Polytope of Type {12,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,20}*1920
Also Known As : {{12,4|2},{4,20|2}}. if this polytope has another name.
Group : SmallGroup(1920,58510)
Rank : 4
Schlafli Type : {12,4,20}
Number of vertices, edges, etc : 12, 24, 40, 20
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 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 : {12,2,20}*960, {12,4,10}*960, {6,4,20}*960
   3-fold quotients : {4,4,20}*640
   4-fold quotients : {12,2,10}*480, {6,2,20}*480, {6,4,10}*480
   5-fold quotients : {12,4,4}*384
   6-fold quotients : {2,4,20}*320, {4,2,20}*320, {4,4,10}*320
   8-fold quotients : {12,2,5}*240, {3,2,20}*240, {6,2,10}*240
   10-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
   12-fold quotients : {2,2,20}*160, {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {4,4,4}*128
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  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);;
s1 := (  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)
(121,546)(122,547)(123,548)(124,549)(125,550)(126,541)(127,542)(128,543)
(129,544)(130,545)(131,551)(132,552)(133,553)(134,554)(135,555)(136,561)
(137,562)(138,563)(139,564)(140,565)(141,556)(142,557)(143,558)(144,559)
(145,560)(146,566)(147,567)(148,568)(149,569)(150,570)(151,576)(152,577)
(153,578)(154,579)(155,580)(156,571)(157,572)(158,573)(159,574)(160,575)
(161,581)(162,582)(163,583)(164,584)(165,585)(166,591)(167,592)(168,593)
(169,594)(170,595)(171,586)(172,587)(173,588)(174,589)(175,590)(176,596)
(177,597)(178,598)(179,599)(180,600)(181,486)(182,487)(183,488)(184,489)
(185,490)(186,481)(187,482)(188,483)(189,484)(190,485)(191,491)(192,492)
(193,493)(194,494)(195,495)(196,501)(197,502)(198,503)(199,504)(200,505)
(201,496)(202,497)(203,498)(204,499)(205,500)(206,506)(207,507)(208,508)
(209,509)(210,510)(211,516)(212,517)(213,518)(214,519)(215,520)(216,511)
(217,512)(218,513)(219,514)(220,515)(221,521)(222,522)(223,523)(224,524)
(225,525)(226,531)(227,532)(228,533)(229,534)(230,535)(231,526)(232,527)
(233,528)(234,529)(235,530)(236,536)(237,537)(238,538)(239,539)(240,540)
(241,891)(242,892)(243,893)(244,894)(245,895)(246,886)(247,887)(248,888)
(249,889)(250,890)(251,896)(252,897)(253,898)(254,899)(255,900)(256,876)
(257,877)(258,878)(259,879)(260,880)(261,871)(262,872)(263,873)(264,874)
(265,875)(266,881)(267,882)(268,883)(269,884)(270,885)(271,861)(272,862)
(273,863)(274,864)(275,865)(276,856)(277,857)(278,858)(279,859)(280,860)
(281,866)(282,867)(283,868)(284,869)(285,870)(286,846)(287,847)(288,848)
(289,849)(290,850)(291,841)(292,842)(293,843)(294,844)(295,845)(296,851)
(297,852)(298,853)(299,854)(300,855)(301,951)(302,952)(303,953)(304,954)
(305,955)(306,946)(307,947)(308,948)(309,949)(310,950)(311,956)(312,957)
(313,958)(314,959)(315,960)(316,936)(317,937)(318,938)(319,939)(320,940)
(321,931)(322,932)(323,933)(324,934)(325,935)(326,941)(327,942)(328,943)
(329,944)(330,945)(331,921)(332,922)(333,923)(334,924)(335,925)(336,916)
(337,917)(338,918)(339,919)(340,920)(341,926)(342,927)(343,928)(344,929)
(345,930)(346,906)(347,907)(348,908)(349,909)(350,910)(351,901)(352,902)
(353,903)(354,904)(355,905)(356,911)(357,912)(358,913)(359,914)(360,915)
