Polytope of Type {6,4,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,10,4}*1920
Also Known As : {{6,4|2},{4,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,208118)
Rank : 5
Schlafli Type : {6,4,10,4}
Number of vertices, edges, etc : 6, 12, 20, 20, 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 : {6,2,10,4}*960, {6,4,10,2}*960
3-fold quotients : {2,4,10,4}*640
4-fold quotients : {3,2,10,4}*480, {6,2,10,2}*480
5-fold quotients : {6,4,2,4}*384a
6-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320
8-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
10-fold quotients : {6,2,2,4}*192, {6,4,2,2}*192a
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,4,2,4}*128
16-fold quotients : {3,2,5,2}*120
20-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
40-fold quotients : {3,2,2,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 65)( 6, 71)( 7, 72)( 8, 73)
( 9, 74)( 10, 75)( 11, 66)( 12, 67)( 13, 68)( 14, 69)( 15, 70)( 16, 76)
( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 86)( 22, 87)( 23, 88)( 24, 89)
( 25, 90)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 91)( 32, 92)
( 33, 93)( 34, 94)( 35, 95)( 36,101)( 37,102)( 38,103)( 39,104)( 40,105)
( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45,100)( 46,106)( 47,107)( 48,108)
( 49,109)( 50,110)( 51,116)( 52,117)( 53,118)( 54,119)( 55,120)( 56,111)
( 57,112)( 58,113)( 59,114)( 60,115)(121,181)(122,182)(123,183)(124,184)
(125,185)(126,191)(127,192)(128,193)(129,194)(130,195)(131,186)(132,187)
(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)(140,200)
(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)(148,203)
(149,204)(150,205)(151,211)(152,212)(153,213)(154,214)(155,215)(156,221)
(157,222)(158,223)(159,224)(160,225)(161,216)(162,217)(163,218)(164,219)
(165,220)(166,226)(167,227)(168,228)(169,229)(170,230)(171,236)(172,237)
(173,238)(174,239)(175,240)(176,231)(177,232)(178,233)(179,234)(180,235)
(241,301)(242,302)(243,303)(244,304)(245,305)(246,311)(247,312)(248,313)
(249,314)(250,315)(251,306)(252,307)(253,308)(254,309)(255,310)(256,316)
(257,317)(258,318)(259,319)(260,320)(261,326)(262,327)(263,328)(264,329)
(265,330)(266,321)(267,322)(268,323)(269,324)(270,325)(271,331)(272,332)
(273,333)(274,334)(275,335)(276,341)(277,342)(278,343)(279,344)(280,345)
(281,336)(282,337)(283,338)(284,339)(285,340)(286,346)(287,347)(288,348)
(289,349)(290,350)(291,356)(292,357)(293,358)(294,359)(295,360)(296,351)
(297,352)(298,353)(299,354)(300,355)(361,421)(362,422)(363,423)(364,424)
(365,425)(366,431)(367,432)(368,433)(369,434)(370,435)(371,426)(372,427)
(373,428)(374,429)(375,430)(376,436)(377,437)(378,438)(379,439)(380,440)
(381,446)(382,447)(383,448)(384,449)(385,450)(386,441)(387,442)(388,443)
(389,444)(390,445)(391,451)(392,452)(393,453)(394,454)(395,455)(396,461)
(397,462)(398,463)(399,464)(400,465)(401,456)(402,457)(403,458)(404,459)
(405,460)(406,466)(407,467)(408,468)(409,469)(410,470)(411,476)(412,477)
(413,478)(414,479)(415,480)(416,471)(417,472)(418,473)(419,474)(420,475)
(481,541)(482,542)(483,543)(484,544)(485,545)(486,551)(487,552)(488,553)
(489,554)(490,555)(491,546)(492,547)(493,548)(494,549)(495,550)(496,556)
(497,557)(498,558)(499,559)(500,560)(501,566)(502,567)(503,568)(504,569)
(505,570)(506,561)(507,562)(508,563)(509,564)(510,565)(511,571)(512,572)
(513,573)(514,574)(515,575)(516,581)(517,582)(518,583)(519,584)(520,585)
(521,576)(522,577)(523,578)(524,579)(525,580)(526,586)(527,587)(528,588)
(529,589)(530,590)(531,596)(532,597)(533,598)(534,599)(535,600)(536,591)
(537,592)(538,593)(539,594)(540,595)(601,661)(602,662)(603,663)(604,664)
(605,665)(606,671)(607,672)(608,673)(609,674)(610,675)(611,666)(612,667)
(613,668)(614,669)(615,670)(616,676)(617,677)(618,678)(619,679)(620,680)
