Polytope of Type {6,4,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4,10}*1920
Also Known As : {{6,4|2},{4,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,205028)
Rank : 5
Schlafli Type : {6,4,4,10}
Number of vertices, edges, etc : 6, 12, 8, 20, 10
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 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 : {6,2,4,10}*960, {6,4,2,10}*960a
3-fold quotients : {2,4,4,10}*640
4-fold quotients : {3,2,4,10}*480, {6,4,2,5}*480a, {6,2,2,10}*480
5-fold quotients : {6,4,4,2}*384
6-fold quotients : {2,2,4,10}*320, {2,4,2,10}*320
8-fold quotients : {3,2,2,10}*240, {6,2,2,5}*240
10-fold quotients : {6,2,4,2}*192, {6,4,2,2}*192a
12-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
15-fold quotients : {2,4,4,2}*128
16-fold quotients : {3,2,2,5}*120
20-fold quotients : {3,2,4,2}*96, {6,2,2,2}*96
24-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
40-fold quotients : {3,2,2,2}*48
60-fold quotients : {2,2,2,2}*32
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 := ( 1,606)( 2,607)( 3,608)( 4,609)( 5,610)( 6,601)( 7,602)( 8,603)
( 9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)( 16,621)
( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)( 24,619)
( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)( 32,637)
( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)( 40,635)
( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)( 48,653)
( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)( 56,656)
( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)( 64,669)
( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)( 72,672)
( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)( 80,685)
( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)( 88,688)
( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)( 96,691)
( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)(104,704)
(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)(112,707)
(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)(120,720)
(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)(128,483)
(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)(136,501)
(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)(144,499)
(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)(152,517)
(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)(160,515)
(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)(168,533)
(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)(176,536)
(177,537)(178,538)(179,539)(180,540)(181,546)(182,547)(183,548)(184,549)
(185,550)(186,541)(187,542)(188,543)(189,544)(190,545)(191,551)(192,552)
(193,553)(194,554)(195,555)(196,561)(197,562)(198,563)(199,564)(200,565)
(201,556)(202,557)(203,558)(204,559)(205,560)(206,566)(207,567)(208,568)
(209,569)(210,570)(211,576)(212,577)(213,578)(214,579)(215,580)(216,571)
(217,572)(218,573)(219,574)(220,575)(221,581)(222,582)(223,583)(224,584)
(225,585)(226,591)(227,592)(228,593)(229,594)(230,595)(231,586)(232,587)
(233,588)(234,589)(235,590)(236,596)(237,597)(238,598)(239,599)(240,600)
(241,846)(242,847)(243,848)(244,849)(245,850)(246,841)(247,842)(248,843)
(249,844)(250,845)(251,851)(252,852)(253,853)(254,854)(255,855)(256,861)
(257,862)(258,863)(259,864)(260,865)(261,856)(262,857)(263,858)(264,859)
(265,860)(266,866)(267,867)(268,868)(269,869)(270,870)(271,876)(272,877)
(273,878)(274,879)(275,880)(276,871)(277,872)(278,873)(279,874)(280,875)
(281,881)(282,882)(283,883)(284,884)(285,885)(286,891)(287,892)(288,893)
(289,894)(290,895)(291,886)(292,887)(293,888)(294,889)(295,890)(296,896)
(297,897)(298,898)(299,899)(300,900)(301,906)(302,907)(303,908)(304,909)
(305,910)(306,901)(307,902)(308,903)(309,904)(310,905)(311,911)(312,912)
(313,913)(314,914)(315,915)(316,921)(317,922)(318,923)(319,924)(320,925)
(321,916)(322,917)(323,918)(324,919)(325,920)(326,926)(327,927)(328,928)
(329,929)(330,930)(331,936)(332,937)(333,938)(334,939)(335,940)(336,931)