(361,831)(362,832)(363,833)(364,834)(365,835)(366,826)(367,827)(368,828)
(369,829)(370,830)(371,836)(372,837)(373,838)(374,839)(375,840)(376,816)
(377,817)(378,818)(379,819)(380,820)(381,811)(382,812)(383,813)(384,814)
(385,815)(386,821)(387,822)(388,823)(389,824)(390,825)(391,801)(392,802)
(393,803)(394,804)(395,805)(396,796)(397,797)(398,798)(399,799)(400,800)
(401,806)(402,807)(403,808)(404,809)(405,810)(406,786)(407,787)(408,788)
(409,789)(410,790)(411,781)(412,782)(413,783)(414,784)(415,785)(416,791)
(417,792)(418,793)(419,794)(420,795)(421,771)(422,772)(423,773)(424,774)
(425,775)(426,766)(427,767)(428,768)(429,769)(430,770)(431,776)(432,777)
(433,778)(434,779)(435,780)(436,756)(437,757)(438,758)(439,759)(440,760)
(441,751)(442,752)(443,753)(444,754)(445,755)(446,761)(447,762)(448,763)
(449,764)(450,765)(451,741)(452,742)(453,743)(454,744)(455,745)(456,736)
(457,737)(458,738)(459,739)(460,740)(461,746)(462,747)(463,748)(464,749)
(465,750)(466,726)(467,727)(468,728)(469,729)(470,730)(471,721)(472,722)
(473,723)(474,724)(475,725)(476,731)(477,732)(478,733)(479,734)(480,735);;
s2 := (  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)(  8,369)
(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)( 16,376)
( 17,380)( 18,379)( 19,378)( 20,377)( 21,381)( 22,385)( 23,384)( 24,383)
( 25,382)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,391)( 32,395)
( 33,394)( 34,393)( 35,392)( 36,396)( 37,400)( 38,399)( 39,398)( 40,397)
( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,406)( 47,410)( 48,409)
( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)( 56,416)
( 57,420)( 58,419)( 59,418)( 60,417)( 61,421)( 62,425)( 63,424)( 64,423)
( 65,422)( 66,426)( 67,430)( 68,429)( 69,428)( 70,427)( 71,431)( 72,435)
( 73,434)( 74,433)( 75,432)( 76,436)( 77,440)( 78,439)( 79,438)( 80,437)
( 81,441)( 82,445)( 83,444)( 84,443)( 85,442)( 86,446)( 87,450)( 88,449)
( 89,448)( 90,447)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)( 96,456)
( 97,460)( 98,459)( 99,458)(100,457)(101,461)(102,465)(103,464)(104,463)
(105,462)(106,466)(107,470)(108,469)(109,468)(110,467)(111,471)(112,475)
(113,474)(114,473)(115,472)(116,476)(117,480)(118,479)(119,478)(120,477)
(121,241)(122,245)(123,244)(124,243)(125,242)(126,246)(127,250)(128,249)
(129,248)(130,247)(131,251)(132,255)(133,254)(134,253)(135,252)(136,256)
(137,260)(138,259)(139,258)(140,257)(141,261)(142,265)(143,264)(144,263)
(145,262)(146,266)(147,270)(148,269)(149,268)(150,267)(151,271)(152,275)
(153,274)(154,273)(155,272)(156,276)(157,280)(158,279)(159,278)(160,277)
(161,281)(162,285)(163,284)(164,283)(165,282)(166,286)(167,290)(168,289)
(169,288)(170,287)(171,291)(172,295)(173,294)(174,293)(175,292)(176,296)
(177,300)(178,299)(179,298)(180,297)(181,301)(182,305)(183,304)(184,303)
(185,302)(186,306)(187,310)(188,309)(189,308)(190,307)(191,311)(192,315)
(193,314)(194,313)(195,312)(196,316)(197,320)(198,319)(199,318)(200,317)
(201,321)(202,325)(203,324)(204,323)(205,322)(206,326)(207,330)(208,329)
(209,328)(210,327)(211,331)(212,335)(213,334)(214,333)(215,332)(216,336)
(217,340)(218,339)(219,338)(220,337)(221,341)(222,345)(223,344)(224,343)
(225,342)(226,346)(227,350)(228,349)(229,348)(230,347)(231,351)(232,355)
(233,354)(234,353)(235,352)(236,356)(237,360)(238,359)(239,358)(240,357)
(481,841)(482,845)(483,844)(484,843)(485,842)(486,846)(487,850)(488,849)
(489,848)(490,847)(491,851)(492,855)(493,854)(494,853)(495,852)(496,856)
(497,860)(498,859)(499,858)(500,857)(501,861)(502,865)(503,864)(504,863)
(505,862)(506,866)(507,870)(508,869)(509,868)(510,867)(511,871)(512,875)
(513,874)(514,873)(515,872)(516,876)(517,880)(518,879)(519,878)(520,877)
(521,881)(522,885)(523,884)(524,883)(525,882)(526,886)(527,890)(528,889)
(529,888)(530,887)(531,891)(532,895)(533,894)(534,893)(535,892)(536,896)
(537,900)(538,899)(539,898)(540,897)(541,901)(542,905)(543,904)(544,903)
(545,902)(546,906)(547,910)(548,909)(549,908)(550,907)(551,911)(552,915)
(553,914)(554,913)(555,912)(556,916)(557,920)(558,919)(559,918)(560,917)
(561,921)(562,925)(563,924)(564,923)(565,922)(566,926)(567,930)(568,929)
(569,928)(570,927)(571,931)(572,935)(573,934)(574,933)(575,932)(576,936)
(577,940)(578,939)(579,938)(580,937)(581,941)(582,945)(583,944)(584,943)
(585,942)(586,946)(587,950)(588,949)(589,948)(590,947)(591,951)(592,955)
(593,954)(594,953)(595,952)(596,956)(597,960)(598,959)(599,958)(600,957)
(601,721)(602,725)(603,724)(604,723)(605,722)(606,726)(607,730)(608,729)
(609,728)(610,727)(611,731)(612,735)(613,734)(614,733)(615,732)(616,736)
(617,740)(618,739)(619,738)(620,737)(621,741)(622,745)(623,744)(624,743)
(625,742)(626,746)(627,750)(628,749)(629,748)(630,747)(631,751)(632,755)
(633,754)(634,753)(635,752)(636,756)(637,760)(638,759)(639,758)(640,757)
(641,761)(642,765)(643,764)(644,763)(645,762)(646,766)(647,770)(648,769)
(649,768)(650,767)(651,771)(652,775)(653,774)(654,773)(655,772)(656,776)
(657,780)(658,779)(659,778)(660,777)(661,781)(662,785)(663,784)(664,783)
(665,782)(666,786)(667,790)(668,789)(669,788)(670,787)(671,791)(672,795)
(673,794)(674,793)(675,792)(676,796)(677,800)(678,799)(679,798)(680,797)
(681,801)(682,805)(683,804)(684,803)(685,802)(686,806)(687,810)(688,809)
(689,808)(690,807)(691,811)(692,815)(693,814)(694,813)(695,812)(696,816)
(697,820)(698,819)(699,818)(700,817)(701,821)(702,825)(703,824)(704,823)
(705,822)(706,826)(707,830)(708,829)(709,828)(710,827)(711,831)(712,835)
(713,834)(714,833)(715,832)(716,836)(717,840)(718,839)(719,838)(720,837);;
s3 := (  1,602)(  2,601)(  3,605)(  4,604)(  5,603)(  6,607)(  7,606)(  8,610)
(  9,609)( 10,608)( 11,612)( 12,611)( 13,615)( 14,614)( 15,613)( 16,617)
( 17,616)( 18,620)( 19,619)( 20,618)( 21,622)( 22,621)( 23,625)( 24,624)
( 25,623)( 26,627)( 27,626)( 28,630)( 29,629)( 30,628)( 31,632)( 32,631)
( 33,635)( 34,634)( 35,633)( 36,637)( 37,636)( 38,640)( 39,639)( 40,638)
( 41,642)( 42,641)( 43,645)( 44,644)( 45,643)( 46,647)( 47,646)( 48,650)
( 49,649)( 50,648)( 51,652)( 52,651)( 53,655)( 54,654)( 55,653)( 56,657)
( 57,656)( 58,660)( 59,659)( 60,658)( 61,662)( 62,661)( 63,665)( 64,664)
( 65,663)( 66,667)( 67,666)( 68,670)( 69,669)( 70,668)( 71,672)( 72,671)
( 73,675)( 74,674)( 75,673)( 76,677)( 77,676)( 78,680)( 79,679)( 80,678)
( 81,682)( 82,681)( 83,685)( 84,684)( 85,683)( 86,687)( 87,686)( 88,690)
( 89,689)( 90,688)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)( 96,697)
( 97,696)( 98,700)( 99,699)(100,698)(101,702)(102,701)(103,705)(104,704)
(105,703)(106,707)(107,706)(108,710)(109,709)(110,708)(111,712)(112,711)
(113,715)(114,714)(115,713)(116,717)(117,716)(118,720)(119,719)(120,718)
(121,482)(122,481)(123,485)(124,484)(125,483)(126,487)(127,486)(128,490)
(129,489)(130,488)(131,492)(132,491)(133,495)(134,494)(135,493)(136,497)
(137,496)(138,500)(139,499)(140,498)(141,502)(142,501)(143,505)(144,504)
(145,503)(146,507)(147,506)(148,510)(149,509)(150,508)(151,512)(152,511)
(153,515)(154,514)(155,513)(156,517)(157,516)(158,520)(159,519)(160,518)
(161,522)(162,521)(163,525)(164,524)(165,523)(166,527)(167,526)(168,530)
(169,529)(170,528)(171,532)(172,531)(173,535)(174,534)(175,533)(176,537)
(177,536)(178,540)(179,539)(180,538)(181,542)(182,541)(183,545)(184,544)
(185,543)(186,547)(187,546)(188,550)(189,549)(190,548)(191,552)(192,551)
(193,555)(194,554)(195,553)(196,557)(197,556)(198,560)(199,559)(200,558)
(201,562)(202,561)(203,565)(204,564)(205,563)(206,567)(207,566)(208,570)
(209,569)(210,568)(211,572)(212,571)(213,575)(214,574)(215,573)(216,577)
(217,576)(218,580)(219,579)(220,578)(221,582)(222,581)(223,585)(224,584)
(225,583)(226,587)(227,586)(228,590)(229,589)(230,588)(231,592)(232,591)
(233,595)(234,594)(235,593)(236,597)(237,596)(238,600)(239,599)(240,598)
(241,857)(242,856)(243,860)(244,859)(245,858)(246,862)(247,861)(248,865)
(249,864)(250,863)(251,867)(252,866)(253,870)(254,869)(255,868)(256,842)
(257,841)(258,845)(259,844)(260,843)(261,847)(262,846)(263,850)(264,849)
(265,848)(266,852)(267,851)(268,855)(269,854)(270,853)(271,887)(272,886)
(273,890)(274,889)(275,888)(276,892)(277,891)(278,895)(279,894)(280,893)
(281,897)(282,896)(283,900)(284,899)(285,898)(286,872)(287,871)(288,875)
(289,874)(290,873)(291,877)(292,876)(293,880)(294,879)(295,878)(296,882)
(297,881)(298,885)(299,884)(300,883)(301,917)(302,916)(303,920)(304,919)
(305,918)(306,922)(307,921)(308,925)(309,924)(310,923)(311,927)(312,926)
(313,930)(314,929)(315,928)(316,902)(317,901)(318,905)(319,904)(320,903)
(321,907)(322,906)(323,910)(324,909)(325,908)(326,912)(327,911)(328,915)
(329,914)(330,913)(331,947)(332,946)(333,950)(334,949)(335,948)(336,952)
(337,951)(338,955)(339,954)(340,953)(341,957)(342,956)(343,960)(344,959)
(345,958)(346,932)(347,931)(348,935)(349,934)(350,933)(351,937)(352,936)
(353,940)(354,939)(355,938)(356,942)(357,941)(358,945)(359,944)(360,943)
(361,737)(362,736)(363,740)(364,739)(365,738)(366,742)(367,741)(368,745)
(369,744)(370,743)(371,747)(372,746)(373,750)(374,749)(375,748)(376,722)
(377,721)(378,725)(379,724)(380,723)(381,727)(382,726)(383,730)(384,729)
(385,728)(386,732)(387,731)(388,735)(389,734)(390,733)(391,767)(392,766)
(393,770)(394,769)(395,768)(396,772)(397,771)(398,775)(399,774)(400,773)
(401,777)(402,776)(403,780)(404,779)(405,778)(406,752)(407,751)(408,755)
(409,754)(410,753)(411,757)(412,756)(413,760)(414,759)(415,758)(416,762)
(417,761)(418,765)(419,764)(420,763)(421,797)(422,796)(423,800)(424,799)
(425,798)(426,802)(427,801)(428,805)(429,804)(430,803)(431,807)(432,806)
(433,810)(434,809)(435,808)(436,782)(437,781)(438,785)(439,784)(440,783)
(441,787)(442,786)(443,790)(444,789)(445,788)(446,792)(447,791)(448,795)
(449,794)(450,793)(451,827)(452,826)(453,830)(454,829)(455,828)(456,832)
(457,831)(458,835)(459,834)(460,833)(461,837)(462,836)(463,840)(464,839)
(465,838)(466,812)(467,811)(468,815)(469,814)(470,813)(471,817)(472,816)
(473,820)(474,819)(475,818)(476,822)(477,821)(478,825)(479,824)(480,823);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,121)(  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);
s1 := 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)(121,546)(122,547)(123,548)(124,549)(125,550)(126,541)(127,542)
(128,543)(129,544)(130,545)(131,551)(132,552)(133,553)(134,554)(135,555)
(136,561)(137,562)(138,563)(139,564)(140,565)(141,556)(142,557)(143,558)
(144,559)(145,560)(146,566)(147,567)(148,568)(149,569)(150,570)(151,576)
(152,577)(153,578)(154,579)(155,580)(156,571)(157,572)(158,573)(159,574)
(160,575)(161,581)(162,582)(163,583)(164,584)(165,585)(166,591)(167,592)
(168,593)(169,594)(170,595)(171,586)(172,587)(173,588)(174,589)(175,590)
(176,596)(177,597)(178,598)(179,599)(180,600)(181,486)(182,487)(183,488)
(184,489)(185,490)(186,481)(187,482)(188,483)(189,484)(190,485)(191,491)
(192,492)(193,493)(194,494)(195,495)(196,501)(197,502)(198,503)(199,504)
(200,505)(201,496)(202,497)(203,498)(204,499)(205,500)(206,506)(207,507)
(208,508)(209,509)(210,510)(211,516)(212,517)(213,518)(214,519)(215,520)
(216,511)(217,512)(218,513)(219,514)(220,515)(221,521)(222,522)(223,523)
(224,524)(225,525)(226,531)(227,532)(228,533)(229,534)(230,535)(231,526)
(232,527)(233,528)(234,529)(235,530)(236,536)(237,537)(238,538)(239,539)
(240,540)(241,891)(242,892)(243,893)(244,894)(245,895)(246,886)(247,887)
(248,888)(249,889)(250,890)(251,896)(252,897)(253,898)(254,899)(255,900)
(256,876)(257,877)(258,878)(259,879)(260,880)(261,871)(262,872)(263,873)
(264,874)(265,875)(266,881)(267,882)(268,883)(269,884)(270,885)(271,861)
(272,862)(273,863)(274,864)(275,865)(276,856)(277,857)(278,858)(279,859)
(280,860)(281,866)(282,867)(283,868)(284,869)(285,870)(286,846)(287,847)
(288,848)(289,849)(290,850)(291,841)(292,842)(293,843)(294,844)(295,845)
(296,851)(297,852)(298,853)(299,854)(300,855)(301,951)(302,952)(303,953)
(304,954)(305,955)(306,946)(307,947)(308,948)(309,949)(310,950)(311,956)
(312,957)(313,958)(314,959)(315,960)(316,936)(317,937)(318,938)(319,939)
(320,940)(321,931)(322,932)(323,933)(324,934)(325,935)(326,941)(327,942)
(328,943)(329,944)(330,945)(331,921)(332,922)(333,923)(334,924)(335,925)
(336,916)(337,917)(338,918)(339,919)(340,920)(341,926)(342,927)(343,928)
(344,929)(345,930)(346,906)(347,907)(348,908)(349,909)(350,910)(351,901)
(352,902)(353,903)(354,904)(355,905)(356,911)(357,912)(358,913)(359,914)
(360,915)(361,831)(362,832)(363,833)(364,834)(365,835)(366,826)(367,827)
(368,828)(369,829)(370,830)(371,836)(372,837)(373,838)(374,839)(375,840)
(376,816)(377,817)(378,818)(379,819)(380,820)(381,811)(382,812)(383,813)
(384,814)(385,815)(386,821)(387,822)(388,823)(389,824)(390,825)(391,801)
(392,802)(393,803)(394,804)(395,805)(396,796)(397,797)(398,798)(399,799)
(400,800)(401,806)(402,807)(403,808)(404,809)(405,810)(406,786)(407,787)
(408,788)(409,789)(410,790)(411,781)(412,782)(413,783)(414,784)(415,785)
(416,791)(417,792)(418,793)(419,794)(420,795)(421,771)(422,772)(423,773)
(424,774)(425,775)(426,766)(427,767)(428,768)(429,769)(430,770)(431,776)
(432,777)(433,778)(434,779)(435,780)(436,756)(437,757)(438,758)(439,759)
(440,760)(441,751)(442,752)(443,753)(444,754)(445,755)(446,761)(447,762)
(448,763)(449,764)(450,765)(451,741)(452,742)(453,743)(454,744)(455,745)
(456,736)(457,737)(458,738)(459,739)(460,740)(461,746)(462,747)(463,748)
(464,749)(465,750)(466,726)(467,727)(468,728)(469,729)(470,730)(471,721)
(472,722)(473,723)(474,724)(475,725)(476,731)(477,732)(478,733)(479,734)
(480,735);
s2 := Sym(960)!(  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)
(  8,369)(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)
( 16,376)( 17,380)( 18,379)( 19,378)( 20,377)( 21,381)( 22,385)( 23,384)
( 24,383)( 25,382)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,391)
( 32,395)( 33,394)( 34,393)( 35,392)( 36,396)( 37,400)( 38,399)( 39,398)
( 40,397)( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,406)( 47,410)
( 48,409)( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)
( 56,416)( 57,420)( 58,419)( 59,418)( 60,417)( 61,421)( 62,425)( 63,424)
( 64,423)( 65,422)( 66,426)( 67,430)( 68,429)( 69,428)( 70,427)( 71,431)
( 72,435)( 73,434)( 74,433)( 75,432)( 76,436)( 77,440)( 78,439)( 79,438)
( 80,437)( 81,441)( 82,445)( 83,444)( 84,443)( 85,442)( 86,446)( 87,450)
( 88,449)( 89,448)( 90,447)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)
( 96,456)( 97,460)( 98,459)( 99,458)(100,457)(101,461)(102,465)(103,464)
(104,463)(105,462)(106,466)(107,470)(108,469)(109,468)(110,467)(111,471)
(112,475)(113,474)(114,473)(115,472)(116,476)(117,480)(118,479)(119,478)
(120,477)(121,241)(122,245)(123,244)(124,243)(125,242)(126,246)(127,250)
(128,249)(129,248)(130,247)(131,251)(132,255)(133,254)(134,253)(135,252)
(136,256)(137,260)(138,259)(139,258)(140,257)(141,261)(142,265)(143,264)
(144,263)(145,262)(146,266)(147,270)(148,269)(149,268)(150,267)(151,271)
(152,275)(153,274)(154,273)(155,272)(156,276)(157,280)(158,279)(159,278)
(160,277)(161,281)(162,285)(163,284)(164,283)(165,282)(166,286)(167,290)
(168,289)(169,288)(170,287)(171,291)(172,295)(173,294)(174,293)(175,292)
(176,296)(177,300)(178,299)(179,298)(180,297)(181,301)(182,305)(183,304)
(184,303)(185,302)(186,306)(187,310)(188,309)(189,308)(190,307)(191,311)
(192,315)(193,314)(194,313)(195,312)(196,316)(197,320)(198,319)(199,318)
(200,317)(201,321)(202,325)(203,324)(204,323)(205,322)(206,326)(207,330)
(208,329)(209,328)(210,327)(211,331)(212,335)(213,334)(214,333)(215,332)
(216,336)(217,340)(218,339)(219,338)(220,337)(221,341)(222,345)(223,344)
(224,343)(225,342)(226,346)(227,350)(228,349)(229,348)(230,347)(231,351)
(232,355)(233,354)(234,353)(235,352)(236,356)(237,360)(238,359)(239,358)
(240,357)(481,841)(482,845)(483,844)(484,843)(485,842)(486,846)(487,850)
(488,849)(489,848)(490,847)(491,851)(492,855)(493,854)(494,853)(495,852)
(496,856)(497,860)(498,859)(499,858)(500,857)(501,861)(502,865)(503,864)
(504,863)(505,862)(506,866)(507,870)(508,869)(509,868)(510,867)(511,871)
(512,875)(513,874)(514,873)(515,872)(516,876)(517,880)(518,879)(519,878)
(520,877)(521,881)(522,885)(523,884)(524,883)(525,882)(526,886)(527,890)
(528,889)(529,888)(530,887)(531,891)(532,895)(533,894)(534,893)(535,892)
(536,896)(537,900)(538,899)(539,898)(540,897)(541,901)(542,905)(543,904)
(544,903)(545,902)(546,906)(547,910)(548,909)(549,908)(550,907)(551,911)
(552,915)(553,914)(554,913)(555,912)(556,916)(557,920)(558,919)(559,918)
(560,917)(561,921)(562,925)(563,924)(564,923)(565,922)(566,926)(567,930)
(568,929)(569,928)(570,927)(571,931)(572,935)(573,934)(574,933)(575,932)
(576,936)(577,940)(578,939)(579,938)(580,937)(581,941)(582,945)(583,944)
(584,943)(585,942)(586,946)(587,950)(588,949)(589,948)(590,947)(591,951)
(592,955)(593,954)(594,953)(595,952)(596,956)(597,960)(598,959)(599,958)
(600,957)(601,721)(602,725)(603,724)(604,723)(605,722)(606,726)(607,730)
(608,729)(609,728)(610,727)(611,731)(612,735)(613,734)(614,733)(615,732)
(616,736)(617,740)(618,739)(619,738)(620,737)(621,741)(622,745)(623,744)
(624,743)(625,742)(626,746)(627,750)(628,749)(629,748)(630,747)(631,751)
(632,755)(633,754)(634,753)(635,752)(636,756)(637,760)(638,759)(639,758)
(640,757)(641,761)(642,765)(643,764)(644,763)(645,762)(646,766)(647,770)
(648,769)(649,768)(650,767)(651,771)(652,775)(653,774)(654,773)(655,772)
(656,776)(657,780)(658,779)(659,778)(660,777)(661,781)(662,785)(663,784)
(664,783)(665,782)(666,786)(667,790)(668,789)(669,788)(670,787)(671,791)
(672,795)(673,794)(674,793)(675,792)(676,796)(677,800)(678,799)(679,798)
(680,797)(681,801)(682,805)(683,804)(684,803)(685,802)(686,806)(687,810)
(688,809)(689,808)(690,807)(691,811)(692,815)(693,814)(694,813)(695,812)
(696,816)(697,820)(698,819)(699,818)(700,817)(701,821)(702,825)(703,824)
(704,823)(705,822)(706,826)(707,830)(708,829)(709,828)(710,827)(711,831)
(712,835)(713,834)(714,833)(715,832)(716,836)(717,840)(718,839)(719,838)
(720,837);
s3 := Sym(960)!(  1,602)(  2,601)(  3,605)(  4,604)(  5,603)(  6,607)(  7,606)
(  8,610)(  9,609)( 10,608)( 11,612)( 12,611)( 13,615)( 14,614)( 15,613)
( 16,617)( 17,616)( 18,620)( 19,619)( 20,618)( 21,622)( 22,621)( 23,625)
( 24,624)( 25,623)( 26,627)( 27,626)( 28,630)( 29,629)( 30,628)( 31,632)
( 32,631)( 33,635)( 34,634)( 35,633)( 36,637)( 37,636)( 38,640)( 39,639)
( 40,638)( 41,642)( 42,641)( 43,645)( 44,644)( 45,643)( 46,647)( 47,646)
( 48,650)( 49,649)( 50,648)( 51,652)( 52,651)( 53,655)( 54,654)( 55,653)
( 56,657)( 57,656)( 58,660)( 59,659)( 60,658)( 61,662)( 62,661)( 63,665)
( 64,664)( 65,663)( 66,667)( 67,666)( 68,670)( 69,669)( 70,668)( 71,672)
( 72,671)( 73,675)( 74,674)( 75,673)( 76,677)( 77,676)( 78,680)( 79,679)
( 80,678)( 81,682)( 82,681)( 83,685)( 84,684)( 85,683)( 86,687)( 87,686)
( 88,690)( 89,689)( 90,688)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)
( 96,697)( 97,696)( 98,700)( 99,699)(100,698)(101,702)(102,701)(103,705)
(104,704)(105,703)(106,707)(107,706)(108,710)(109,709)(110,708)(111,712)
(112,711)(113,715)(114,714)(115,713)(116,717)(117,716)(118,720)(119,719)
(120,718)(121,482)(122,481)(123,485)(124,484)(125,483)(126,487)(127,486)
(128,490)(129,489)(130,488)(131,492)(132,491)(133,495)(134,494)(135,493)
