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