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