(337,932)(338,933)(339,934)(340,935)(341,941)(342,942)(343,943)(344,944)
(345,945)(346,951)(347,952)(348,953)(349,954)(350,955)(351,946)(352,947)
(353,948)(354,949)(355,950)(356,956)(357,957)(358,958)(359,959)(360,960)
(361,726)(362,727)(363,728)(364,729)(365,730)(366,721)(367,722)(368,723)
(369,724)(370,725)(371,731)(372,732)(373,733)(374,734)(375,735)(376,741)
(377,742)(378,743)(379,744)(380,745)(381,736)(382,737)(383,738)(384,739)
(385,740)(386,746)(387,747)(388,748)(389,749)(390,750)(391,756)(392,757)
(393,758)(394,759)(395,760)(396,751)(397,752)(398,753)(399,754)(400,755)
(401,761)(402,762)(403,763)(404,764)(405,765)(406,771)(407,772)(408,773)
(409,774)(410,775)(411,766)(412,767)(413,768)(414,769)(415,770)(416,776)
(417,777)(418,778)(419,779)(420,780)(421,786)(422,787)(423,788)(424,789)
(425,790)(426,781)(427,782)(428,783)(429,784)(430,785)(431,791)(432,792)
(433,793)(434,794)(435,795)(436,801)(437,802)(438,803)(439,804)(440,805)
(441,796)(442,797)(443,798)(444,799)(445,800)(446,806)(447,807)(448,808)
(449,809)(450,810)(451,816)(452,817)(453,818)(454,819)(455,820)(456,811)
(457,812)(458,813)(459,814)(460,815)(461,821)(462,822)(463,823)(464,824)
(465,825)(466,831)(467,832)(468,833)(469,834)(470,835)(471,826)(472,827)
(473,828)(474,829)(475,830)(476,836)(477,837)(478,838)(479,839)(480,840);;
s2 := (241,256)(242,257)(243,258)(244,259)(245,260)(246,261)(247,262)(248,263)
(249,264)(250,265)(251,266)(252,267)(253,268)(254,269)(255,270)(271,286)
(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)(279,294)
(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,316)(302,317)
(303,318)(304,319)(305,320)(306,321)(307,322)(308,323)(309,324)(310,325)
(311,326)(312,327)(313,328)(314,329)(315,330)(331,346)(332,347)(333,348)
(334,349)(335,350)(336,351)(337,352)(338,353)(339,354)(340,355)(341,356)
(342,357)(343,358)(344,359)(345,360)(361,376)(362,377)(363,378)(364,379)
(365,380)(366,381)(367,382)(368,383)(369,384)(370,385)(371,386)(372,387)
(373,388)(374,389)(375,390)(391,406)(392,407)(393,408)(394,409)(395,410)
(396,411)(397,412)(398,413)(399,414)(400,415)(401,416)(402,417)(403,418)
(404,419)(405,420)(421,436)(422,437)(423,438)(424,439)(425,440)(426,441)
(427,442)(428,443)(429,444)(430,445)(431,446)(432,447)(433,448)(434,449)
(435,450)(451,466)(452,467)(453,468)(454,469)(455,470)(456,471)(457,472)
(458,473)(459,474)(460,475)(461,476)(462,477)(463,478)(464,479)(465,480)
(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)(488,518)
(489,519)(490,520)(491,521)(492,522)(493,523)(494,524)(495,525)(496,526)
(497,527)(498,528)(499,529)(500,530)(501,531)(502,532)(503,533)(504,534)
(505,535)(506,536)(507,537)(508,538)(509,539)(510,540)(541,571)(542,572)
(543,573)(544,574)(545,575)(546,576)(547,577)(548,578)(549,579)(550,580)
(551,581)(552,582)(553,583)(554,584)(555,585)(556,586)(557,587)(558,588)
(559,589)(560,590)(561,591)(562,592)(563,593)(564,594)(565,595)(566,596)
(567,597)(568,598)(569,599)(570,600)(601,631)(602,632)(603,633)(604,634)
(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,641)(612,642)
(613,643)(614,644)(615,645)(616,646)(617,647)(618,648)(619,649)(620,650)
(621,651)(622,652)(623,653)(624,654)(625,655)(626,656)(627,657)(628,658)
(629,659)(630,660)(661,691)(662,692)(663,693)(664,694)(665,695)(666,696)
(667,697)(668,698)(669,699)(670,700)(671,701)(672,702)(673,703)(674,704)
(675,705)(676,706)(677,707)(678,708)(679,709)(680,710)(681,711)(682,712)
(683,713)(684,714)(685,715)(686,716)(687,717)(688,718)(689,719)(690,720)
(721,766)(722,767)(723,768)(724,769)(725,770)(726,771)(727,772)(728,773)
(729,774)(730,775)(731,776)(732,777)(733,778)(734,779)(735,780)(736,751)
(737,752)(738,753)(739,754)(740,755)(741,756)(742,757)(743,758)(744,759)
(745,760)(746,761)(747,762)(748,763)(749,764)(750,765)(781,826)(782,827)
(783,828)(784,829)(785,830)(786,831)(787,832)(788,833)(789,834)(790,835)
(791,836)(792,837)(793,838)(794,839)(795,840)(796,811)(797,812)(798,813)
