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