Polytope of Type {20,4,12}

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