(799,814)(800,815)(801,816)(802,817)(803,818)(804,819)(805,820)(806,821)
(807,822)(808,823)(809,824)(810,825)(841,886)(842,887)(843,888)(844,889)
(845,890)(846,891)(847,892)(848,893)(849,894)(850,895)(851,896)(852,897)
(853,898)(854,899)(855,900)(856,871)(857,872)(858,873)(859,874)(860,875)
(861,876)(862,877)(863,878)(864,879)(865,880)(866,881)(867,882)(868,883)
(869,884)(870,885)(901,946)(902,947)(903,948)(904,949)(905,950)(906,951)
(907,952)(908,953)(909,954)(910,955)(911,956)(912,957)(913,958)(914,959)
(915,960)(916,931)(917,932)(918,933)(919,934)(920,935)(921,936)(922,937)
(923,938)(924,939)(925,940)(926,941)(927,942)(928,943)(929,944)(930,945);;
s3 := ( 1,301)( 2,305)( 3,304)( 4,303)( 5,302)( 6,306)( 7,310)( 8,309)
( 9,308)( 10,307)( 11,311)( 12,315)( 13,314)( 14,313)( 15,312)( 16,316)
( 17,320)( 18,319)( 19,318)( 20,317)( 21,321)( 22,325)( 23,324)( 24,323)
( 25,322)( 26,326)( 27,330)( 28,329)( 29,328)( 30,327)( 31,331)( 32,335)
( 33,334)( 34,333)( 35,332)( 36,336)( 37,340)( 38,339)( 39,338)( 40,337)
( 41,341)( 42,345)( 43,344)( 44,343)( 45,342)( 46,346)( 47,350)( 48,349)
( 49,348)( 50,347)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)( 56,356)
( 57,360)( 58,359)( 59,358)( 60,357)( 61,241)( 62,245)( 63,244)( 64,243)
( 65,242)( 66,246)( 67,250)( 68,249)( 69,248)( 70,247)( 71,251)( 72,255)
( 73,254)( 74,253)( 75,252)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,261)( 82,265)( 83,264)( 84,263)( 85,262)( 86,266)( 87,270)( 88,269)
( 89,268)( 90,267)( 91,271)( 92,275)( 93,274)( 94,273)( 95,272)( 96,276)
( 97,280)( 98,279)( 99,278)(100,277)(101,281)(102,285)(103,284)(104,283)
(105,282)(106,286)(107,290)(108,289)(109,288)(110,287)(111,291)(112,295)
(113,294)(114,293)(115,292)(116,296)(117,300)(118,299)(119,298)(120,297)
(121,421)(122,425)(123,424)(124,423)(125,422)(126,426)(127,430)(128,429)
(129,428)(130,427)(131,431)(132,435)(133,434)(134,433)(135,432)(136,436)
(137,440)(138,439)(139,438)(140,437)(141,441)(142,445)(143,444)(144,443)
(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,451)(152,455)
(153,454)(154,453)(155,452)(156,456)(157,460)(158,459)(159,458)(160,457)
(161,461)(162,465)(163,464)(164,463)(165,462)(166,466)(167,470)(168,469)
(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)(176,476)
(177,480)(178,479)(179,478)(180,477)(181,361)(182,365)(183,364)(184,363)
(185,362)(186,366)(187,370)(188,369)(189,368)(190,367)(191,371)(192,375)
(193,374)(194,373)(195,372)(196,376)(197,380)(198,379)(199,378)(200,377)
(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)(208,389)
(209,388)(210,387)(211,391)(212,395)(213,394)(214,393)(215,392)(216,396)
(217,400)(218,399)(219,398)(220,397)(221,401)(222,405)(223,404)(224,403)
(225,402)(226,406)(227,410)(228,409)(229,408)(230,407)(231,411)(232,415)
(233,414)(234,413)(235,412)(236,416)(237,420)(238,419)(239,418)(240,417)
(481,781)(482,785)(483,784)(484,783)(485,782)(486,786)(487,790)(488,789)
(489,788)(490,787)(491,791)(492,795)(493,794)(494,793)(495,792)(496,796)
(497,800)(498,799)(499,798)(500,797)(501,801)(502,805)(503,804)(504,803)
(505,802)(506,806)(507,810)(508,809)(509,808)(510,807)(511,811)(512,815)
(513,814)(514,813)(515,812)(516,816)(517,820)(518,819)(519,818)(520,817)
(521,821)(522,825)(523,824)(524,823)(525,822)(526,826)(527,830)(528,829)
(529,828)(530,827)(531,831)(532,835)(533,834)(534,833)(535,832)(536,836)
(537,840)(538,839)(539,838)(540,837)(541,721)(542,725)(543,724)(544,723)
(545,722)(546,726)(547,730)(548,729)(549,728)(550,727)(551,731)(552,735)
(553,734)(554,733)(555,732)(556,736)(557,740)(558,739)(559,738)(560,737)
(561,741)(562,745)(563,744)(564,743)(565,742)(566,746)(567,750)(568,749)
(569,748)(570,747)(571,751)(572,755)(573,754)(574,753)(575,752)(576,756)
(577,760)(578,759)(579,758)(580,757)(581,761)(582,765)(583,764)(584,763)
(585,762)(586,766)(587,770)(588,769)(589,768)(590,767)(591,771)(592,775)