(621,686)(622,687)(623,688)(624,689)(625,690)(626,681)(627,682)(628,683)
(629,684)(630,685)(631,691)(632,692)(633,693)(634,694)(635,695)(636,701)
(637,702)(638,703)(639,704)(640,705)(641,696)(642,697)(643,698)(644,699)
(645,700)(646,706)(647,707)(648,708)(649,709)(650,710)(651,716)(652,717)
(653,718)(654,719)(655,720)(656,711)(657,712)(658,713)(659,714)(660,715)
(721,781)(722,782)(723,783)(724,784)(725,785)(726,791)(727,792)(728,793)
(729,794)(730,795)(731,786)(732,787)(733,788)(734,789)(735,790)(736,796)
(737,797)(738,798)(739,799)(740,800)(741,806)(742,807)(743,808)(744,809)
(745,810)(746,801)(747,802)(748,803)(749,804)(750,805)(751,811)(752,812)
(753,813)(754,814)(755,815)(756,821)(757,822)(758,823)(759,824)(760,825)
(761,816)(762,817)(763,818)(764,819)(765,820)(766,826)(767,827)(768,828)
(769,829)(770,830)(771,836)(772,837)(773,838)(774,839)(775,840)(776,831)
(777,832)(778,833)(779,834)(780,835)(841,901)(842,902)(843,903)(844,904)
(845,905)(846,911)(847,912)(848,913)(849,914)(850,915)(851,906)(852,907)
(853,908)(854,909)(855,910)(856,916)(857,917)(858,918)(859,919)(860,920)
(861,926)(862,927)(863,928)(864,929)(865,930)(866,921)(867,922)(868,923)
(869,924)(870,925)(871,931)(872,932)(873,933)(874,934)(875,935)(876,941)
(877,942)(878,943)(879,944)(880,945)(881,936)(882,937)(883,938)(884,939)
(885,940)(886,946)(887,947)(888,948)(889,949)(890,950)(891,956)(892,957)
(893,958)(894,959)(895,960)(896,951)(897,952)(898,953)(899,954)(900,955);;
s1 := ( 1,546)( 2,547)( 3,548)( 4,549)( 5,550)( 6,541)( 7,542)( 8,543)
( 9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)( 16,561)
( 17,562)( 18,563)( 19,564)( 20,565)( 21,556)( 22,557)( 23,558)( 24,559)
( 25,560)( 26,566)( 27,567)( 28,568)( 29,569)( 30,570)( 31,576)( 32,577)
( 33,578)( 34,579)( 35,580)( 36,571)( 37,572)( 38,573)( 39,574)( 40,575)
( 41,581)( 42,582)( 43,583)( 44,584)( 45,585)( 46,591)( 47,592)( 48,593)
( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)( 56,596)
( 57,597)( 58,598)( 59,599)( 60,600)( 61,486)( 62,487)( 63,488)( 64,489)
( 65,490)( 66,481)( 67,482)( 68,483)( 69,484)( 70,485)( 71,491)( 72,492)
( 73,493)( 74,494)( 75,495)( 76,501)( 77,502)( 78,503)( 79,504)( 80,505)
( 81,496)( 82,497)( 83,498)( 84,499)( 85,500)( 86,506)( 87,507)( 88,508)
( 89,509)( 90,510)( 91,516)( 92,517)( 93,518)( 94,519)( 95,520)( 96,511)
( 97,512)( 98,513)( 99,514)(100,515)(101,521)(102,522)(103,523)(104,524)
(105,525)(106,531)(107,532)(108,533)(109,534)(110,535)(111,526)(112,527)
(113,528)(114,529)(115,530)(116,536)(117,537)(118,538)(119,539)(120,540)
(121,696)(122,697)(123,698)(124,699)(125,700)(126,691)(127,692)(128,693)
(129,694)(130,695)(131,701)(132,702)(133,703)(134,704)(135,705)(136,711)
(137,712)(138,713)(139,714)(140,715)(141,706)(142,707)(143,708)(144,709)
(145,710)(146,716)(147,717)(148,718)(149,719)(150,720)(151,666)(152,667)
(153,668)(154,669)(155,670)(156,661)(157,662)(158,663)(159,664)(160,665)
(161,671)(162,672)(163,673)(164,674)(165,675)(166,681)(167,682)(168,683)
(169,684)(170,685)(171,676)(172,677)(173,678)(174,679)(175,680)(176,686)
(177,687)(178,688)(179,689)(180,690)(181,636)(182,637)(183,638)(184,639)
(185,640)(186,631)(187,632)(188,633)(189,634)(190,635)(191,641)(192,642)
(193,643)(194,644)(195,645)(196,651)(197,652)(198,653)(199,654)(200,655)
(201,646)(202,647)(203,648)(204,649)(205,650)(206,656)(207,657)(208,658)
(209,659)(210,660)(211,606)(212,607)(213,608)(214,609)(215,610)(216,601)
(217,602)(218,603)(219,604)(220,605)(221,611)(222,612)(223,613)(224,614)
(225,615)(226,621)(227,622)(228,623)(229,624)(230,625)(231,616)(232,617)
(233,618)(234,619)(235,620)(236,626)(237,627)(238,628)(239,629)(240,630)
(241,786)(242,787)(243,788)(244,789)(245,790)(246,781)(247,782)(248,783)
(249,784)(250,785)(251,791)(252,792)(253,793)(254,794)(255,795)(256,801)
(257,802)(258,803)(259,804)(260,805)(261,796)(262,797)(263,798)(264,799)
(265,800)(266,806)(267,807)(268,808)(269,809)(270,810)(271,816)(272,817)
(273,818)(274,819)(275,820)(276,811)(277,812)(278,813)(279,814)(280,815)
(281,821)(282,822)(283,823)(284,824)(285,825)(286,831)(287,832)(288,833)
(289,834)(290,835)(291,826)(292,827)(293,828)(294,829)(295,830)(296,836)
(297,837)(298,838)(299,839)(300,840)(301,726)(302,727)(303,728)(304,729)
(305,730)(306,721)(307,722)(308,723)(309,724)(310,725)(311,731)(312,732)
(313,733)(314,734)(315,735)(316,741)(317,742)(318,743)(319,744)(320,745)
(321,736)(322,737)(323,738)(324,739)(325,740)(326,746)(327,747)(328,748)
(329,749)(330,750)(331,756)(332,757)(333,758)(334,759)(335,760)(336,751)
(337,752)(338,753)(339,754)(340,755)(341,761)(342,762)(343,763)(344,764)
(345,765)(346,771)(347,772)(348,773)(349,774)(350,775)(351,766)(352,767)
(353,768)(354,769)(355,770)(356,776)(357,777)(358,778)(359,779)(360,780)
(361,936)(362,937)(363,938)(364,939)(365,940)(366,931)(367,932)(368,933)
(369,934)(370,935)(371,941)(372,942)(373,943)(374,944)(375,945)(376,951)
(377,952)(378,953)(379,954)(380,955)(381,946)(382,947)(383,948)(384,949)
(385,950)(386,956)(387,957)(388,958)(389,959)(390,960)(391,906)(392,907)
(393,908)(394,909)(395,910)(396,901)(397,902)(398,903)(399,904)(400,905)
(401,911)(402,912)(403,913)(404,914)(405,915)(406,921)(407,922)(408,923)
(409,924)(410,925)(411,916)(412,917)(413,918)(414,919)(415,920)(416,926)
(417,927)(418,928)(419,929)(420,930)(421,876)(422,877)(423,878)(424,879)
(425,880)(426,871)(427,872)(428,873)(429,874)(430,875)(431,881)(432,882)
(433,883)(434,884)(435,885)(436,891)(437,892)(438,893)(439,894)(440,895)
(441,886)(442,887)(443,888)(444,889)(445,890)(446,896)(447,897)(448,898)
(449,899)(450,900)(451,846)(452,847)(453,848)(454,849)(455,850)(456,841)
(457,842)(458,843)(459,844)(460,845)(461,851)(462,852)(463,853)(464,854)
(465,855)(466,861)(467,862)(468,863)(469,864)(470,865)(471,856)(472,857)
(473,858)(474,859)(475,860)(476,866)(477,867)(478,868)(479,869)(480,870);;
s2 := ( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,126)( 7,130)( 8,129)
( 9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)( 24,143)
( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)(248,369)
(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)(264,383)
(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)(280,397)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)(296,416)
(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)(304,423)
(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)(312,435)
(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)(328,449)
(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)(336,456)
(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)(344,463)
(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)(352,475)
(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)(360,477)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)
(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)(504,623)
(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)(520,637)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)(552,675)
(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)(568,689)
(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)(576,696)
(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)(584,703)
(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)(592,715)
(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)(600,717)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)(728,849)
(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)(744,863)
(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)(760,877)
(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)(776,896)
(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)(784,903)
(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)(792,915)
(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)(800,917)
(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)(808,929)
(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)(816,936)
(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)(824,943)
(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)(832,955)
(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)(840,957);;
s3 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)
( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,377)(242,376)(243,380)(244,379)(245,378)(246,382)(247,381)(248,385)
(249,384)(250,383)(251,387)(252,386)(253,390)(254,389)(255,388)(256,362)
(257,361)(258,365)(259,364)(260,363)(261,367)(262,366)(263,370)(264,369)
(265,368)(266,372)(267,371)(268,375)(269,374)(270,373)(271,407)(272,406)
(273,410)(274,409)(275,408)(276,412)(277,411)(278,415)(279,414)(280,413)
(281,417)(282,416)(283,420)(284,419)(285,418)(286,392)(287,391)(288,395)
(289,394)(290,393)(291,397)(292,396)(293,400)(294,399)(295,398)(296,402)
(297,401)(298,405)(299,404)(300,403)(301,437)(302,436)(303,440)(304,439)
(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)(312,446)
(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)(320,423)
(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)(328,435)
(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)(336,472)
(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)(344,479)
(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)(352,456)
(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)(360,463)
(481,632)(482,631)(483,635)(484,634)(485,633)(486,637)(487,636)(488,640)
(489,639)(490,638)(491,642)(492,641)(493,645)(494,644)(495,643)(496,647)
(497,646)(498,650)(499,649)(500,648)(501,652)(502,651)(503,655)(504,654)
(505,653)(506,657)(507,656)(508,660)(509,659)(510,658)(511,602)(512,601)
(513,605)(514,604)(515,603)(516,607)(517,606)(518,610)(519,609)(520,608)
(521,612)(522,611)(523,615)(524,614)(525,613)(526,617)(527,616)(528,620)
(529,619)(530,618)(531,622)(532,621)(533,625)(534,624)(535,623)(536,627)
(537,626)(538,630)(539,629)(540,628)(541,692)(542,691)(543,695)(544,694)
(545,693)(546,697)(547,696)(548,700)(549,699)(550,698)(551,702)(552,701)
(553,705)(554,704)(555,703)(556,707)(557,706)(558,710)(559,709)(560,708)
(561,712)(562,711)(563,715)(564,714)(565,713)(566,717)(567,716)(568,720)
(569,719)(570,718)(571,662)(572,661)(573,665)(574,664)(575,663)(576,667)
(577,666)(578,670)(579,669)(580,668)(581,672)(582,671)(583,675)(584,674)
(585,673)(586,677)(587,676)(588,680)(589,679)(590,678)(591,682)(592,681)
(593,685)(594,684)(595,683)(596,687)(597,686)(598,690)(599,689)(600,688)
(721,887)(722,886)(723,890)(724,889)(725,888)(726,892)(727,891)(728,895)
(729,894)(730,893)(731,897)(732,896)(733,900)(734,899)(735,898)(736,872)
(737,871)(738,875)(739,874)(740,873)(741,877)(742,876)(743,880)(744,879)
(745,878)(746,882)(747,881)(748,885)(749,884)(750,883)(751,857)(752,856)
(753,860)(754,859)(755,858)(756,862)(757,861)(758,865)(759,864)(760,863)
(761,867)(762,866)(763,870)(764,869)(765,868)(766,842)(767,841)(768,845)
(769,844)(770,843)(771,847)(772,846)(773,850)(774,849)(775,848)(776,852)
(777,851)(778,855)(779,854)(780,853)(781,947)(782,946)(783,950)(784,949)
(785,948)(786,952)(787,951)(788,955)(789,954)(790,953)(791,957)(792,956)
(793,960)(794,959)(795,958)(796,932)(797,931)(798,935)(799,934)(800,933)
(801,937)(802,936)(803,940)(804,939)(805,938)(806,942)(807,941)(808,945)
(809,944)(810,943)(811,917)(812,916)(813,920)(814,919)(815,918)(816,922)
(817,921)(818,925)(819,924)(820,923)(821,927)(822,926)(823,930)(824,929)
(825,928)(826,902)(827,901)(828,905)(829,904)(830,903)(831,907)(832,906)
(833,910)(834,909)(835,908)(836,912)(837,911)(838,915)(839,914)(840,913);;
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*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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 65)( 6, 71)( 7, 72)
( 8, 73)( 9, 74)( 10, 75)( 11, 66)( 12, 67)( 13, 68)( 14, 69)( 15, 70)
( 16, 76)( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 86)( 22, 87)( 23, 88)
( 24, 89)( 25, 90)( 26, 81)( 27, 82)( 28, 83)( 29, 84)( 30, 85)( 31, 91)
( 32, 92)( 33, 93)( 34, 94)( 35, 95)( 36,101)( 37,102)( 38,103)( 39,104)
( 40,105)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45,100)( 46,106)( 47,107)
( 48,108)( 49,109)( 50,110)( 51,116)( 52,117)( 53,118)( 54,119)( 55,120)
( 56,111)( 57,112)( 58,113)( 59,114)( 60,115)(121,181)(122,182)(123,183)
(124,184)(125,185)(126,191)(127,192)(128,193)(129,194)(130,195)(131,186)
(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)(138,198)(139,199)
(140,200)(141,206)(142,207)(143,208)(144,209)(145,210)(146,201)(147,202)
(148,203)(149,204)(150,205)(151,211)(152,212)(153,213)(154,214)(155,215)
(156,221)(157,222)(158,223)(159,224)(160,225)(161,216)(162,217)(163,218)
(164,219)(165,220)(166,226)(167,227)(168,228)(169,229)(170,230)(171,236)
(172,237)(173,238)(174,239)(175,240)(176,231)(177,232)(178,233)(179,234)
(180,235)(241,301)(242,302)(243,303)(244,304)(245,305)(246,311)(247,312)
(248,313)(249,314)(250,315)(251,306)(252,307)(253,308)(254,309)(255,310)
(256,316)(257,317)(258,318)(259,319)(260,320)(261,326)(262,327)(263,328)
(264,329)(265,330)(266,321)(267,322)(268,323)(269,324)(270,325)(271,331)
(272,332)(273,333)(274,334)(275,335)(276,341)(277,342)(278,343)(279,344)
(280,345)(281,336)(282,337)(283,338)(284,339)(285,340)(286,346)(287,347)
(288,348)(289,349)(290,350)(291,356)(292,357)(293,358)(294,359)(295,360)
(296,351)(297,352)(298,353)(299,354)(300,355)(361,421)(362,422)(363,423)
(364,424)(365,425)(366,431)(367,432)(368,433)(369,434)(370,435)(371,426)
(372,427)(373,428)(374,429)(375,430)(376,436)(377,437)(378,438)(379,439)
(380,440)(381,446)(382,447)(383,448)(384,449)(385,450)(386,441)(387,442)
(388,443)(389,444)(390,445)(391,451)(392,452)(393,453)(394,454)(395,455)
(396,461)(397,462)(398,463)(399,464)(400,465)(401,456)(402,457)(403,458)
(404,459)(405,460)(406,466)(407,467)(408,468)(409,469)(410,470)(411,476)
(412,477)(413,478)(414,479)(415,480)(416,471)(417,472)(418,473)(419,474)
(420,475)(481,541)(482,542)(483,543)(484,544)(485,545)(486,551)(487,552)
(488,553)(489,554)(490,555)(491,546)(492,547)(493,548)(494,549)(495,550)
(496,556)(497,557)(498,558)(499,559)(500,560)(501,566)(502,567)(503,568)
(504,569)(505,570)(506,561)(507,562)(508,563)(509,564)(510,565)(511,571)
(512,572)(513,573)(514,574)(515,575)(516,581)(517,582)(518,583)(519,584)
(520,585)(521,576)(522,577)(523,578)(524,579)(525,580)(526,586)(527,587)
(528,588)(529,589)(530,590)(531,596)(532,597)(533,598)(534,599)(535,600)
(536,591)(537,592)(538,593)(539,594)(540,595)(601,661)(602,662)(603,663)
(604,664)(605,665)(606,671)(607,672)(608,673)(609,674)(610,675)(611,666)
(612,667)(613,668)(614,669)(615,670)(616,676)(617,677)(618,678)(619,679)
(620,680)(621,686)(622,687)(623,688)(624,689)(625,690)(626,681)(627,682)
(628,683)(629,684)(630,685)(631,691)(632,692)(633,693)(634,694)(635,695)
(636,701)(637,702)(638,703)(639,704)(640,705)(641,696)(642,697)(643,698)
(644,699)(645,700)(646,706)(647,707)(648,708)(649,709)(650,710)(651,716)
(652,717)(653,718)(654,719)(655,720)(656,711)(657,712)(658,713)(659,714)
(660,715)(721,781)(722,782)(723,783)(724,784)(725,785)(726,791)(727,792)
(728,793)(729,794)(730,795)(731,786)(732,787)(733,788)(734,789)(735,790)
(736,796)(737,797)(738,798)(739,799)(740,800)(741,806)(742,807)(743,808)
(744,809)(745,810)(746,801)(747,802)(748,803)(749,804)(750,805)(751,811)
(752,812)(753,813)(754,814)(755,815)(756,821)(757,822)(758,823)(759,824)
(760,825)(761,816)(762,817)(763,818)(764,819)(765,820)(766,826)(767,827)
(768,828)(769,829)(770,830)(771,836)(772,837)(773,838)(774,839)(775,840)
(776,831)(777,832)(778,833)(779,834)(780,835)(841,901)(842,902)(843,903)
(844,904)(845,905)(846,911)(847,912)(848,913)(849,914)(850,915)(851,906)
(852,907)(853,908)(854,909)(855,910)(856,916)(857,917)(858,918)(859,919)
(860,920)(861,926)(862,927)(863,928)(864,929)(865,930)(866,921)(867,922)
(868,923)(869,924)(870,925)(871,931)(872,932)(873,933)(874,934)(875,935)
(876,941)(877,942)(878,943)(879,944)(880,945)(881,936)(882,937)(883,938)
(884,939)(885,940)(886,946)(887,947)(888,948)(889,949)(890,950)(891,956)
(892,957)(893,958)(894,959)(895,960)(896,951)(897,952)(898,953)(899,954)
(900,955);
s1 := Sym(960)!( 1,546)( 2,547)( 3,548)( 4,549)( 5,550)( 6,541)( 7,542)
( 8,543)( 9,544)( 10,545)( 11,551)( 12,552)( 13,553)( 14,554)( 15,555)
( 16,561)( 17,562)( 18,563)( 19,564)( 20,565)( 21,556)( 22,557)( 23,558)
( 24,559)( 25,560)( 26,566)( 27,567)( 28,568)( 29,569)( 30,570)( 31,576)
( 32,577)( 33,578)( 34,579)( 35,580)( 36,571)( 37,572)( 38,573)( 39,574)
( 40,575)( 41,581)( 42,582)( 43,583)( 44,584)( 45,585)( 46,591)( 47,592)
( 48,593)( 49,594)( 50,595)( 51,586)( 52,587)( 53,588)( 54,589)( 55,590)
( 56,596)( 57,597)( 58,598)( 59,599)( 60,600)( 61,486)( 62,487)( 63,488)
( 64,489)( 65,490)( 66,481)( 67,482)( 68,483)( 69,484)( 70,485)( 71,491)
( 72,492)( 73,493)( 74,494)( 75,495)( 76,501)( 77,502)( 78,503)( 79,504)
( 80,505)( 81,496)( 82,497)( 83,498)( 84,499)( 85,500)( 86,506)( 87,507)
( 88,508)( 89,509)( 90,510)( 91,516)( 92,517)( 93,518)( 94,519)( 95,520)
( 96,511)( 97,512)( 98,513)( 99,514)(100,515)(101,521)(102,522)(103,523)
(104,524)(105,525)(106,531)(107,532)(108,533)(109,534)(110,535)(111,526)
(112,527)(113,528)(114,529)(115,530)(116,536)(117,537)(118,538)(119,539)
(120,540)(121,696)(122,697)(123,698)(124,699)(125,700)(126,691)(127,692)
(128,693)(129,694)(130,695)(131,701)(132,702)(133,703)(134,704)(135,705)
(136,711)(137,712)(138,713)(139,714)(140,715)(141,706)(142,707)(143,708)
(144,709)(145,710)(146,716)(147,717)(148,718)(149,719)(150,720)(151,666)
(152,667)(153,668)(154,669)(155,670)(156,661)(157,662)(158,663)(159,664)
(160,665)(161,671)(162,672)(163,673)(164,674)(165,675)(166,681)(167,682)
(168,683)(169,684)(170,685)(171,676)(172,677)(173,678)(174,679)(175,680)
(176,686)(177,687)(178,688)(179,689)(180,690)(181,636)(182,637)(183,638)
(184,639)(185,640)(186,631)(187,632)(188,633)(189,634)(190,635)(191,641)
(192,642)(193,643)(194,644)(195,645)(196,651)(197,652)(198,653)(199,654)
(200,655)(201,646)(202,647)(203,648)(204,649)(205,650)(206,656)(207,657)
(208,658)(209,659)(210,660)(211,606)(212,607)(213,608)(214,609)(215,610)
(216,601)(217,602)(218,603)(219,604)(220,605)(221,611)(222,612)(223,613)
(224,614)(225,615)(226,621)(227,622)(228,623)(229,624)(230,625)(231,616)
(232,617)(233,618)(234,619)(235,620)(236,626)(237,627)(238,628)(239,629)
(240,630)(241,786)(242,787)(243,788)(244,789)(245,790)(246,781)(247,782)
(248,783)(249,784)(250,785)(251,791)(252,792)(253,793)(254,794)(255,795)
(256,801)(257,802)(258,803)(259,804)(260,805)(261,796)(262,797)(263,798)
(264,799)(265,800)(266,806)(267,807)(268,808)(269,809)(270,810)(271,816)
(272,817)(273,818)(274,819)(275,820)(276,811)(277,812)(278,813)(279,814)
(280,815)(281,821)(282,822)(283,823)(284,824)(285,825)(286,831)(287,832)
(288,833)(289,834)(290,835)(291,826)(292,827)(293,828)(294,829)(295,830)
(296,836)(297,837)(298,838)(299,839)(300,840)(301,726)(302,727)(303,728)
(304,729)(305,730)(306,721)(307,722)(308,723)(309,724)(310,725)(311,731)
(312,732)(313,733)(314,734)(315,735)(316,741)(317,742)(318,743)(319,744)
(320,745)(321,736)(322,737)(323,738)(324,739)(325,740)(326,746)(327,747)
(328,748)(329,749)(330,750)(331,756)(332,757)(333,758)(334,759)(335,760)
(336,751)(337,752)(338,753)(339,754)(340,755)(341,761)(342,762)(343,763)
(344,764)(345,765)(346,771)(347,772)(348,773)(349,774)(350,775)(351,766)
(352,767)(353,768)(354,769)(355,770)(356,776)(357,777)(358,778)(359,779)
(360,780)(361,936)(362,937)(363,938)(364,939)(365,940)(366,931)(367,932)
(368,933)(369,934)(370,935)(371,941)(372,942)(373,943)(374,944)(375,945)
(376,951)(377,952)(378,953)(379,954)(380,955)(381,946)(382,947)(383,948)
(384,949)(385,950)(386,956)(387,957)(388,958)(389,959)(390,960)(391,906)
(392,907)(393,908)(394,909)(395,910)(396,901)(397,902)(398,903)(399,904)
(400,905)(401,911)(402,912)(403,913)(404,914)(405,915)(406,921)(407,922)
(408,923)(409,924)(410,925)(411,916)(412,917)(413,918)(414,919)(415,920)
(416,926)(417,927)(418,928)(419,929)(420,930)(421,876)(422,877)(423,878)
(424,879)(425,880)(426,871)(427,872)(428,873)(429,874)(430,875)(431,881)
(432,882)(433,883)(434,884)(435,885)(436,891)(437,892)(438,893)(439,894)
(440,895)(441,886)(442,887)(443,888)(444,889)(445,890)(446,896)(447,897)
(448,898)(449,899)(450,900)(451,846)(452,847)(453,848)(454,849)(455,850)
(456,841)(457,842)(458,843)(459,844)(460,845)(461,851)(462,852)(463,853)
(464,854)(465,855)(466,861)(467,862)(468,863)(469,864)(470,865)(471,856)
(472,857)(473,858)(474,859)(475,860)(476,866)(477,867)(478,868)(479,869)
(480,870);
s2 := Sym(960)!( 1,121)( 2,125)( 3,124)( 4,123)( 5,122)( 6,126)( 7,130)
( 8,129)( 9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)
( 24,143)( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237)(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)
(248,369)(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)
(264,383)(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)
(280,397)(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)
(296,416)(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)
(304,423)(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)
(312,435)(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)
(328,449)(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)
(336,456)(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)
(344,463)(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)
(352,475)(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)
(360,477)(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)
(488,609)(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)
(504,623)(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)
(520,637)(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)
(552,675)(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)
(568,689)(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,696)(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)
(584,703)(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)
(592,715)(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)
(600,717)(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)
(728,849)(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)
(744,863)(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)
(760,877)(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)
(776,896)(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)
(784,903)(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)
(792,915)(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)
(800,917)(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)
(808,929)(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)
(816,936)(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)
(824,943)(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)
(832,955)(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)
(840,957);
s3 := Sym(960)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)
( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,377)(242,376)(243,380)(244,379)(245,378)(246,382)(247,381)
(248,385)(249,384)(250,383)(251,387)(252,386)(253,390)(254,389)(255,388)
(256,362)(257,361)(258,365)(259,364)(260,363)(261,367)(262,366)(263,370)
(264,369)(265,368)(266,372)(267,371)(268,375)(269,374)(270,373)(271,407)
(272,406)(273,410)(274,409)(275,408)(276,412)(277,411)(278,415)(279,414)
(280,413)(281,417)(282,416)(283,420)(284,419)(285,418)(286,392)(287,391)
(288,395)(289,394)(290,393)(291,397)(292,396)(293,400)(294,399)(295,398)
(296,402)(297,401)(298,405)(299,404)(300,403)(301,437)(302,436)(303,440)
(304,439)(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)
(312,446)(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)
(320,423)(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)
(328,435)(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)
(336,472)(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)
(344,479)(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)
(352,456)(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)
(360,463)(481,632)(482,631)(483,635)(484,634)(485,633)(486,637)(487,636)
(488,640)(489,639)(490,638)(491,642)(492,641)(493,645)(494,644)(495,643)
(496,647)(497,646)(498,650)(499,649)(500,648)(501,652)(502,651)(503,655)
(504,654)(505,653)(506,657)(507,656)(508,660)(509,659)(510,658)(511,602)
(512,601)(513,605)(514,604)(515,603)(516,607)(517,606)(518,610)(519,609)
(520,608)(521,612)(522,611)(523,615)(524,614)(525,613)(526,617)(527,616)
(528,620)(529,619)(530,618)(531,622)(532,621)(533,625)(534,624)(535,623)
(536,627)(537,626)(538,630)(539,629)(540,628)(541,692)(542,691)(543,695)
(544,694)(545,693)(546,697)(547,696)(548,700)(549,699)(550,698)(551,702)
(552,701)(553,705)(554,704)(555,703)(556,707)(557,706)(558,710)(559,709)
(560,708)(561,712)(562,711)(563,715)(564,714)(565,713)(566,717)(567,716)
(568,720)(569,719)(570,718)(571,662)(572,661)(573,665)(574,664)(575,663)
(576,667)(577,666)(578,670)(579,669)(580,668)(581,672)(582,671)(583,675)
(584,674)(585,673)(586,677)(587,676)(588,680)(589,679)(590,678)(591,682)
(592,681)(593,685)(594,684)(595,683)(596,687)(597,686)(598,690)(599,689)
(600,688)(721,887)(722,886)(723,890)(724,889)(725,888)(726,892)(727,891)
(728,895)(729,894)(730,893)(731,897)(732,896)(733,900)(734,899)(735,898)
(736,872)(737,871)(738,875)(739,874)(740,873)(741,877)(742,876)(743,880)
(744,879)(745,878)(746,882)(747,881)(748,885)(749,884)(750,883)(751,857)
(752,856)(753,860)(754,859)(755,858)(756,862)(757,861)(758,865)(759,864)
(760,863)(761,867)(762,866)(763,870)(764,869)(765,868)(766,842)(767,841)
(768,845)(769,844)(770,843)(771,847)(772,846)(773,850)(774,849)(775,848)
(776,852)(777,851)(778,855)(779,854)(780,853)(781,947)(782,946)(783,950)
(784,949)(785,948)(786,952)(787,951)(788,955)(789,954)(790,953)(791,957)
(792,956)(793,960)(794,959)(795,958)(796,932)(797,931)(798,935)(799,934)
(800,933)(801,937)(802,936)(803,940)(804,939)(805,938)(806,942)(807,941)
(808,945)(809,944)(810,943)(811,917)(812,916)(813,920)(814,919)(815,918)
(816,922)(817,921)(818,925)(819,924)(820,923)(821,927)(822,926)(823,930)
(824,929)(825,928)(826,902)(827,901)(828,905)(829,904)(830,903)(831,907)
(832,906)(833,910)(834,909)(835,908)(836,912)(837,911)(838,915)(839,914)
(840,913);
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*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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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