Polytope of Type {4,10,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,6,4}*1920a
Also Known As : {{4,10|2},{10,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,208117)
Rank : 5
Schlafli Type : {4,10,6,4}
Number of vertices, edges, etc : 4, 20, 30, 12, 4
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 : {2,10,6,4}*960a, {4,10,6,2}*960
3-fold quotients : {4,10,2,4}*640
4-fold quotients : {2,10,6,2}*480
5-fold quotients : {4,2,6,4}*384a
6-fold quotients : {2,10,2,4}*320, {4,10,2,2}*320
10-fold quotients : {2,2,6,4}*192a, {4,2,6,2}*192
12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
15-fold quotients : {4,2,2,4}*128
20-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
24-fold quotients : {2,5,2,2}*80
30-fold quotients : {2,2,2,4}*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)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)(184,694)
(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)(192,702)
(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)(200,710)
(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)(208,718)
(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)(216,666)
(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)(224,674)
(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)(232,682)
(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)(240,690)
(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)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)(424,934)
(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)(432,942)
(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)(440,950)
(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)(448,958)
(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)(456,906)
(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)(464,914)
(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)(472,922)
(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)(480,930);;
s1 := ( 1,181)( 2,185)( 3,184)( 4,183)( 5,182)( 6,186)( 7,190)( 8,189)
( 9,188)( 10,187)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)( 16,196)
( 17,200)( 18,199)( 19,198)( 20,197)( 21,201)( 22,205)( 23,204)( 24,203)
( 25,202)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,211)( 32,215)
( 33,214)( 34,213)( 35,212)( 36,216)( 37,220)( 38,219)( 39,218)( 40,217)
( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,226)( 47,230)( 48,229)
( 49,228)( 50,227)( 51,231)( 52,235)( 53,234)( 54,233)( 55,232)( 56,236)
( 57,240)( 58,239)( 59,238)( 60,237)( 61,121)( 62,125)( 63,124)( 64,123)
( 65,122)( 66,126)( 67,130)( 68,129)( 69,128)( 70,127)( 71,131)( 72,135)
( 73,134)( 74,133)( 75,132)( 76,136)( 77,140)( 78,139)( 79,138)( 80,137)
( 81,141)( 82,145)( 83,144)( 84,143)( 85,142)( 86,146)( 87,150)( 88,149)
( 89,148)( 90,147)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,156)
( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)(104,163)
(105,162)(106,166)(107,170)(108,169)(109,168)(110,167)(111,171)(112,175)
(113,174)(114,173)(115,172)(116,176)(117,180)(118,179)(119,178)(120,177)
(241,421)(242,425)(243,424)(244,423)(245,422)(246,426)(247,430)(248,429)
(249,428)(250,427)(251,431)(252,435)(253,434)(254,433)(255,432)(256,436)
(257,440)(258,439)(259,438)(260,437)(261,441)(262,445)(263,444)(264,443)
(265,442)(266,446)(267,450)(268,449)(269,448)(270,447)(271,451)(272,455)
(273,454)(274,453)(275,452)(276,456)(277,460)(278,459)(279,458)(280,457)
(281,461)(282,465)(283,464)(284,463)(285,462)(286,466)(287,470)(288,469)
(289,468)(290,467)(291,471)(292,475)(293,474)(294,473)(295,472)(296,476)
(297,480)(298,479)(299,478)(300,477)(301,361)(302,365)(303,364)(304,363)
(305,362)(306,366)(307,370)(308,369)(309,368)(310,367)(311,371)(312,375)
(313,374)(314,373)(315,372)(316,376)(317,380)(318,379)(319,378)(320,377)
(321,381)(322,385)(323,384)(324,383)(325,382)(326,386)(327,390)(328,389)