(593,774)(594,773)(595,772)(596,776)(597,780)(598,779)(599,778)(600,777)
(601,901)(602,905)(603,904)(604,903)(605,902)(606,906)(607,910)(608,909)
(609,908)(610,907)(611,911)(612,915)(613,914)(614,913)(615,912)(616,916)
(617,920)(618,919)(619,918)(620,917)(621,921)(622,925)(623,924)(624,923)
(625,922)(626,926)(627,930)(628,929)(629,928)(630,927)(631,931)(632,935)
(633,934)(634,933)(635,932)(636,936)(637,940)(638,939)(639,938)(640,937)
(641,941)(642,945)(643,944)(644,943)(645,942)(646,946)(647,950)(648,949)
(649,948)(650,947)(651,951)(652,955)(653,954)(654,953)(655,952)(656,956)
(657,960)(658,959)(659,958)(660,957)(661,841)(662,845)(663,844)(664,843)
(665,842)(666,846)(667,850)(668,849)(669,848)(670,847)(671,851)(672,855)
(673,854)(674,853)(675,852)(676,856)(677,860)(678,859)(679,858)(680,857)
(681,861)(682,865)(683,864)(684,863)(685,862)(686,866)(687,870)(688,869)
(689,868)(690,867)(691,871)(692,875)(693,874)(694,873)(695,872)(696,876)
(697,880)(698,879)(699,878)(700,877)(701,881)(702,885)(703,884)(704,883)
(705,882)(706,886)(707,890)(708,889)(709,888)(710,887)(711,891)(712,895)
(713,894)(714,893)(715,892)(716,896)(717,900)(718,899)(719,898)(720,897);;
s4 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)( 8, 70)
( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)
( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)( 32, 91)
( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)
( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)( 48,110)
( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)( 56,117)
( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)(124,184)
(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)(132,191)
(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)(140,198)
(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)(148,210)
(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)(156,217)
(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)(164,224)
(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)(172,231)
(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)(180,238)
(241,302)(242,301)(243,305)(244,304)(245,303)(246,307)(247,306)(248,310)
(249,309)(250,308)(251,312)(252,311)(253,315)(254,314)(255,313)(256,317)
(257,316)(258,320)(259,319)(260,318)(261,322)(262,321)(263,325)(264,324)
(265,323)(266,327)(267,326)(268,330)(269,329)(270,328)(271,332)(272,331)
(273,335)(274,334)(275,333)(276,337)(277,336)(278,340)(279,339)(280,338)
(281,342)(282,341)(283,345)(284,344)(285,343)(286,347)(287,346)(288,350)
(289,349)(290,348)(291,352)(292,351)(293,355)(294,354)(295,353)(296,357)
(297,356)(298,360)(299,359)(300,358)(361,422)(362,421)(363,425)(364,424)
(365,423)(366,427)(367,426)(368,430)(369,429)(370,428)(371,432)(372,431)
(373,435)(374,434)(375,433)(376,437)(377,436)(378,440)(379,439)(380,438)
(381,442)(382,441)(383,445)(384,444)(385,443)(386,447)(387,446)(388,450)
(389,449)(390,448)(391,452)(392,451)(393,455)(394,454)(395,453)(396,457)
(397,456)(398,460)(399,459)(400,458)(401,462)(402,461)(403,465)(404,464)
(405,463)(406,467)(407,466)(408,470)(409,469)(410,468)(411,472)(412,471)
(413,475)(414,474)(415,473)(416,477)(417,476)(418,480)(419,479)(420,478)
(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)
(721,782)(722,781)(723,785)(724,784)(725,783)(726,787)(727,786)(728,790)
(729,789)(730,788)(731,792)(732,791)(733,795)(734,794)(735,793)(736,797)
(737,796)(738,800)(739,799)(740,798)(741,802)(742,801)(743,805)(744,804)
(745,803)(746,807)(747,806)(748,810)(749,809)(750,808)(751,812)(752,811)
(753,815)(754,814)(755,813)(756,817)(757,816)(758,820)(759,819)(760,818)
(761,822)(762,821)(763,825)(764,824)(765,823)(766,827)(767,826)(768,830)
(769,829)(770,828)(771,832)(772,831)(773,835)(774,834)(775,833)(776,837)
(777,836)(778,840)(779,839)(780,838)(841,902)(842,901)(843,905)(844,904)
(845,903)(846,907)(847,906)(848,910)(849,909)(850,908)(851,912)(852,911)
(853,915)(854,914)(855,913)(856,917)(857,916)(858,920)(859,919)(860,918)
(861,922)(862,921)(863,925)(864,924)(865,923)(866,927)(867,926)(868,930)
(869,929)(870,928)(871,932)(872,931)(873,935)(874,934)(875,933)(876,937)
(877,936)(878,940)(879,939)(880,938)(881,942)(882,941)(883,945)(884,944)
(885,943)(886,947)(887,946)(888,950)(889,949)(890,948)(891,952)(892,951)
(893,955)(894,954)(895,953)(896,957)(897,956)(898,960)(899,959)(900,958);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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)!( 1,606)( 2,607)( 3,608)( 4,609)( 5,610)( 6,601)( 7,602)
( 8,603)( 9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)
( 16,621)( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)
( 24,619)( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)
( 32,637)( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)
( 40,635)( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)
( 48,653)( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)
( 56,656)( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)
( 64,669)( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)
( 72,672)( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)
( 80,685)( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)
( 88,688)( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)
( 96,691)( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)
(104,704)(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)
(112,707)(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)
(120,720)(121,486)(122,487)(123,488)(124,489)(125,490)(126,481)(127,482)
(128,483)(129,484)(130,485)(131,491)(132,492)(133,493)(134,494)(135,495)
(136,501)(137,502)(138,503)(139,504)(140,505)(141,496)(142,497)(143,498)
(144,499)(145,500)(146,506)(147,507)(148,508)(149,509)(150,510)(151,516)
(152,517)(153,518)(154,519)(155,520)(156,511)(157,512)(158,513)(159,514)
(160,515)(161,521)(162,522)(163,523)(164,524)(165,525)(166,531)(167,532)
(168,533)(169,534)(170,535)(171,526)(172,527)(173,528)(174,529)(175,530)
(176,536)(177,537)(178,538)(179,539)(180,540)(181,546)(182,547)(183,548)
(184,549)(185,550)(186,541)(187,542)(188,543)(189,544)(190,545)(191,551)
(192,552)(193,553)(194,554)(195,555)(196,561)(197,562)(198,563)(199,564)
(200,565)(201,556)(202,557)(203,558)(204,559)(205,560)(206,566)(207,567)
(208,568)(209,569)(210,570)(211,576)(212,577)(213,578)(214,579)(215,580)
(216,571)(217,572)(218,573)(219,574)(220,575)(221,581)(222,582)(223,583)
(224,584)(225,585)(226,591)(227,592)(228,593)(229,594)(230,595)(231,586)
(232,587)(233,588)(234,589)(235,590)(236,596)(237,597)(238,598)(239,599)
(240,600)(241,846)(242,847)(243,848)(244,849)(245,850)(246,841)(247,842)
(248,843)(249,844)(250,845)(251,851)(252,852)(253,853)(254,854)(255,855)
(256,861)(257,862)(258,863)(259,864)(260,865)(261,856)(262,857)(263,858)
(264,859)(265,860)(266,866)(267,867)(268,868)(269,869)(270,870)(271,876)
(272,877)(273,878)(274,879)(275,880)(276,871)(277,872)(278,873)(279,874)
(280,875)(281,881)(282,882)(283,883)(284,884)(285,885)(286,891)(287,892)
(288,893)(289,894)(290,895)(291,886)(292,887)(293,888)(294,889)(295,890)
(296,896)(297,897)(298,898)(299,899)(300,900)(301,906)(302,907)(303,908)
(304,909)(305,910)(306,901)(307,902)(308,903)(309,904)(310,905)(311,911)
(312,912)(313,913)(314,914)(315,915)(316,921)(317,922)(318,923)(319,924)
(320,925)(321,916)(322,917)(323,918)(324,919)(325,920)(326,926)(327,927)
(328,928)(329,929)(330,930)(331,936)(332,937)(333,938)(334,939)(335,940)
(336,931)(337,932)(338,933)(339,934)(340,935)(341,941)(342,942)(343,943)
(344,944)(345,945)(346,951)(347,952)(348,953)(349,954)(350,955)(351,946)
(352,947)(353,948)(354,949)(355,950)(356,956)(357,957)(358,958)(359,959)
(360,960)(361,726)(362,727)(363,728)(364,729)(365,730)(366,721)(367,722)
(368,723)(369,724)(370,725)(371,731)(372,732)(373,733)(374,734)(375,735)
(376,741)(377,742)(378,743)(379,744)(380,745)(381,736)(382,737)(383,738)
(384,739)(385,740)(386,746)(387,747)(388,748)(389,749)(390,750)(391,756)
(392,757)(393,758)(394,759)(395,760)(396,751)(397,752)(398,753)(399,754)
(400,755)(401,761)(402,762)(403,763)(404,764)(405,765)(406,771)(407,772)
(408,773)(409,774)(410,775)(411,766)(412,767)(413,768)(414,769)(415,770)
(416,776)(417,777)(418,778)(419,779)(420,780)(421,786)(422,787)(423,788)
(424,789)(425,790)(426,781)(427,782)(428,783)(429,784)(430,785)(431,791)
(432,792)(433,793)(434,794)(435,795)(436,801)(437,802)(438,803)(439,804)
(440,805)(441,796)(442,797)(443,798)(444,799)(445,800)(446,806)(447,807)
(448,808)(449,809)(450,810)(451,816)(452,817)(453,818)(454,819)(455,820)
(456,811)(457,812)(458,813)(459,814)(460,815)(461,821)(462,822)(463,823)
(464,824)(465,825)(466,831)(467,832)(468,833)(469,834)(470,835)(471,826)
(472,827)(473,828)(474,829)(475,830)(476,836)(477,837)(478,838)(479,839)
(480,840);
s2 := Sym(960)!(241,256)(242,257)(243,258)(244,259)(245,260)(246,261)(247,262)
(248,263)(249,264)(250,265)(251,266)(252,267)(253,268)(254,269)(255,270)
(271,286)(272,287)(273,288)(274,289)(275,290)(276,291)(277,292)(278,293)
(279,294)(280,295)(281,296)(282,297)(283,298)(284,299)(285,300)(301,316)
(302,317)(303,318)(304,319)(305,320)(306,321)(307,322)(308,323)(309,324)
(310,325)(311,326)(312,327)(313,328)(314,329)(315,330)(331,346)(332,347)
(333,348)(334,349)(335,350)(336,351)(337,352)(338,353)(339,354)(340,355)
(341,356)(342,357)(343,358)(344,359)(345,360)(361,376)(362,377)(363,378)
(364,379)(365,380)(366,381)(367,382)(368,383)(369,384)(370,385)(371,386)
(372,387)(373,388)(374,389)(375,390)(391,406)(392,407)(393,408)(394,409)
(395,410)(396,411)(397,412)(398,413)(399,414)(400,415)(401,416)(402,417)
(403,418)(404,419)(405,420)(421,436)(422,437)(423,438)(424,439)(425,440)
(426,441)(427,442)(428,443)(429,444)(430,445)(431,446)(432,447)(433,448)
(434,449)(435,450)(451,466)(452,467)(453,468)(454,469)(455,470)(456,471)
(457,472)(458,473)(459,474)(460,475)(461,476)(462,477)(463,478)(464,479)
(465,480)(481,511)(482,512)(483,513)(484,514)(485,515)(486,516)(487,517)
(488,518)(489,519)(490,520)(491,521)(492,522)(493,523)(494,524)(495,525)
(496,526)(497,527)(498,528)(499,529)(500,530)(501,531)(502,532)(503,533)
(504,534)(505,535)(506,536)(507,537)(508,538)(509,539)(510,540)(541,571)
(542,572)(543,573)(544,574)(545,575)(546,576)(547,577)(548,578)(549,579)
(550,580)(551,581)(552,582)(553,583)(554,584)(555,585)(556,586)(557,587)
(558,588)(559,589)(560,590)(561,591)(562,592)(563,593)(564,594)(565,595)
(566,596)(567,597)(568,598)(569,599)(570,600)(601,631)(602,632)(603,633)
(604,634)(605,635)(606,636)(607,637)(608,638)(609,639)(610,640)(611,641)
(612,642)(613,643)(614,644)(615,645)(616,646)(617,647)(618,648)(619,649)
(620,650)(621,651)(622,652)(623,653)(624,654)(625,655)(626,656)(627,657)
(628,658)(629,659)(630,660)(661,691)(662,692)(663,693)(664,694)(665,695)
(666,696)(667,697)(668,698)(669,699)(670,700)(671,701)(672,702)(673,703)
(674,704)(675,705)(676,706)(677,707)(678,708)(679,709)(680,710)(681,711)
(682,712)(683,713)(684,714)(685,715)(686,716)(687,717)(688,718)(689,719)
(690,720)(721,766)(722,767)(723,768)(724,769)(725,770)(726,771)(727,772)
(728,773)(729,774)(730,775)(731,776)(732,777)(733,778)(734,779)(735,780)
(736,751)(737,752)(738,753)(739,754)(740,755)(741,756)(742,757)(743,758)
(744,759)(745,760)(746,761)(747,762)(748,763)(749,764)(750,765)(781,826)
(782,827)(783,828)(784,829)(785,830)(786,831)(787,832)(788,833)(789,834)
(790,835)(791,836)(792,837)(793,838)(794,839)(795,840)(796,811)(797,812)
(798,813)(799,814)(800,815)(801,816)(802,817)(803,818)(804,819)(805,820)
(806,821)(807,822)(808,823)(809,824)(810,825)(841,886)(842,887)(843,888)
(844,889)(845,890)(846,891)(847,892)(848,893)(849,894)(850,895)(851,896)
(852,897)(853,898)(854,899)(855,900)(856,871)(857,872)(858,873)(859,874)
(860,875)(861,876)(862,877)(863,878)(864,879)(865,880)(866,881)(867,882)
(868,883)(869,884)(870,885)(901,946)(902,947)(903,948)(904,949)(905,950)