(136,497)(137,496)(138,500)(139,499)(140,498)(141,502)(142,501)(143,505)
(144,504)(145,503)(146,507)(147,506)(148,510)(149,509)(150,508)(151,512)
(152,511)(153,515)(154,514)(155,513)(156,517)(157,516)(158,520)(159,519)
(160,518)(161,522)(162,521)(163,525)(164,524)(165,523)(166,527)(167,526)
(168,530)(169,529)(170,528)(171,532)(172,531)(173,535)(174,534)(175,533)
(176,537)(177,536)(178,540)(179,539)(180,538)(181,542)(182,541)(183,545)
(184,544)(185,543)(186,547)(187,546)(188,550)(189,549)(190,548)(191,552)
(192,551)(193,555)(194,554)(195,553)(196,557)(197,556)(198,560)(199,559)
(200,558)(201,562)(202,561)(203,565)(204,564)(205,563)(206,567)(207,566)
(208,570)(209,569)(210,568)(211,572)(212,571)(213,575)(214,574)(215,573)
(216,577)(217,576)(218,580)(219,579)(220,578)(221,582)(222,581)(223,585)
(224,584)(225,583)(226,587)(227,586)(228,590)(229,589)(230,588)(231,592)
(232,591)(233,595)(234,594)(235,593)(236,597)(237,596)(238,600)(239,599)
(240,598)(241,857)(242,856)(243,860)(244,859)(245,858)(246,862)(247,861)
(248,865)(249,864)(250,863)(251,867)(252,866)(253,870)(254,869)(255,868)
(256,842)(257,841)(258,845)(259,844)(260,843)(261,847)(262,846)(263,850)
(264,849)(265,848)(266,852)(267,851)(268,855)(269,854)(270,853)(271,887)
(272,886)(273,890)(274,889)(275,888)(276,892)(277,891)(278,895)(279,894)
(280,893)(281,897)(282,896)(283,900)(284,899)(285,898)(286,872)(287,871)
(288,875)(289,874)(290,873)(291,877)(292,876)(293,880)(294,879)(295,878)
(296,882)(297,881)(298,885)(299,884)(300,883)(301,917)(302,916)(303,920)
(304,919)(305,918)(306,922)(307,921)(308,925)(309,924)(310,923)(311,927)
(312,926)(313,930)(314,929)(315,928)(316,902)(317,901)(318,905)(319,904)
(320,903)(321,907)(322,906)(323,910)(324,909)(325,908)(326,912)(327,911)
(328,915)(329,914)(330,913)(331,947)(332,946)(333,950)(334,949)(335,948)
(336,952)(337,951)(338,955)(339,954)(340,953)(341,957)(342,956)(343,960)
(344,959)(345,958)(346,932)(347,931)(348,935)(349,934)(350,933)(351,937)
(352,936)(353,940)(354,939)(355,938)(356,942)(357,941)(358,945)(359,944)
(360,943)(361,737)(362,736)(363,740)(364,739)(365,738)(366,742)(367,741)
(368,745)(369,744)(370,743)(371,747)(372,746)(373,750)(374,749)(375,748)
(376,722)(377,721)(378,725)(379,724)(380,723)(381,727)(382,726)(383,730)
(384,729)(385,728)(386,732)(387,731)(388,735)(389,734)(390,733)(391,767)
(392,766)(393,770)(394,769)(395,768)(396,772)(397,771)(398,775)(399,774)
(400,773)(401,777)(402,776)(403,780)(404,779)(405,778)(406,752)(407,751)
(408,755)(409,754)(410,753)(411,757)(412,756)(413,760)(414,759)(415,758)
(416,762)(417,761)(418,765)(419,764)(420,763)(421,797)(422,796)(423,800)
(424,799)(425,798)(426,802)(427,801)(428,805)(429,804)(430,803)(431,807)
(432,806)(433,810)(434,809)(435,808)(436,782)(437,781)(438,785)(439,784)
(440,783)(441,787)(442,786)(443,790)(444,789)(445,788)(446,792)(447,791)
(448,795)(449,794)(450,793)(451,827)(452,826)(453,830)(454,829)(455,828)
(456,832)(457,831)(458,835)(459,834)(460,833)(461,837)(462,836)(463,840)
(464,839)(465,838)(466,812)(467,811)(468,815)(469,814)(470,813)(471,817)
(472,816)(473,820)(474,819)(475,818)(476,822)(477,821)(478,825)(479,824)
(480,823);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope