,906)(557,907)(558,908)(559,909)
(560,910)(561,901)(562,902)(563,903)(564,904)(565,905)(566,911)(567,912)
(568,913)(569,914)(570,915)(571,951)(572,952)(573,953)(574,954)(575,955)
(576,946)(577,947)(578,948)(579,949)(580,950)(581,956)(582,957)(583,958)
(584,959)(585,960)(586,936)(587,937)(588,938)(589,939)(590,940)(591,931)
(592,932)(593,933)(594,934)(595,935)(596,941)(597,942)(598,943)(599,944)
(600,945)(601,726)(602,727)(603,728)(604,729)(605,730)(606,721)(607,722)
(608,723)(609,724)(610,725)(611,731)(612,732)(613,733)(614,734)(615,735)
(616,741)(617,742)(618,743)(619,744)(620,745)(621,736)(622,737)(623,738)
(624,739)(625,740)(626,746)(627,747)(628,748)(629,749)(630,750)(631,756)
(632,757)(633,758)(634,759)(635,760)(636,751)(637,752)(638,753)(639,754)
(640,755)(641,761)(642,762)(643,763)(644,764)(645,765)(646,771)(647,772)
(648,773)(649,774)(650,775)(651,766)(652,767)(653,768)(654,769)(655,770)
(656,776)(657,777)(658,778)(659,779)(660,780)(661,801)(662,802)(663,803)
(664,804)(665,805)(666,796)(667,797)(668,798)(669,799)(670,800)(671,806)
(672,807)(673,808)(674,809)(675,810)(676,786)(677,787)(678,788)(679,789)
(680,790)(681,781)(682,782)(683,783)(684,784)(685,785)(686,791)(687,792)
(688,793)(689,794)(690,795)(691,831)(692,832)(693,833)(694,834)(695,835)
(696,826)(697,827)(698,828)(699,829)(700,830)(701,836)(702,837)(703,838)
(704,839)(705,840)(706,816)(707,817)(708,818)(709,819)(710,820)(711,811)
(712,812)(713,813)(714,814)(715,815)(716,821)(717,822)(718,823)(719,824)
(720,825);
s2 := 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)(721,826)(722,830)(723,829)
(724,828)(725,827)(726,831)(727,835)(728,834)(729,833)(730,832)(731,836)
(732,840)(733,839)(734,838)(735,837)(736,811)(737,815)(738,814)(739,813)
(740,812)(741,816)(742,820)(743,819)(744,818)(745,817)(746,821)(747,825)
(748,824)(749,823)(750,822)(751,796)(752,800)(753,799)(754,798)(755,797)
(756,801)(757,805)(758,804)(759,803)(760,802)(761,806)(762,810)(763,809)
(764,808)(765,807)(766,781)(767,785)(768,784)(769,783)(770,782)(771,786)
(772,790)(773,789)(774,788)(775,787)(776,791)(777,795)(778,794)(779,793)
(780,792)(841,946)(842,950)(843,949)(844,948)(845,947)(846,951)(847,955)
(848,954)(849,953)(850,952)(851,956)(852,960)(853,959)(854,958)(855,957)
(856,931)(857,935)(858,934)(859,933)(860,932)(861,936)(862,940)(863,939)
(864,938)(865,937)(866,941)(867,945)(868,944)(869,943)(870,942)(871,916)
(872,920)(873,919)(874,918)(875,917)(876,921)(877,925)(878,924)(879,923)
(880,922)(881,926)(882,930)(883,929)(884,928)(885,927)(886,901)(887,905)
(888,904)(889,903)(890,902)(891,906)(892,910)(893,909)(894,908)(895,907)
(896,911)(897,915)(898,914)(899,913)(900,912);
s3 := Sym(960)!( 1,482)( 2,481)( 3,485)( 4,484)( 5,483)( 6,487)( 7,486)
( 8,490)( 9,489)( 10,488)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)
( 16,497)( 17,496)( 18,500)( 19,499)( 20,498)( 21,502)( 22,501)( 23,505)
( 24,504)( 25,503)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,527)
( 32,526)( 33,530)( 34,529)( 35,528)( 36,532)( 37,531)( 38,535)( 39,534)
( 40,533)( 41,537)( 42,536)( 43,540)( 44,539)( 45,538)( 46,512)( 47,511)
( 48,515)( 49,514)( 50,513)( 51,517)( 52,516)( 53,520)( 54,519)( 55,518)
( 56,522)( 57,521)( 58,525)( 59,524)( 60,523)( 61,557)( 62,556)( 63,560)
( 64,559)( 65,558)( 66,562)( 67,561)( 68,565)( 69,564)( 70,563)( 71,567)
( 72,566)( 73,570)( 74,569)( 75,568)( 76,542)( 77,541)( 78,545)( 79,544)
( 80,543)( 81,547)( 82,546)( 83,550)( 84,549)( 85,548)( 86,552)( 87,551)
( 88,555)( 89,554)( 90,553)( 91,572)( 92,571)( 93,575)( 94,574)( 95,573)
( 96,577)( 97,576)( 98,580)( 99,579)(100,578)(101,582)(102,581)(103,585)
(104,584)(105,583)(106,587)(107,586)(108,590)(109,589)(110,588)(111,592)
(112,591)(113,595)(114,594)(115,593)(116,597)(117,596)(118,600)(119,599)
(120,598)(121,602)(122,601)(123,605)(124,604)(125,603)(126,607)(127,606)
(128,610)(129,609)(130,608)(131,612)(132,611)(133,615)(134,614)(135,613)
(136,617)(137,616)(138,620)(139,619)(140,618)(141,622)(142,621)(143,625)
(144,624)(145,623)(146,627)(147,626)(148,630)(149,629)(150,628)(151,647)
(152,646)(153,650)(154,649)(155,648)(156,652)(157,651)(158,655)(159,654)
(160,653)(161,657)(162,656)(163,660)(164,659)(165,658)(166,632)(167,631)
(168,635)(169,634)(170,633)(171,637)(172,636)(173,640)(174,639)(175,638)
(176,642)(177,641)(178,645)(179,644)(180,643)(181,677)(182,676)(183,680)
(184,679)(185,678)(186,682)(187,681)(188,685)(189,684)(190,683)(191,687)
(192,686)(193,690)(194,689)(195,688)(196,662)(197,661)(198,665)(199,664)
(200,663)(201,667)(202,666)(203,670)(204,669)(205,668)(206,672)(207,671)
(208,675)(209,674)(210,673)(211,692)(212,691)(213,695)(214,694)(215,693)
(216,697)(217,696)(218,700)(219,699)(220,698)(221,702)(222,701)(223,705)
(224,704)(225,703)(226,707)(227,706)(228,710)(229,709)(230,708)(231,712)
(232,711)(233,715)(234,714)(235,713)(236,717)(237,716)(238,720)(239,719)
(240,718)(241,722)(242,721)(243,725)(244,724)(245,723)(246,727)(247,726)
(248,730)(249,729)(250,728)(251,732)(252,731)(253,735)(254,734)(255,733)
(256,737)(257,736)(258,740)(259,739)(260,738)(261,742)(262,741)(263,745)
(264,744)(265,743)(266,747)(267,746)(268,750)(269,749)(270,748)(271,767)
(272,766)(273,770)(274,769)(275,768)(276,772)(277,771)(278,775)(279,774)
(280,773)(281,777)(282,776)(283,780)(284,779)(285,778)(286,752)(287,751)
(288,755)(289,754)(290,753)(291,757)(292,756)(293,760)(294,759)(295,758)
(296,762)(297,761)(298,765)(299,764)(300,763)(301,797)(302,796)(303,800)
(304,799)(305,798)(306,802)(307,801)(308,805)(309,804)(310,803)(311,807)
(312,806)(313,810)(314,809)(315,808)(316,782)(317,781)(318,785)(319,784)
(320,783)(321,787)(322,786)(323,790)(324,789)(325,788)(326,792)(327,791)
(328,795)(329,794)(330,793)(331,812)(332,811)(333,815)(334,814)(335,813)
(336,817)(337,816)(338,820)(339,819)(340,818)(341,822)(342,821)(343,825)
(344,824)(345,823)(346,827)(347,826)(348,830)(349,829)(350,828)(351,832)
(352,831)(353,835)(354,834)(355,833)(356,837)(357,836)(358,840)(359,839)
(360,838)(361,842)(362,841)(363,845)(364,844)(365,843)(366,847)(367,846)
(368,850)(369,849)(370,848)(371,852)(372,851)(373,855)(374,854)(375,853)
(376,857)(377,856)(378,860)(379,859)(380,858)(381,862)(382,861)(383,865)
(384,864)(385,863)(386,867)(387,866)(388,870)(389,869)(390,868)(391,887)
(392,886)(393,890)(394,889)(395,888)(396,892)(397,891)(398,895)(399,894)
(400,893)(401,897)(402,896)(403,900)(404,899)(405,898)(406,872)(407,871)
(408,875)(409,874)(410,873)(411,877)(412,876)(413,880)(414,879)(415,878)
(416,882)(417,881)(418,885)(419,884)(420,883)(421,917)(422,916)(423,920)
(424,919)(425,918)(426,922)(427,921)(428,925)(429,924)(430,923)(431,927)
(432,926)(433,930)(434,929)(435,928)(436,902)(437,901)(438,905)(439,904)
(440,903)(441,907)(442,906)(443,910)(444,909)(445,908)(446,912)(447,911)
(448,915)(449,914)(450,913)(451,932)(452,931)(453,935)(454,934)(455,933)
(456,937)(457,936)(458,940)(459,939)(460,938)(461,942)(462,941)(463,945)
(464,944)(465,943)(466,947)(467,946)(468,950)(469,949)(470,948)(471,952)
(472,951)(473,955)(474,954)(475,953)(476,957)(477,956)(478,960)(479,959)
(480,958);
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*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >;
References : None.
to this polytope