(329,388)(330,387)(331,391)(332,395)(333,394)(334,393)(335,392)(336,396)
(337,400)(338,399)(339,398)(340,397)(341,401)(342,405)(343,404)(344,403)
(345,402)(346,406)(347,410)(348,409)(349,408)(350,407)(351,411)(352,415)
(353,414)(354,413)(355,412)(356,416)(357,420)(358,419)(359,418)(360,417)
(481,661)(482,665)(483,664)(484,663)(485,662)(486,666)(487,670)(488,669)
(489,668)(490,667)(491,671)(492,675)(493,674)(494,673)(495,672)(496,676)
(497,680)(498,679)(499,678)(500,677)(501,681)(502,685)(503,684)(504,683)
(505,682)(506,686)(507,690)(508,689)(509,688)(510,687)(511,691)(512,695)
(513,694)(514,693)(515,692)(516,696)(517,700)(518,699)(519,698)(520,697)
(521,701)(522,705)(523,704)(524,703)(525,702)(526,706)(527,710)(528,709)
(529,708)(530,707)(531,711)(532,715)(533,714)(534,713)(535,712)(536,716)
(537,720)(538,719)(539,718)(540,717)(541,601)(542,605)(543,604)(544,603)
(545,602)(546,606)(547,610)(548,609)(549,608)(550,607)(551,611)(552,615)
(553,614)(554,613)(555,612)(556,616)(557,620)(558,619)(559,618)(560,617)
(561,621)(562,625)(563,624)(564,623)(565,622)(566,626)(567,630)(568,629)
(569,628)(570,627)(571,631)(572,635)(573,634)(574,633)(575,632)(576,636)
(577,640)(578,639)(579,638)(580,637)(581,641)(582,645)(583,644)(584,643)
(585,642)(586,646)(587,650)(588,649)(589,648)(590,647)(591,651)(592,655)
(593,654)(594,653)(595,652)(596,656)(597,660)(598,659)(599,658)(600,657)
(721,901)(722,905)(723,904)(724,903)(725,902)(726,906)(727,910)(728,909)
(729,908)(730,907)(731,911)(732,915)(733,914)(734,913)(735,912)(736,916)
(737,920)(738,919)(739,918)(740,917)(741,921)(742,925)(743,924)(744,923)
(745,922)(746,926)(747,930)(748,929)(749,928)(750,927)(751,931)(752,935)
(753,934)(754,933)(755,932)(756,936)(757,940)(758,939)(759,938)(760,937)
(761,941)(762,945)(763,944)(764,943)(765,942)(766,946)(767,950)(768,949)
(769,948)(770,947)(771,951)(772,955)(773,954)(774,953)(775,952)(776,956)
(777,960)(778,959)(779,958)(780,957)(781,841)(782,845)(783,844)(784,843)
(785,842)(786,846)(787,850)(788,849)(789,848)(790,847)(791,851)(792,855)
(793,854)(794,853)(795,852)(796,856)(797,860)(798,859)(799,858)(800,857)
(801,861)(802,865)(803,864)(804,863)(805,862)(806,866)(807,870)(808,869)
(809,868)(810,867)(811,871)(812,875)(813,874)(814,873)(815,872)(816,876)
(817,880)(818,879)(819,878)(820,877)(821,881)(822,885)(823,884)(824,883)
(825,882)(826,886)(827,890)(828,889)(829,888)(830,887)(831,891)(832,895)
(833,894)(834,893)(835,892)(836,896)(837,900)(838,899)(839,898)(840,897);;
s2 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)( 8, 75)
( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)( 24, 89)
( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)( 32, 91)
( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)( 40,103)
( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)( 48,110)
( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)( 56,112)
( 57,111)( 58,115)( 59,114)( 60,113)(121,182)(122,181)(123,185)(124,184)
(125,183)(126,192)(127,191)(128,195)(129,194)(130,193)(131,187)(132,186)
(133,190)(134,189)(135,188)(136,197)(137,196)(138,200)(139,199)(140,198)
(141,207)(142,206)(143,210)(144,209)(145,208)(146,202)(147,201)(148,205)
(149,204)(150,203)(151,212)(152,211)(153,215)(154,214)(155,213)(156,222)
(157,221)(158,225)(159,224)(160,223)(161,217)(162,216)(163,220)(164,219)
(165,218)(166,227)(167,226)(168,230)(169,229)(170,228)(171,237)(172,236)
(173,240)(174,239)(175,238)(176,232)(177,231)(178,235)(179,234)(180,233)
(241,302)(242,301)(243,305)(244,304)(245,303)(246,312)(247,311)(248,315)
(249,314)(250,313)(251,307)(252,306)(253,310)(254,309)(255,308)(256,317)
(257,316)(258,320)(259,319)(260,318)(261,327)(262,326)(263,330)(264,329)
(265,328)(266,322)(267,321)(268,325)(269,324)(270,323)(271,332)(272,331)
(273,335)(274,334)(275,333)(276,342)(277,341)(278,345)(279,344)(280,343)