(906,951)(907,952)(908,953)(909,954)(910,955)(911,956)(912,957)(913,958)
(914,959)(915,960)(916,931)(917,932)(918,933)(919,934)(920,935)(921,936)
(922,937)(923,938)(924,939)(925,940)(926,941)(927,942)(928,943)(929,944)
(930,945);
s3 := Sym(960)!( 1,301)( 2,305)( 3,304)( 4,303)( 5,302)( 6,306)( 7,310)
( 8,309)( 9,308)( 10,307)( 11,311)( 12,315)( 13,314)( 14,313)( 15,312)
( 16,316)( 17,320)( 18,319)( 19,318)( 20,317)( 21,321)( 22,325)( 23,324)
( 24,323)( 25,322)( 26,326)( 27,330)( 28,329)( 29,328)( 30,327)( 31,331)
( 32,335)( 33,334)( 34,333)( 35,332)( 36,336)( 37,340)( 38,339)( 39,338)
( 40,337)( 41,341)( 42,345)( 43,344)( 44,343)( 45,342)( 46,346)( 47,350)
( 48,349)( 49,348)( 50,347)( 51,351)( 52,355)( 53,354)( 54,353)( 55,352)
( 56,356)( 57,360)( 58,359)( 59,358)( 60,357)( 61,241)( 62,245)( 63,244)
( 64,243)( 65,242)( 66,246)( 67,250)( 68,249)( 69,248)( 70,247)( 71,251)
( 72,255)( 73,254)( 74,253)( 75,252)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,261)( 82,265)( 83,264)( 84,263)( 85,262)( 86,266)( 87,270)
( 88,269)( 89,268)( 90,267)( 91,271)( 92,275)( 93,274)( 94,273)( 95,272)
( 96,276)( 97,280)( 98,279)( 99,278)(100,277)(101,281)(102,285)(103,284)
(104,283)(105,282)(106,286)(107,290)(108,289)(109,288)(110,287)(111,291)
(112,295)(113,294)(114,293)(115,292)(116,296)(117,300)(118,299)(119,298)
(120,297)(121,421)(122,425)(123,424)(124,423)(125,422)(126,426)(127,430)
(128,429)(129,428)(130,427)(131,431)(132,435)(133,434)(134,433)(135,432)
(136,436)(137,440)(138,439)(139,438)(140,437)(141,441)(142,445)(143,444)
(144,443)(145,442)(146,446)(147,450)(148,449)(149,448)(150,447)(151,451)
(152,455)(153,454)(154,453)(155,452)(156,456)(157,460)(158,459)(159,458)
(160,457)(161,461)(162,465)(163,464)(164,463)(165,462)(166,466)(167,470)
(168,469)(169,468)(170,467)(171,471)(172,475)(173,474)(174,473)(175,472)
(176,476)(177,480)(178,479)(179,478)(180,477)(181,361)(182,365)(183,364)
(184,363)(185,362)(186,366)(187,370)(188,369)(189,368)(190,367)(191,371)
(192,375)(193,374)(194,373)(195,372)(196,376)(197,380)(198,379)(199,378)
(200,377)(201,381)(202,385)(203,384)(204,383)(205,382)(206,386)(207,390)
(208,389)(209,388)(210,387)(211,391)(212,395)(213,394)(214,393)(215,392)
(216,396)(217,400)(218,399)(219,398)(220,397)(221,401)(222,405)(223,404)
(224,403)(225,402)(226,406)(227,410)(228,409)(229,408)(230,407)(231,411)
(232,415)(233,414)(234,413)(235,412)(236,416)(237,420)(238,419)(239,418)
(240,417)(481,781)(482,785)(483,784)(484,783)(485,782)(486,786)(487,790)
(488,789)(489,788)(490,787)(491,791)(492,795)(493,794)(494,793)(495,792)
(496,796)(497,800)(498,799)(499,798)(500,797)(501,801)(502,805)(503,804)
(504,803)(505,802)(506,806)(507,810)(508,809)(509,808)(510,807)(511,811)
(512,815)(513,814)(514,813)(515,812)(516,816)(517,820)(518,819)(519,818)
(520,817)(521,821)(522,825)(523,824)(524,823)(525,822)(526,826)(527,830)
(528,829)(529,828)(530,827)(531,831)(532,835)(533,834)(534,833)(535,832)
(536,836)(537,840)(538,839)(539,838)(540,837)(541,721)(542,725)(543,724)
(544,723)(545,722)(546,726)(547,730)(548,729)(549,728)(550,727)(551,731)
(552,735)(553,734)(554,733)(555,732)(556,736)(557,740)(558,739)(559,738)
(560,737)(561,741)(562,745)(563,744)(564,743)(565,742)(566,746)(567,750)
(568,749)(569,748)(570,747)(571,751)(572,755)(573,754)(574,753)(575,752)
(576,756)(577,760)(578,759)(579,758)(580,757)(581,761)(582,765)(583,764)
(584,763)(585,762)(586,766)(587,770)(588,769)(589,768)(590,767)(591,771)
(592,775)(593,774)(594,773)(595,772)(596,776)(597,780)(598,779)(599,778)
(600,777)(601,901)(602,905)(603,904)(604,903)(605,902)(606,906)(607,910)
(608,909)(609,908)(610,907)(611,911)(612,915)(613,914)(614,913)(615,912)
(616,916)(617,920)(618,919)(619,918)(620,917)(621,921)(622,925)(623,924)
(624,923)(625,922)(626,926)(627,930)(628,929)(629,928)(630,927)(631,931)
(632,935)(633,934)(634,933)(635,932)(636,936)(637,940)(638,939)(639,938)
(640,937)(641,941)(642,945)(643,944)(644,943)(645,942)(646,946)(647,950)
