Polytope of Type {20,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12,4}*1920a
Also Known As : {{20,12|2},{12,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,58503)
Rank : 4
Schlafli Type : {20,12,4}
Number of vertices, edges, etc : 20, 120, 24, 4
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 : {10,12,4}*960a, {20,6,4}*960a, {20,12,2}*960
   3-fold quotients : {20,4,4}*640
   4-fold quotients : {10,12,2}*480, {20,6,2}*480a, {10,6,4}*480a
   5-fold quotients : {4,12,4}*384a
   6-fold quotients : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
   12-fold quotients : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {4,4,4}*128
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
   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
   40-fold quotients : {2,6,2}*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 : {2,3,2}*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 := (  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,252)(  7,251)(  8,255)
(  9,254)( 10,253)( 11,247)( 12,246)( 13,250)( 14,249)( 15,248)( 16,257)
( 17,256)( 18,260)( 19,259)( 20,258)( 21,267)( 22,266)( 23,270)( 24,269)
( 25,268)( 26,262)( 27,261)( 28,265)( 29,264)( 30,263)( 31,272)( 32,271)
( 33,275)( 34,274)( 35,273)( 36,282)( 37,281)( 38,285)( 39,284)( 40,283)
( 41,277)( 42,276)( 43,280)( 44,279)( 45,278)( 46,287)( 47,286)( 48,290)
( 49,289)( 50,288)( 51,297)( 52,296)( 53,300)( 54,299)( 55,298)( 56,292)
( 57,291)( 58,295)( 59,294)( 60,293)( 61,302)( 62,301)( 63,305)( 64,304)
( 65,303)( 66,312)( 67,311)( 68,315)( 69,314)( 70,313)( 71,307)( 72,306)
( 73,310)( 74,309)( 75,308)( 76,317)( 77,316)( 78,320)( 79,319)( 80,318)
( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,322)( 87,321)( 88,325)
( 89,324)( 90,323)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)( 96,342)
( 97,341)( 98,345)( 99,344)(100,343)(101,337)(102,336)(103,340)(104,339)
(105,338)(106,347)(107,346)(108,350)(109,349)(110,348)(111,357)(112,356)
(113,360)(114,359)(115,358)(116,352)(117,351)(118,355)(119,354)(120,353)
(121,362)(122,361)(123,365)(124,364)(125,363)(126,372)(127,371)(128,375)
(129,374)(130,373)(131,367)(132,366)(133,370)(134,369)(135,368)(136,377)
(137,376)(138,380)(139,379)(140,378)(141,387)(142,386)(143,390)(144,389)
(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,392)(152,391)
(153,395)(154,394)(155,393)(156,402)(157,401)(158,405)(159,404)(160,403)
(161,397)(162,396)(163,400)(164,399)(165,398)(166,407)(167,406)(168,410)
(169,409)(170,408)(171,417)(172,416)(173,420)(174,419)(175,418)(176,412)
(177,411)(178,415)(179,414)(180,413)(181,422)(182,421)(183,425)(184,424)
(185,423)(186,432)(187,431)(188,435)(189,434)(190,433)(191,427)(192,426)
(193,430)(194,429)(195,428)(196,437)(197,436)(198,440)(199,439)(200,438)
(201,447)(202,446)(203,450)(204,449)(205,448)(206,442)(207,441)(208,445)
(209,444)(210,443)(211,452)(212,451)(213,455)(214,454)(215,453)(216,462)
(217,461)(218,465)(219,464)(220,463)(221,457)(222,456)(223,460)(224,459)
(225,458)(226,467)(227,466)(228,470)(229,469)(230,468)(231,477)(232,476)
(233,480)(234,479)(235,478)(236,472)(237,471)(238,475)(239,474)(240,473)
(481,722)(482,721)(483,725)(484,724)(485,723)(486,732)(487,731)(488,735)
(489,734)(490,733)(491,727)(492,726)(493,730)(494,729)(495,728)(496,737)
(497,736)(498,740)(499,739)(500,738)(501,747)(502,746)(503,750)(504,749)
(505,748)(506,742)(507,741)(508,745)(509,744)(510,743)(511,752)(512,751)