(281,337)(282,336)(283,340)(284,339)(285,338)(286,347)(287,346)(288,350)
(289,349)(290,348)(291,357)(292,356)(293,360)(294,359)(295,358)(296,352)
(297,351)(298,355)(299,354)(300,353)(361,422)(362,421)(363,425)(364,424)
(365,423)(366,432)(367,431)(368,435)(369,434)(370,433)(371,427)(372,426)
(373,430)(374,429)(375,428)(376,437)(377,436)(378,440)(379,439)(380,438)
(381,447)(382,446)(383,450)(384,449)(385,448)(386,442)(387,441)(388,445)
(389,444)(390,443)(391,452)(392,451)(393,455)(394,454)(395,453)(396,462)
(397,461)(398,465)(399,464)(400,463)(401,457)(402,456)(403,460)(404,459)
(405,458)(406,467)(407,466)(408,470)(409,469)(410,468)(411,477)(412,476)
(413,480)(414,479)(415,478)(416,472)(417,471)(418,475)(419,474)(420,473)
(481,542)(482,541)(483,545)(484,544)(485,543)(486,552)(487,551)(488,555)
(489,554)(490,553)(491,547)(492,546)(493,550)(494,549)(495,548)(496,557)
(497,556)(498,560)(499,559)(500,558)(501,567)(502,566)(503,570)(504,569)
(505,568)(506,562)(507,561)(508,565)(509,564)(510,563)(511,572)(512,571)
(513,575)(514,574)(515,573)(516,582)(517,581)(518,585)(519,584)(520,583)
(521,577)(522,576)(523,580)(524,579)(525,578)(526,587)(527,586)(528,590)
(529,589)(530,588)(531,597)(532,596)(533,600)(534,599)(535,598)(536,592)
(537,591)(538,595)(539,594)(540,593)(601,662)(602,661)(603,665)(604,664)
(605,663)(606,672)(607,671)(608,675)(609,674)(610,673)(611,667)(612,666)
(613,670)(614,669)(615,668)(616,677)(617,676)(618,680)(619,679)(620,678)
(621,687)(622,686)(623,690)(624,689)(625,688)(626,682)(627,681)(628,685)
(629,684)(630,683)(631,692)(632,691)(633,695)(634,694)(635,693)(636,702)
(637,701)(638,705)(639,704)(640,703)(641,697)(642,696)(643,700)(644,699)
(645,698)(646,707)(647,706)(648,710)(649,709)(650,708)(651,717)(652,716)
(653,720)(654,719)(655,718)(656,712)(657,711)(658,715)(659,714)(660,713)
(721,782)(722,781)(723,785)(724,784)(725,783)(726,792)(727,791)(728,795)
(729,794)(730,793)(731,787)(732,786)(733,790)(734,789)(735,788)(736,797)
(737,796)(738,800)(739,799)(740,798)(741,807)(742,806)(743,810)(744,809)
(745,808)(746,802)(747,801)(748,805)(749,804)(750,803)(751,812)(752,811)
(753,815)(754,814)(755,813)(756,822)(757,821)(758,825)(759,824)(760,823)
(761,817)(762,816)(763,820)(764,819)(765,818)(766,827)(767,826)(768,830)
(769,829)(770,828)(771,837)(772,836)(773,840)(774,839)(775,838)(776,832)
(777,831)(778,835)(779,834)(780,833)(841,902)(842,901)(843,905)(844,904)
(845,903)(846,912)(847,911)(848,915)(849,914)(850,913)(851,907)(852,906)
(853,910)(854,909)(855,908)(856,917)(857,916)(858,920)(859,919)(860,918)
(861,927)(862,926)(863,930)(864,929)(865,928)(866,922)(867,921)(868,925)
(869,924)(870,923)(871,932)(872,931)(873,935)(874,934)(875,933)(876,942)
(877,941)(878,945)(879,944)(880,943)(881,937)(882,936)(883,940)(884,939)
(885,938)(886,947)(887,946)(888,950)(889,949)(890,948)(891,957)(892,956)
(893,960)(894,959)(895,958)(896,952)(897,951)(898,955)(899,954)(900,953);;
s3 := ( 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)
(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)(248,378)
(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)(256,366)
(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)(264,364)
(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)(272,412)
(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)(280,410)
(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)(288,398)
(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)(296,401)
(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)(304,444)
(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)(312,447)
(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)(320,430)
(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)(328,433)
(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)(336,466)