(648,949)(649,948)(650,947)(651,951)(652,955)(653,954)(654,953)(655,952)
(656,956)(657,960)(658,959)(659,958)(660,957)(661,841)(662,845)(663,844)
(664,843)(665,842)(666,846)(667,850)(668,849)(669,848)(670,847)(671,851)
(672,855)(673,854)(674,853)(675,852)(676,856)(677,860)(678,859)(679,858)
(680,857)(681,861)(682,865)(683,864)(684,863)(685,862)(686,866)(687,870)
(688,869)(689,868)(690,867)(691,871)(692,875)(693,874)(694,873)(695,872)
(696,876)(697,880)(698,879)(699,878)(700,877)(701,881)(702,885)(703,884)
(704,883)(705,882)(706,886)(707,890)(708,889)(709,888)(710,887)(711,891)
(712,895)(713,894)(714,893)(715,892)(716,896)(717,900)(718,899)(719,898)
(720,897);
s4 := Sym(960)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)
( 8, 70)( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)
( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)
( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)
( 40, 98)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)
( 48,110)( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)
( 56,117)( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)
(124,184)(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)
(132,191)(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)
(140,198)(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)
(148,210)(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)
(156,217)(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)
(164,224)(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)
(172,231)(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)
(180,238)(241,302)(242,301)(243,305)(244,304)(245,303)(246,307)(247,306)
(248,310)(249,309)(250,308)(251,312)(252,311)(253,315)(254,314)(255,313)
(256,317)(257,316)(258,320)(259,319)(260,318)(261,322)(262,321)(263,325)
(264,324)(265,323)(266,327)(267,326)(268,330)(269,329)(270,328)(271,332)
(272,331)(273,335)(274,334)(275,333)(276,337)(277,336)(278,340)(279,339)
(280,338)(281,342)(282,341)(283,345)(284,344)(285,343)(286,347)(287,346)
(288,350)(289,349)(290,348)(291,352)(292,351)(293,355)(294,354)(295,353)
(296,357)(297,356)(298,360)(299,359)(300,358)(361,422)(362,421)(363,425)
(364,424)(365,423)(366,427)(367,426)(368,430)(369,429)(370,428)(371,432)
(372,431)(373,435)(374,434)(375,433)(376,437)(377,436)(378,440)(379,439)
(380,438)(381,442)(382,441)(383,445)(384,444)(385,443)(386,447)(387,446)
(388,450)(389,449)(390,448)(391,452)(392,451)(393,455)(394,454)(395,453)
(396,457)(397,456)(398,460)(399,459)(400,458)(401,462)(402,461)(403,465)
(404,464)(405,463)(406,467)(407,466)(408,470)(409,469)(410,468)(411,472)
(412,471)(413,475)(414,474)(415,473)(416,477)(417,476)(418,480)(419,479)
(420,478)(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)(721,782)(722,781)(723,785)(724,784)(725,783)(726,787)(727,786)
(728,790)(729,789)(730,788)(731,792)(732,791)(733,795)(734,794)(735,793)
(736,797)(737,796)(738,800)(739,799)(740,798)(741,802)(742,801)(743,805)
(744,804)(745,803)(746,807)(747,806)(748,810)(749,809)(750,808)(751,812)
(752,811)(753,815)(754,814)(755,813)(756,817)(757,816)(758,820)(759,819)
(760,818)(761,822)(762,821)(763,825)(764,824)(765,823)(766,827)(767,826)
(768,830)(769,829)(770,828)(771,832)(772,831)(773,835)(774,834)(775,833)
(776,837)(777,836)(778,840)(779,839)(780,838)(841,902)(842,901)(843,905)
(844,904)(845,903)(846,907)(847,906)(848,910)(849,909)(850,908)(851,912)
(852,911)(853,915)(854,914)(855,913)(856,917)(857,916)(858,920)(859,919)
(860,918)(861,922)(862,921)(863,925)(864,924)(865,923)(866,927)(867,926)
(868,930)(869,929)(870,928)(871,932)(872,931)(873,935)(874,934)(875,933)
(876,937)(877,936)(878,940)(879,939)(880,938)(881,942)(882,941)(883,945)
(884,944)(885,943)(886,947)(887,946)(888,950)(889,949)(890,948)(891,952)
(892,951)(893,955)(894,954)(895,953)(896,957)(897,956)(898,960)(899,959)
(900,958);
poly := sub<Sym(960)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope