Questions?
See the FAQ
or other info.

Polytope of Type {10,4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,6,4}*1920a
Also Known As : {{10,4|2},{4,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,208116)
Rank : 5
Schlafli Type : {10,4,6,4}
Number of vertices, edges, etc : 10, 20, 12, 12, 4
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,6,4}*960a, {10,4,6,2}*960
   3-fold quotients : {10,4,2,4}*640
   4-fold quotients : {5,2,6,4}*480a, {10,2,6,2}*480
   5-fold quotients : {2,4,6,4}*384a
   6-fold quotients : {10,2,2,4}*320, {10,4,2,2}*320
   8-fold quotients : {5,2,6,2}*240, {10,2,3,2}*240
   10-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
   12-fold quotients : {5,2,2,4}*160, {10,2,2,2}*160
   15-fold quotients : {2,4,2,4}*128
   16-fold quotients : {5,2,3,2}*120
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {5,2,2,2}*80
   30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 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)
(121,692)(122,691)(123,695)(124,694)(125,693)(126,697)(127,696)(128,700)
(129,699)(130,698)(131,702)(132,701)(133,705)(134,704)(135,703)(136,707)
(137,706)(138,710)(139,709)(140,708)(141,712)(142,711)(143,715)(144,714)
(145,713)(146,717)(147,716)(148,720)(149,719)(150,718)(151,662)(152,661)
(153,665)(154,664)(155,663)(156,667)(157,666)(158,670)(159,669)(160,668)
(161,672)(162,671)(163,675)(164,674)(165,673)(166,677)(167,676)(168,680)
(169,679)(170,678)(171,682)(172,681)(173,685)(174,684)(175,683)(176,687)
(177,686)(178,690)(179,689)(180,688)(181,632)(182,631)(183,635)(184,634)
(185,633)(186,637)(187,636)(188,640)(189,639)(190,638)(191,642)(192,641)
(193,645)(194,644)(195,643)(196,647)(197,646)(198,650)(199,649)(200,648)
(201,652)(202,651)(203,655)(204,654)(205,653)(206,657)(207,656)(208,660)
(209,659)(210,658)(211,602)(212,601)(213,605)(214,604)(215,603)(216,607)
(217,606)(218,610)(219,609)(220,608)(221,612)(222,611)(223,615)(224,614)
(225,613)(226,617)(227,616)(228,620)(229,619)(230,618)(231,622)(232,621)
(233,625)(234,624)(235,623)(236,627)(237,626)(238,630)(239,629)(240,628)
(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)
(361,932)(362,931)(363,935)(364,934)(365,933)(366,937)(367,936)(368,940)
(369,939)(370,938)(371,942)(372,941)(373,945)(374,944)(375,943)(376,947)
(377,946)(378,950)(379,949)(380,948)(381,952)(382,951)(383,955)(384,954)
(385,953)(386,957)(387,956)(388,960)(389,959)(390,958)(391,902)(392,901)
(393,905)(394,904)(395,903)(396,907)(397,906)(398,910)(399,909)(400,908)
(401,912)(402,911)(403,915)(404,914)(405,913)(406,917)(407,916)(408,920)
(409,919)(410,918)(411,922)(412,921)(413,925)(414,924)(415,923)(416,927)
(417,926)(418,930)(419,929)(420,928)(421,872)(422,871)(423,875)(424,874)
(425,873)(426,877)(427,876)(428,880)(429,879)(430,878)(431,882)(432,881)
(433,885)(434,884)(435,883)(436,887)(437,886)(438,890)(439,889)(440,888)
(441,892)(442,891)(443,895)(444,894)(445,893)(446,897)(447,896)(448,900)
(449,899)(450,898)(451,842)(452,841)(453,845)(454,844)(455,843)(456,847)
(457,846)(458,850)(459,849)(460,848)(461,852)(462,851)(463,855)(464,854)
(465,853)(466,857)(467,856)(468,860)(469,859)(470,858)(471,862)(472,861)
(473,865)(474,864)(475,863)(476,867)(477,866)(478,870)(479,869)(480,868);;
s2 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)(  8,133)
(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)( 24,149)
( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)( 72,187)
( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)( 88,203)
( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,221)
( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)(104,219)
(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)(248,373)
(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)(264,389)
(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)(280,405)
(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)(296,411)
(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)(312,427)
(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)(328,443)
(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)(336,461)
(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)(344,459)
(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)(352,477)
(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)(360,475)
(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)
(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)
(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)
(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)(512,632)
(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)(520,645)
(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)(528,648)
(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)(536,651)
(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)(544,664)
(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)(552,667)
(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)(560,680)
(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)(568,683)
(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)(576,701)
(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)(584,699)
(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)(592,717)
(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)(600,715)
(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)
(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)
(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)
(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)(752,872)
(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)(760,885)
(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)(768,888)
(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)(776,891)
(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)(784,904)
(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)(792,907)
(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)(800,920)
(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)(808,923)
(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)(816,941)
(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)(824,939)
(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)(832,957)
(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)(840,955);;
s3 := (  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)(  8,123)
(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)
( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)
(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)(248,378)
(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)(256,366)
(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)(264,364)
(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)(272,412)
(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)(280,410)
(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)(288,398)
(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)(296,401)
(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)(304,444)
(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)(312,447)
(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)(320,430)
(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)(328,433)
(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)(336,466)
(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)(344,479)
(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)(352,452)
(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)(360,465)
(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)(488,633)
(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)(496,651)
(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)(504,649)
(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)(512,607)
(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)(520,605)
(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)(528,623)
(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)(536,626)
(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)(544,699)
(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)(552,702)
(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)(560,715)
(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)(568,718)
(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)(576,661)
(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)(584,674)
(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)(592,677)
(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)(600,690)
(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)(728,888)
(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)(736,876)
(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)(744,874)
(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)(752,862)
(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)(760,860)
(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)(768,848)
(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)(776,851)
(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)(784,954)
(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)(792,957)
(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)(800,940)
(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)(808,943)
(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)(816,916)
(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)(824,929)
(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)(832,902)
(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)(840,915);;
s4 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)(121,692)(122,691)(123,695)(124,694)(125,693)(126,697)(127,696)
(128,700)(129,699)(130,698)(131,702)(132,701)(133,705)(134,704)(135,703)
(136,707)(137,706)(138,710)(139,709)(140,708)(141,712)(142,711)(143,715)
(144,714)(145,713)(146,717)(147,716)(148,720)(149,719)(150,718)(151,662)
(152,661)(153,665)(154,664)(155,663)(156,667)(157,666)(158,670)(159,669)
(160,668)(161,672)(162,671)(163,675)(164,674)(165,673)(166,677)(167,676)
(168,680)(169,679)(170,678)(171,682)(172,681)(173,685)(174,684)(175,683)
(176,687)(177,686)(178,690)(179,689)(180,688)(181,632)(182,631)(183,635)
(184,634)(185,633)(186,637)(187,636)(188,640)(189,639)(190,638)(191,642)
(192,641)(193,645)(194,644)(195,643)(196,647)(197,646)(198,650)(199,649)
(200,648)(201,652)(202,651)(203,655)(204,654)(205,653)(206,657)(207,656)
(208,660)(209,659)(210,658)(211,602)(212,601)(213,605)(214,604)(215,603)
(216,607)(217,606)(218,610)(219,609)(220,608)(221,612)(222,611)(223,615)
(224,614)(225,613)(226,617)(227,616)(228,620)(229,619)(230,618)(231,622)
(232,621)(233,625)(234,624)(235,623)(236,627)(237,626)(238,630)(239,629)
(240,628)(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)(361,932)(362,931)(363,935)(364,934)(365,933)(366,937)(367,936)
(368,940)(369,939)(370,938)(371,942)(372,941)(373,945)(374,944)(375,943)
(376,947)(377,946)(378,950)(379,949)(380,948)(381,952)(382,951)(383,955)
(384,954)(385,953)(386,957)(387,956)(388,960)(389,959)(390,958)(391,902)
(392,901)(393,905)(394,904)(395,903)(396,907)(397,906)(398,910)(399,909)
(400,908)(401,912)(402,911)(403,915)(404,914)(405,913)(406,917)(407,916)
(408,920)(409,919)(410,918)(411,922)(412,921)(413,925)(414,924)(415,923)
(416,927)(417,926)(418,930)(419,929)(420,928)(421,872)(422,871)(423,875)
(424,874)(425,873)(426,877)(427,876)(428,880)(429,879)(430,878)(431,882)
(432,881)(433,885)(434,884)(435,883)(436,887)(437,886)(438,890)(439,889)
(440,888)(441,892)(442,891)(443,895)(444,894)(445,893)(446,897)(447,896)
(448,900)(449,899)(450,898)(451,842)(452,841)(453,845)(454,844)(455,843)
(456,847)(457,846)(458,850)(459,849)(460,848)(461,852)(462,851)(463,855)
(464,854)(465,853)(466,857)(467,856)(468,860)(469,859)(470,858)(471,862)
(472,861)(473,865)(474,864)(475,863)(476,867)(477,866)(478,870)(479,869)
(480,868);
s2 := Sym(960)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,131)(  7,132)
(  8,133)(  9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)
( 24,149)( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)
( 72,187)( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)
( 88,203)( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,221)( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235)(241,361)(242,362)(243,363)(244,364)(245,365)(246,371)(247,372)
(248,373)(249,374)(250,375)(251,366)(252,367)(253,368)(254,369)(255,370)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,386)(262,387)(263,388)
(264,389)(265,390)(266,381)(267,382)(268,383)(269,384)(270,385)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,401)(277,402)(278,403)(279,404)
(280,405)(281,396)(282,397)(283,398)(284,399)(285,400)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,416)(292,417)(293,418)(294,419)(295,420)
(296,411)(297,412)(298,413)(299,414)(300,415)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,431)(307,432)(308,433)(309,434)(310,435)(311,426)
(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,446)(322,447)(323,448)(324,449)(325,450)(326,441)(327,442)
(328,443)(329,444)(330,445)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,461)(337,462)(338,463)(339,464)(340,465)(341,456)(342,457)(343,458)
(344,459)(345,460)(346,466)(347,467)(348,468)(349,469)(350,470)(351,476)
(352,477)(353,478)(354,479)(355,480)(356,471)(357,472)(358,473)(359,474)
(360,475)(481,601)(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)
(488,613)(489,614)(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)
(496,616)(497,617)(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)
(504,629)(505,630)(506,621)(507,622)(508,623)(509,624)(510,625)(511,631)
(512,632)(513,633)(514,634)(515,635)(516,641)(517,642)(518,643)(519,644)
(520,645)(521,636)(522,637)(523,638)(524,639)(525,640)(526,646)(527,647)
(528,648)(529,649)(530,650)(531,656)(532,657)(533,658)(534,659)(535,660)
(536,651)(537,652)(538,653)(539,654)(540,655)(541,661)(542,662)(543,663)
(544,664)(545,665)(546,671)(547,672)(548,673)(549,674)(550,675)(551,666)
(552,667)(553,668)(554,669)(555,670)(556,676)(557,677)(558,678)(559,679)
(560,680)(561,686)(562,687)(563,688)(564,689)(565,690)(566,681)(567,682)
(568,683)(569,684)(570,685)(571,691)(572,692)(573,693)(574,694)(575,695)
(576,701)(577,702)(578,703)(579,704)(580,705)(581,696)(582,697)(583,698)
(584,699)(585,700)(586,706)(587,707)(588,708)(589,709)(590,710)(591,716)
(592,717)(593,718)(594,719)(595,720)(596,711)(597,712)(598,713)(599,714)
(600,715)(721,841)(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)
(728,853)(729,854)(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)
(736,856)(737,857)(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)
(744,869)(745,870)(746,861)(747,862)(748,863)(749,864)(750,865)(751,871)
(752,872)(753,873)(754,874)(755,875)(756,881)(757,882)(758,883)(759,884)
(760,885)(761,876)(762,877)(763,878)(764,879)(765,880)(766,886)(767,887)
(768,888)(769,889)(770,890)(771,896)(772,897)(773,898)(774,899)(775,900)
(776,891)(777,892)(778,893)(779,894)(780,895)(781,901)(782,902)(783,903)
(784,904)(785,905)(786,911)(787,912)(788,913)(789,914)(790,915)(791,906)
(792,907)(793,908)(794,909)(795,910)(796,916)(797,917)(798,918)(799,919)
(800,920)(801,926)(802,927)(803,928)(804,929)(805,930)(806,921)(807,922)
(808,923)(809,924)(810,925)(811,931)(812,932)(813,933)(814,934)(815,935)
(816,941)(817,942)(818,943)(819,944)(820,945)(821,936)(822,937)(823,938)
(824,939)(825,940)(826,946)(827,947)(828,948)(829,949)(830,950)(831,956)
(832,957)(833,958)(834,959)(835,960)(836,951)(837,952)(838,953)(839,954)
(840,955);
s3 := Sym(960)!(  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)
(  8,123)(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)
( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,381)(242,382)(243,383)(244,384)(245,385)(246,376)(247,377)
(248,378)(249,379)(250,380)(251,386)(252,387)(253,388)(254,389)(255,390)
(256,366)(257,367)(258,368)(259,369)(260,370)(261,361)(262,362)(263,363)
(264,364)(265,365)(266,371)(267,372)(268,373)(269,374)(270,375)(271,411)
(272,412)(273,413)(274,414)(275,415)(276,406)(277,407)(278,408)(279,409)
(280,410)(281,416)(282,417)(283,418)(284,419)(285,420)(286,396)(287,397)
(288,398)(289,399)(290,400)(291,391)(292,392)(293,393)(294,394)(295,395)
(296,401)(297,402)(298,403)(299,404)(300,405)(301,441)(302,442)(303,443)
(304,444)(305,445)(306,436)(307,437)(308,438)(309,439)(310,440)(311,446)
(312,447)(313,448)(314,449)(315,450)(316,426)(317,427)(318,428)(319,429)
(320,430)(321,421)(322,422)(323,423)(324,424)(325,425)(326,431)(327,432)
(328,433)(329,434)(330,435)(331,471)(332,472)(333,473)(334,474)(335,475)
(336,466)(337,467)(338,468)(339,469)(340,470)(341,476)(342,477)(343,478)
(344,479)(345,480)(346,456)(347,457)(348,458)(349,459)(350,460)(351,451)
(352,452)(353,453)(354,454)(355,455)(356,461)(357,462)(358,463)(359,464)
(360,465)(481,636)(482,637)(483,638)(484,639)(485,640)(486,631)(487,632)
(488,633)(489,634)(490,635)(491,641)(492,642)(493,643)(494,644)(495,645)
(496,651)(497,652)(498,653)(499,654)(500,655)(501,646)(502,647)(503,648)
(504,649)(505,650)(506,656)(507,657)(508,658)(509,659)(510,660)(511,606)
(512,607)(513,608)(514,609)(515,610)(516,601)(517,602)(518,603)(519,604)
(520,605)(521,611)(522,612)(523,613)(524,614)(525,615)(526,621)(527,622)
(528,623)(529,624)(530,625)(531,616)(532,617)(533,618)(534,619)(535,620)
(536,626)(537,627)(538,628)(539,629)(540,630)(541,696)(542,697)(543,698)
(544,699)(545,700)(546,691)(547,692)(548,693)(549,694)(550,695)(551,701)
(552,702)(553,703)(554,704)(555,705)(556,711)(557,712)(558,713)(559,714)
(560,715)(561,706)(562,707)(563,708)(564,709)(565,710)(566,716)(567,717)
(568,718)(569,719)(570,720)(571,666)(572,667)(573,668)(574,669)(575,670)
(576,661)(577,662)(578,663)(579,664)(580,665)(581,671)(582,672)(583,673)
(584,674)(585,675)(586,681)(587,682)(588,683)(589,684)(590,685)(591,676)
(592,677)(593,678)(594,679)(595,680)(596,686)(597,687)(598,688)(599,689)
(600,690)(721,891)(722,892)(723,893)(724,894)(725,895)(726,886)(727,887)
(728,888)(729,889)(730,890)(731,896)(732,897)(733,898)(734,899)(735,900)
(736,876)(737,877)(738,878)(739,879)(740,880)(741,871)(742,872)(743,873)
(744,874)(745,875)(746,881)(747,882)(748,883)(749,884)(750,885)(751,861)
(752,862)(753,863)(754,864)(755,865)(756,856)(757,857)(758,858)(759,859)
(760,860)(761,866)(762,867)(763,868)(764,869)(765,870)(766,846)(767,847)
(768,848)(769,849)(770,850)(771,841)(772,842)(773,843)(774,844)(775,845)
(776,851)(777,852)(778,853)(779,854)(780,855)(781,951)(782,952)(783,953)
(784,954)(785,955)(786,946)(787,947)(788,948)(789,949)(790,950)(791,956)
(792,957)(793,958)(794,959)(795,960)(796,936)(797,937)(798,938)(799,939)
(800,940)(801,931)(802,932)(803,933)(804,934)(805,935)(806,941)(807,942)
(808,943)(809,944)(810,945)(811,921)(812,922)(813,923)(814,924)(815,925)
(816,916)(817,917)(818,918)(819,919)(820,920)(821,926)(822,927)(823,928)
(824,929)(825,930)(826,906)(827,907)(828,908)(829,909)(830,910)(831,901)
(832,902)(833,903)(834,904)(835,905)(836,911)(837,912)(838,913)(839,914)
(840,915);
s4 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
poly := sub<Sym(960)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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