(513,755)(514,754)(515,753)(516,762)(517,761)(518,765)(519,764)(520,763)
(521,757)(522,756)(523,760)(524,759)(525,758)(526,767)(527,766)(528,770)
(529,769)(530,768)(531,777)(532,776)(533,780)(534,779)(535,778)(536,772)
(537,771)(538,775)(539,774)(540,773)(541,782)(542,781)(543,785)(544,784)
(545,783)(546,792)(547,791)(548,795)(549,794)(550,793)(551,787)(552,786)
(553,790)(554,789)(555,788)(556,797)(557,796)(558,800)(559,799)(560,798)
(561,807)(562,806)(563,810)(564,809)(565,808)(566,802)(567,801)(568,805)
(569,804)(570,803)(571,812)(572,811)(573,815)(574,814)(575,813)(576,822)
(577,821)(578,825)(579,824)(580,823)(581,817)(582,816)(583,820)(584,819)
(585,818)(586,827)(587,826)(588,830)(589,829)(590,828)(591,837)(592,836)
(593,840)(594,839)(595,838)(596,832)(597,831)(598,835)(599,834)(600,833)
(601,842)(602,841)(603,845)(604,844)(605,843)(606,852)(607,851)(608,855)
(609,854)(610,853)(611,847)(612,846)(613,850)(614,849)(615,848)(616,857)
(617,856)(618,860)(619,859)(620,858)(621,867)(622,866)(623,870)(624,869)
(625,868)(626,862)(627,861)(628,865)(629,864)(630,863)(631,872)(632,871)
(633,875)(634,874)(635,873)(636,882)(637,881)(638,885)(639,884)(640,883)
(641,877)(642,876)(643,880)(644,879)(645,878)(646,887)(647,886)(648,890)
(649,889)(650,888)(651,897)(652,896)(653,900)(654,899)(655,898)(656,892)
(657,891)(658,895)(659,894)(660,893)(661,902)(662,901)(663,905)(664,904)
(665,903)(666,912)(667,911)(668,915)(669,914)(670,913)(671,907)(672,906)
(673,910)(674,909)(675,908)(676,917)(677,916)(678,920)(679,919)(680,918)
(681,927)(682,926)(683,930)(684,929)(685,928)(686,922)(687,921)(688,925)
(689,924)(690,923)(691,932)(692,931)(693,935)(694,934)(695,933)(696,942)
(697,941)(698,945)(699,944)(700,943)(701,937)(702,936)(703,940)(704,939)
(705,938)(706,947)(707,946)(708,950)(709,949)(710,948)(711,957)(712,956)
(713,960)(714,959)(715,958)(716,952)(717,951)(718,955)(719,954)(720,953);;
s2 := (  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)(  8,603)
(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)( 16,621)
( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)( 24,619)
( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)( 32,637)
( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)( 40,635)
( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)( 48,653)
( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)( 56,656)
( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)( 64,669)
( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)( 72,672)
( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)( 80,685)
( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)( 88,688)
( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)( 96,691)
( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)(104,704)
(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)(112,707)
(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)(120,720)
(121,546)(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);;
s3 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)
(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)
( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)
( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)
(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)(280,400)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)
(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)
(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480)
(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)(488,608)
(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)(496,616)
(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)(504,624)
(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,631)(512,632)
(513,633)(514,634)(515,635)(516,636)(517,637)(518,638)(519,639)(520,640)
(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)(528,648)
(529,649)(530,650)(531,651)(532,652)(533,653)(534,654)(535,655)(536,656)
(537,657)(538,658)(539,659)(540,660)(541,661)(542,662)(543,663)(544,664)
(545,665)(546,666)(547,667)(548,668)(549,669)(550,670)(551,671)(552,672)
(553,673)(554,674)(555,675)(556,676)(557,677)(558,678)(559,679)(560,680)
(561,681)(562,682)(563,683)(564,684)(565,685)(566,686)(567,687)(568,688)
(569,689)(570,690)(571,691)(572,692)(573,693)(574,694)(575,695)(576,696)
(577,697)(578,698)(579,699)(580,700)(581,701)(582,702)(583,703)(584,704)
(585,705)(586,706)(587,707)(588,708)(589,709)(590,710)(591,711)(592,712)
(593,713)(594,714)(595,715)(596,716)(597,717)(598,718)(599,719)(600,720)
(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)(728,848)
(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)(736,856)
(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)(744,864)
(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,871)(752,872)
(753,873)(754,874)(755,875)(756,876)(757,877)(758,878)(759,879)(760,880)
(761,881)(762,882)(763,883)(764,884)(765,885)(766,886)(767,887)(768,888)
(769,889)(770,890)(771,891)(772,892)(773,893)(774,894)(775,895)(776,896)
(777,897)(778,898)(779,899)(780,900)(781,901)(782,902)(783,903)(784,904)
(785,905)(786,906)(787,907)(788,908)(789,909)(790,910)(791,911)(792,912)
(793,913)(794,914)(795,915)(796,916)(797,917)(798,918)(799,919)(800,920)
(801,921)(802,922)(803,923)(804,924)(805,925)(806,926)(807,927)(808,928)
(809,929)(810,930)(811,931)(812,932)(813,933)(814,934)(815,935)(816,936)
(817,937)(818,938)(819,939)(820,940)(821,941)(822,942)(823,943)(824,944)
(825,945)(826,946)(827,947)(828,948)(829,949)(830,950)(831,951)(832,952)
(833,953)(834,954)(835,955)(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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  1,242)(  2,241)(  3,245)(  4,244)(  5,243)(  6,252)(  7,251)
(  8,255)(  9,254)( 10,253)( 11,247)( 12,246)( 13,250)( 14,249)( 15,248)
( 16,257)( 17,256)( 18,260)( 19,259)( 20,258)( 21,267)( 22,266)( 23,270)
( 24,269)( 25,268)( 26,262)( 27,261)( 28,265)( 29,264)( 30,263)( 31,272)
( 32,271)( 33,275)( 34,274)( 35,273)( 36,282)( 37,281)( 38,285)( 39,284)
( 40,283)( 41,277)( 42,276)( 43,280)( 44,279)( 45,278)( 46,287)( 47,286)
( 48,290)( 49,289)( 50,288)( 51,297)( 52,296)( 53,300)( 54,299)( 55,298)
( 56,292)( 57,291)( 58,295)( 59,294)( 60,293)( 61,302)( 62,301)( 63,305)
( 64,304)( 65,303)( 66,312)( 67,311)( 68,315)( 69,314)( 70,313)( 71,307)
( 72,306)( 73,310)( 74,309)( 75,308)( 76,317)( 77,316)( 78,320)( 79,319)
( 80,318)( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,322)( 87,321)
( 88,325)( 89,324)( 90,323)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)
( 96,342)( 97,341)( 98,345)( 99,344)(100,343)(101,337)(102,336)(103,340)
(104,339)(105,338)(106,347)(107,346)(108,350)(109,349)(110,348)(111,357)
(112,356)(113,360)(114,359)(115,358)(116,352)(117,351)(118,355)(119,354)
(120,353)(121,362)(122,361)(123,365)(124,364)(125,363)(126,372)(127,371)
(128,375)(129,374)(130,373)(131,367)(132,366)(133,370)(134,369)(135,368)
(136,377)(137,376)(138,380)(139,379)(140,378)(141,387)(142,386)(143,390)
(144,389)(145,388)(146,382)(147,381)(148,385)(149,384)(150,383)(151,392)
(152,391)(153,395)(154,394)(155,393)(156,402)(157,401)(158,405)(159,404)
(160,403)(161,397)(162,396)(163,400)(164,399)(165,398)(166,407)(167,406)
(168,410)(169,409)(170,408)(171,417)(172,416)(173,420)(174,419)(175,418)
(176,412)(177,411)(178,415)(179,414)(180,413)(181,422)(182,421)(183,425)
(184,424)(185,423)(186,432)(187,431)(188,435)(189,434)(190,433)(191,427)
(192,426)(193,430)(194,429)(195,428)(196,437)(197,436)(198,440)(199,439)
(200,438)(201,447)(202,446)(203,450)(204,449)(205,448)(206,442)(207,441)
(208,445)(209,444)(210,443)(211,452)(212,451)(213,455)(214,454)(215,453)
(216,462)(217,461)(218,465)(219,464)(220,463)(221,457)(222,456)(223,460)
(224,459)(225,458)(226,467)(227,466)(228,470)(229,469)(230,468)(231,477)
(232,476)(233,480)(234,479)(235,478)(236,472)(237,471)(238,475)(239,474)
(240,473)(481,722)(482,721)(483,725)(484,724)(485,723)(486,732)(487,731)
(488,735)(489,734)(490,733)(491,727)(492,726)(493,730)(494,729)(495,728)
(496,737)(497,736)(498,740)(499,739)(500,738)(501,747)(502,746)(503,750)
(504,749)(505,748)(506,742)(507,741)(508,745)(509,744)(510,743)(511,752)
(512,751)(513,755)(514,754)(515,753)(516,762)(517,761)(518,765)(519,764)
(520,763)(521,757)(522,756)(523,760)(524,759)(525,758)(526,767)(527,766)
(528,770)(529,769)(530,768)(531,777)(532,776)(533,780)(534,779)(535,778)
(536,772)(537,771)(538,775)(539,774)(540,773)(541,782)(542,781)(543,785)
(544,784)(545,783)(546,792)(547,791)(548,795)(549,794)(550,793)(551,787)
(552,786)(553,790)(554,789)(555,788)(556,797)(557,796)(558,800)(559,799)
(560,798)(561,807)(562,806)(563,810)(564,809)(565,808)(566,802)(567,801)
(568,805)(569,804)(570,803)(571,812)(572,811)(573,815)(574,814)(575,813)
(576,822)(577,821)(578,825)(579,824)(580,823)(581,817)(582,816)(583,820)
(584,819)(585,818)(586,827)(587,826)(588,830)(589,829)(590,828)(591,837)
(592,836)(593,840)(594,839)(595,838)(596,832)(597,831)(598,835)(599,834)
(600,833)(601,842)(602,841)(603,845)(604,844)(605,843)(606,852)(607,851)
(608,855)(609,854)(610,853)(611,847)(612,846)(613,850)(614,849)(615,848)
(616,857)(617,856)(618,860)(619,859)(620,858)(621,867)(622,866)(623,870)
(624,869)(625,868)(626,862)(627,861)(628,865)(629,864)(630,863)(631,872)
(632,871)(633,875)(634,874)(635,873)(636,882)(637,881)(638,885)(639,884)
(640,883)(641,877)(642,876)(643,880)(644,879)(645,878)(646,887)(647,886)
(648,890)(649,889)(650,888)(651,897)(652,896)(653,900)(654,899)(655,898)
(656,892)(657,891)(658,895)(659,894)(660,893)(661,902)(662,901)(663,905)
(664,904)(665,903)(666,912)(667,911)(668,915)(669,914)(670,913)(671,907)
(672,906)(673,910)(674,909)(675,908)(676,917)(677,916)(678,920)(679,919)
(680,918)(681,927)(682,926)(683,930)(684,929)(685,928)(686,922)(687,921)
(688,925)(689,924)(690,923)(691,932)(692,931)(693,935)(694,934)(695,933)
(696,942)(697,941)(698,945)(699,944)(700,943)(701,937)(702,936)(703,940)
(704,939)(705,938)(706,947)(707,946)(708,950)(709,949)(710,948)(711,957)
(712,956)(713,960)(714,959)(715,958)(716,952)(717,951)(718,955)(719,954)
(720,953);
s2 := Sym(960)!(  1,606)(  2,607)(  3,608)(  4,609)(  5,610)(  6,601)(  7,602)
(  8,603)(  9,604)( 10,605)( 11,611)( 12,612)( 13,613)( 14,614)( 15,615)
( 16,621)( 17,622)( 18,623)( 19,624)( 20,625)( 21,616)( 22,617)( 23,618)
( 24,619)( 25,620)( 26,626)( 27,627)( 28,628)( 29,629)( 30,630)( 31,636)
( 32,637)( 33,638)( 34,639)( 35,640)( 36,631)( 37,632)( 38,633)( 39,634)
( 40,635)( 41,641)( 42,642)( 43,643)( 44,644)( 45,645)( 46,651)( 47,652)
( 48,653)( 49,654)( 50,655)( 51,646)( 52,647)( 53,648)( 54,649)( 55,650)
( 56,656)( 57,657)( 58,658)( 59,659)( 60,660)( 61,666)( 62,667)( 63,668)
( 64,669)( 65,670)( 66,661)( 67,662)( 68,663)( 69,664)( 70,665)( 71,671)
( 72,672)( 73,673)( 74,674)( 75,675)( 76,681)( 77,682)( 78,683)( 79,684)
( 80,685)( 81,676)( 82,677)( 83,678)( 84,679)( 85,680)( 86,686)( 87,687)
( 88,688)( 89,689)( 90,690)( 91,696)( 92,697)( 93,698)( 94,699)( 95,700)
( 96,691)( 97,692)( 98,693)( 99,694)(100,695)(101,701)(102,702)(103,703)
(104,704)(105,705)(106,711)(107,712)(108,713)(109,714)(110,715)(111,706)
(112,707)(113,708)(114,709)(115,710)(116,716)(117,717)(118,718)(119,719)
(120,720)(121,546)(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);
s3 := Sym(960)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)
(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)
( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)
(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)
(280,400)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)
(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)
(360,480)(481,601)(482,602)(483,603)(484,604)(485,605)(486,606)(487,607)
(488,608)(489,609)(490,610)(491,611)(492,612)(493,613)(494,614)(495,615)
(496,616)(497,617)(498,618)(499,619)(500,620)(501,621)(502,622)(503,623)
(504,624)(505,625)(506,626)(507,627)(508,628)(509,629)(510,630)(511,631)
(512,632)(513,633)(514,634)(515,635)(516,636)(517,637)(518,638)(519,639)
(520,640)(521,641)(522,642)(523,643)(524,644)(525,645)(526,646)(527,647)
(528,648)(529,649)(530,650)(531,651)(532,652)(533,653)(534,654)(535,655)
(536,656)(537,657)(538,658)(539,659)(540,660)(541,661)(542,662)(543,663)
(544,664)(545,665)(546,666)(547,667)(548,668)(549,669)(550,670)(551,671)
(552,672)(553,673)(554,674)(555,675)(556,676)(557,677)(558,678)(559,679)
(560,680)(561,681)(562,682)(563,683)(564,684)(565,685)(566,686)(567,687)
(568,688)(569,689)(570,690)(571,691)(572,692)(573,693)(574,694)(575,695)
(576,696)(577,697)(578,698)(579,699)(580,700)(581,701)(582,702)(583,703)
(584,704)(585,705)(586,706)(587,707)(588,708)(589,709)(590,710)(591,711)
(592,712)(593,713)(594,714)(595,715)(596,716)(597,717)(598,718)(599,719)
(600,720)(721,841)(722,842)(723,843)(724,844)(725,845)(726,846)(727,847)
(728,848)(729,849)(730,850)(731,851)(732,852)(733,853)(734,854)(735,855)
(736,856)(737,857)(738,858)(739,859)(740,860)(741,861)(742,862)(743,863)
(744,864)(745,865)(746,866)(747,867)(748,868)(749,869)(750,870)(751,871)
(752,872)(753,873)(754,874)(755,875)(756,876)(757,877)(758,878)(759,879)
(760,880)(761,881)(762,882)(763,883)(764,884)(765,885)(766,886)(767,887)
(768,888)(769,889)(770,890)(771,891)(772,892)(773,893)(774,894)(775,895)
(776,896)(777,897)(778,898)(779,899)(780,900)(781,901)(782,902)(783,903)
(784,904)(785,905)(786,906)(787,907)(788,908)(789,909)(790,910)(791,911)
(792,912)(793,913)(794,914)(795,915)(796,916)(797,917)(798,918)(799,919)
(800,920)(801,921)(802,922)(803,923)(804,924)(805,925)(806,926)(807,927)
(808,928)(809,929)(810,930)(811,931)(812,932)(813,933)(814,934)(815,935)
(816,936)(817,937)(818,938)(819,939)(820,940)(821,941)(822,942)(823,943)
(824,944)(825,945)(826,946)(827,947)(828,948)(829,949)(830,950)(831,951)
(832,952)(833,953)(834,954)(835,955)(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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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