(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)(344,479)
(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)(352,452)
(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)(360,465)
(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)(488,633)
(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)(496,651)
(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)(504,649)
(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)(512,607)
(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)(520,605)
(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)(528,623)
(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)(536,626)
(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)(544,699)
(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)(552,702)
(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)(560,715)
(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)(568,718)
(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)(576,661)
(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)(584,674)
(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)(592,677)
(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)(600,690)
(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)(728,888)
(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)(736,876)
(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)(744,874)
(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)(752,862)
(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)(760,860)
(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)(768,848)
(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)(776,851)
(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)(784,954)
(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)(792,957)
(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)(800,940)
(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)(808,943)
(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)(816,916)
(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)(824,929)
(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)(832,902)
(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)(840,915);;
s4 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
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*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)
(184,694)(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)
(192,702)(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)
(200,710)(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)
(208,718)(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)
(216,666)(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)
(224,674)(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)
(232,682)(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)
(240,690)(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)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)
(424,934)(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)
(432,942)(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)
(440,950)(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)
(448,958)(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)
(456,906)(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)
(464,914)(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)
(472,922)(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)
(480,930);
s1 := Sym(960)!( 1,181)( 2,185)( 3,184)( 4,183)( 5,182)( 6,186)( 7,190)
( 8,189)( 9,188)( 10,187)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)
( 16,196)( 17,200)( 18,199)( 19,198)( 20,197)( 21,201)( 22,205)( 23,204)
( 24,203)( 25,202)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,211)
( 32,215)( 33,214)( 34,213)( 35,212)( 36,216)( 37,220)( 38,219)( 39,218)
( 40,217)( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,226)( 47,230)
( 48,229)( 49,228)( 50,227)( 51,231)( 52,235)( 53,234)( 54,233)( 55,232)
( 56,236)( 57,240)( 58,239)( 59,238)( 60,237)( 61,121)( 62,125)( 63,124)
( 64,123)( 65,122)( 66,126)( 67,130)( 68,129)( 69,128)( 70,127)( 71,131)
( 72,135)( 73,134)( 74,133)( 75,132)( 76,136)( 77,140)( 78,139)( 79,138)
( 80,137)( 81,141)( 82,145)( 83,144)( 84,143)( 85,142)( 86,146)( 87,150)
( 88,149)( 89,148)( 90,147)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)
( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)
(104,163)(105,162)(106,166)(107,170)(108,169)(109,168)(110,167)(111,171)
(112,175)(113,174)(114,173)(115,172)(116,176)(117,180)(118,179)(119,178)
(120,177)(241,421)(242,425)(243,424)(244,423)(245,422)(246,426)(247,430)
(248,429)(249,428)(250,427)(251,431)(252,435)(253,434)(254,433)(255,432)
(256,436)(257,440)(258,439)(259,438)(260,437)(261,441)(262,445)(263,444)
(264,443)(265,442)(266,446)(267,450)(268,449)(269,448)(270,447)(271,451)
(272,455)(273,454)(274,453)(275,452)(276,456)(277,460)(278,459)(279,458)
(280,457)(281,461)(282,465)(283,464)(284,463)(285,462)(286,466)(287,470)
(288,469)(289,468)(290,467)(291,471)(292,475)(293,474)(294,473)(295,472)
(296,476)(297,480)(298,479)(299,478)(300,477)(301,361)(302,365)(303,364)
(304,363)(305,362)(306,366)(307,370)(308,369)(309,368)(310,367)(311,371)
(312,375)(313,374)(314,373)(315,372)(316,376)(317,380)(318,379)(319,378)
(320,377)(321,381)(322,385)(323,384)(324,383)(325,382)(326,386)(327,390)
(328,389)(329,388)(330,387)(331,391)(332,395)(333,394)(334,393)(335,392)
(336,396)(337,400)(338,399)(339,398)(340,397)(341,401)(342,405)(343,404)
(344,403)(345,402)(346,406)(347,410)(348,409)(349,408)(350,407)(351,411)
(352,415)(353,414)(354,413)(355,412)(356,416)(357,420)(358,419)(359,418)
(360,417)(481,661)(482,665)(483,664)(484,663)(485,662)(486,666)(487,670)
(488,669)(489,668)(490,667)(491,671)(492,675)(493,674)(494,673)(495,672)
(496,676)(497,680)(498,679)(499,678)(500,677)(501,681)(502,685)(503,684)
(504,683)(505,682)(506,686)(507,690)(508,689)(509,688)(510,687)(511,691)
(512,695)(513,694)(514,693)(515,692)(516,696)(517,700)(518,699)(519,698)
(520,697)(521,701)(522,705)(523,704)(524,703)(525,702)(526,706)(527,710)
(528,709)(529,708)(530,707)(531,711)(532,715)(533,714)(534,713)(535,712)
(536,716)(537,720)(538,719)(539,718)(540,717)(541,601)(542,605)(543,604)
(544,603)(545,602)(546,606)(547,610)(548,609)(549,608)(550,607)(551,611)
(552,615)(553,614)(554,613)(555,612)(556,616)(557,620)(558,619)(559,618)
(560,617)(561,621)(562,625)(563,624)(564,623)(565,622)(566,626)(567,630)
(568,629)(569,628)(570,627)(571,631)(572,635)(573,634)(574,633)(575,632)
(576,636)(577,640)(578,639)(579,638)(580,637)(581,641)(582,645)(583,644)
(584,643)(585,642)(586,646)(587,650)(588,649)(589,648)(590,647)(591,651)
(592,655)(593,654)(594,653)(595,652)(596,656)(597,660)(598,659)(599,658)
(600,657)(721,901)(722,905)(723,904)(724,903)(725,902)(726,906)(727,910)
(728,909)(729,908)(730,907)(731,911)(732,915)(733,914)(734,913)(735,912)
(736,916)(737,920)(738,919)(739,918)(740,917)(741,921)(742,925)(743,924)
(744,923)(745,922)(746,926)(747,930)(748,929)(749,928)(750,927)(751,931)
(752,935)(753,934)(754,933)(755,932)(756,936)(757,940)(758,939)(759,938)
(760,937)(761,941)(762,945)(763,944)(764,943)(765,942)(766,946)(767,950)
(768,949)(769,948)(770,947)(771,951)(772,955)(773,954)(774,953)(775,952)
(776,956)(777,960)(778,959)(779,958)(780,957)(781,841)(782,845)(783,844)
(784,843)(785,842)(786,846)(787,850)(788,849)(789,848)(790,847)(791,851)
(792,855)(793,854)(794,853)(795,852)(796,856)(797,860)(798,859)(799,858)
(800,857)(801,861)(802,865)(803,864)(804,863)(805,862)(806,866)(807,870)
(808,869)(809,868)(810,867)(811,871)(812,875)(813,874)(814,873)(815,872)
(816,876)(817,880)(818,879)(819,878)(820,877)(821,881)(822,885)(823,884)
(824,883)(825,882)(826,886)(827,890)(828,889)(829,888)(830,887)(831,891)
(832,895)(833,894)(834,893)(835,892)(836,896)(837,900)(838,899)(839,898)
(840,897);
s2 := Sym(960)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 72)( 7, 71)
( 8, 75)( 9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)
( 24, 89)( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31, 92)
( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36,102)( 37,101)( 38,105)( 39,104)
( 40,103)( 41, 97)( 42, 96)( 43,100)( 44, 99)( 45, 98)( 46,107)( 47,106)
( 48,110)( 49,109)( 50,108)( 51,117)( 52,116)( 53,120)( 54,119)( 55,118)
( 56,112)( 57,111)( 58,115)( 59,114)( 60,113)(121,182)(122,181)(123,185)
(124,184)(125,183)(126,192)(127,191)(128,195)(129,194)(130,193)(131,187)
(132,186)(133,190)(134,189)(135,188)(136,197)(137,196)(138,200)(139,199)
(140,198)(141,207)(142,206)(143,210)(144,209)(145,208)(146,202)(147,201)
(148,205)(149,204)(150,203)(151,212)(152,211)(153,215)(154,214)(155,213)
(156,222)(157,221)(158,225)(159,224)(160,223)(161,217)(162,216)(163,220)
(164,219)(165,218)(166,227)(167,226)(168,230)(169,229)(170,228)(171,237)
(172,236)(173,240)(174,239)(175,238)(176,232)(177,231)(178,235)(179,234)
(180,233)(241,302)(242,301)(243,305)(244,304)(245,303)(246,312)(247,311)
(248,315)(249,314)(250,313)(251,307)(252,306)(253,310)(254,309)(255,308)
(256,317)(257,316)(258,320)(259,319)(260,318)(261,327)(262,326)(263,330)
(264,329)(265,328)(266,322)(267,321)(268,325)(269,324)(270,323)(271,332)
(272,331)(273,335)(274,334)(275,333)(276,342)(277,341)(278,345)(279,344)
(280,343)(281,337)(282,336)(283,340)(284,339)(285,338)(286,347)(287,346)
(288,350)(289,349)(290,348)(291,357)(292,356)(293,360)(294,359)(295,358)
(296,352)(297,351)(298,355)(299,354)(300,353)(361,422)(362,421)(363,425)
(364,424)(365,423)(366,432)(367,431)(368,435)(369,434)(370,433)(371,427)
(372,426)(373,430)(374,429)(375,428)(376,437)(377,436)(378,440)(379,439)
(380,438)(381,447)(382,446)(383,450)(384,449)(385,448)(386,442)(387,441)
(388,445)(389,444)(390,443)(391,452)(392,451)(393,455)(394,454)(395,453)
(396,462)(397,461)(398,465)(399,464)(400,463)(401,457)(402,456)(403,460)
(404,459)(405,458)(406,467)(407,466)(408,470)(409,469)(410,468)(411,477)
(412,476)(413,480)(414,479)(415,478)(416,472)(417,471)(418,475)(419,474)
(420,473)(481,542)(482,541)(483,545)(484,544)(485,543)(486,552)(487,551)
(488,555)(489,554)(490,553)(491,547)(492,546)(493,550)(494,549)(495,548)
(496,557)(497,556)(498,560)(499,559)(500,558)(501,567)(502,566)(503,570)
(504,569)(505,568)(506,562)(507,561)(508,565)(509,564)(510,563)(511,572)
(512,571)(513,575)(514,574)(515,573)(516,582)(517,581)(518,585)(519,584)
(520,583)(521,577)(522,576)(523,580)(524,579)(525,578)(526,587)(527,586)
(528,590)(529,589)(530,588)(531,597)(532,596)(533,600)(534,599)(535,598)
(536,592)(537,591)(538,595)(539,594)(540,593)(601,662)(602,661)(603,665)
(604,664)(605,663)(606,672)(607,671)(608,675)(609,674)(610,673)(611,667)
(612,666)(613,670)(614,669)(615,668)(616,677)(617,676)(618,680)(619,679)
(620,678)(621,687)(622,686)(623,690)(624,689)(625,688)(626,682)(627,681)
(628,685)(629,684)(630,683)(631,692)(632,691)(633,695)(634,694)(635,693)
(636,702)(637,701)(638,705)(639,704)(640,703)(641,697)(642,696)(643,700)
(644,699)(645,698)(646,707)(647,706)(648,710)(649,709)(650,708)(651,717)
(652,716)(653,720)(654,719)(655,718)(656,712)(657,711)(658,715)(659,714)
(660,713)(721,782)(722,781)(723,785)(724,784)(725,783)(726,792)(727,791)
(728,795)(729,794)(730,793)(731,787)(732,786)(733,790)(734,789)(735,788)
(736,797)(737,796)(738,800)(739,799)(740,798)(741,807)(742,806)(743,810)
(744,809)(745,808)(746,802)(747,801)(748,805)(749,804)(750,803)(751,812)
(752,811)(753,815)(754,814)(755,813)(756,822)(757,821)(758,825)(759,824)
(760,823)(761,817)(762,816)(763,820)(764,819)(765,818)(766,827)(767,826)
(768,830)(769,829)(770,828)(771,837)(772,836)(773,840)(774,839)(775,838)
(776,832)(777,831)(778,835)(779,834)(780,833)(841,902)(842,901)(843,905)
(844,904)(845,903)(846,912)(847,911)(848,915)(849,914)(850,913)(851,907)
(852,906)(853,910)(854,909)(855,908)(856,917)(857,916)(858,920)(859,919)
(860,918)(861,927)(862,926)(863,930)(864,929)(865,928)(866,922)(867,921)
(868,925)(869,924)(870,923)(871,932)(872,931)(873,935)(874,934)(875,933)
(876,942)(877,941)(878,945)(879,944)(880,943)(881,937)(882,936)(883,940)
(884,939)(885,938)(886,947)(887,946)(888,950)(889,949)(890,948)(891,957)
(892,956)(893,960)(894,959)(895,958)(896,952)(897,951)(898,955)(899,954)
(900,953);
s3 := 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)(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)
(248,378)(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)
(256,366)(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)
(264,364)(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)
(272,412)(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)
(280,410)(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)
(288,398)(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)
(296,401)(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)
(304,444)(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)
(312,447)(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)
(320,430)(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)
(328,433)(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)
(336,466)(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)
(344,479)(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)
(352,452)(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)
(360,465)(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)
(488,633)(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)
(496,651)(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)
(504,649)(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)
(512,607)(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)
(520,605)(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)
(528,623)(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,626)(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)
(544,699)(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)
(552,702)(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)
(560,715)(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)
(568,718)(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)
(576,661)(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)
(584,674)(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)
(592,677)(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)
(600,690)(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)
(728,888)(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)
(736,876)(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)
(744,874)(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)
(752,862)(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)
(760,860)(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)
(768,848)(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)
(776,851)(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)
(784,954)(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)
(792,957)(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)
(800,940)(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)
(808,943)(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)
(816,916)(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)
(824,929)(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)
(832,902)(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)
(840,915);
s4 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
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*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope