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