Polytope of Type {12,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,20,4}*1920
Also Known As : {{12,20|2},{20,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,58500)
Rank : 4
Schlafli Type : {12,20,4}
Number of vertices, edges, etc : 12, 120, 40, 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 : {6,20,4}*960, {12,10,4}*960, {12,20,2}*960
   3-fold quotients : {4,20,4}*640
   4-fold quotients : {12,10,2}*480, {6,20,2}*480a, {6,10,4}*480
   5-fold quotients : {12,4,4}*384
   6-fold quotients : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320
   8-fold quotients : {6,10,2}*240
   10-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
   12-fold quotients : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {4,4,4}*128
   20-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,5,2}*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 := (  1,601)(  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)
(121,481)(122,482)(123,483)(124,484)(125,485)(126,491)(127,492)(128,493)
(129,494)(130,495)(131,486)(132,487)(133,488)(134,489)(135,490)(136,496)
(137,497)(138,498)(139,499)(140,500)(141,506)(142,507)(143,508)(144,509)
(145,510)(146,501)(147,502)(148,503)(149,504)(150,505)(151,511)(152,512)
(153,513)(154,514)(155,515)(156,521)(157,522)(158,523)(159,524)(160,525)
(161,516)(162,517)(163,518)(164,519)(165,520)(166,526)(167,527)(168,528)
(169,529)(170,530)(171,536)(172,537)(173,538)(174,539)(175,540)(176,531)
(177,532)(178,533)(179,534)(180,535)(181,541)(182,542)(183,543)(184,544)
(185,545)(186,551)(187,552)(188,553)(189,554)(190,555)(191,546)(192,547)
(193,548)(194,549)(195,550)(196,556)(197,557)(198,558)(199,559)(200,560)
(201,566)(202,567)(203,568)(204,569)(205,570)(206,561)(207,562)(208,563)
(209,564)(210,565)(211,571)(212,572)(213,573)(214,574)(215,575)(216,581)
(217,582)(218,583)(219,584)(220,585)(221,576)(222,577)(223,578)(224,579)
(225,580)(226,586)(227,587)(228,588)(229,589)(230,590)(231,596)(232,597)
(233,598)(234,599)(235,600)(236,591)(237,592)(238,593)(239,594)(240,595)
(241,856)(242,857)(243,858)(244,859)(245,860)(246,866)(247,867)(248,868)
(249,869)(250,870)(251,861)(252,862)(253,863)(254,864)(255,865)(256,841)
(257,842)(258,843)(259,844)(260,845)(261,851)(262,852)(263,853)(264,854)
(265,855)(266,846)(267,847)(268,848)(269,849)(270,850)(271,886)(272,887)
(273,888)(274,889)(275,890)(276,896)(277,897)(278,898)(279,899)(280,900)
(281,891)(282,892)(283,893)(284,894)(285,895)(286,871)(287,872)(288,873)
(289,874)(290,875)(291,881)(292,882)(293,883)(294,884)(295,885)(296,876)
(297,877)(298,878)(299,879)(300,880)(301,916)(302,917)(303,918)(304,919)
(305,920)(306,926)(307,927)(308,928)(309,929)(310,930)(311,921)(312,922)
(313,923)(314,924)(315,925)(316,901)(317,902)(318,903)(319,904)(320,905)
(321,911)(322,912)(323,913)(324,914)(325,915)(326,906)(327,907)(328,908)
(329,909)(330,910)(331,946)(332,947)(333,948)(334,949)(335,950)(336,956)
(337,957)(338,958)(339,959)(340,960)(341,951)(342,952)(343,953)(344,954)
(345,955)(346,931)(347,932)(348,933)(349,934)(350,935)(351,941)(352,942)
(353,943)(354,944)(355,945)(356,936)(357,937)(358,938)(359,939)(360,940)
(361,736)(362,737)(363,738)(364,739)(365,740)(366,746)(367,747)(368,748)
(369,749)(370,750)(371,741)(372,742)(373,743)(374,744)(375,745)(376,721)
(377,722)(378,723)(379,724)(380,725)(381,731)(382,732)(383,733)(384,734)
(385,735)(386,726)(387,727)(388,728)(389,729)(390,730)(391,766)(392,767)
(393,768)(394,769)(395,770)(396,776)(397,777)(398,778)(399,779)(400,780)
(401,771)(402,772)(403,773)(404,774)(405,775)(406,751)(407,752)(408,753)
(409,754)(410,755)(411,761)(412,762)(413,763)(414,764)(415,765)(416,756)
(417,757)(418,758)(419,759)(420,760)(421,796)(422,797)(423,798)(424,799)
(425,800)(426,806)(427,807)(428,808)(429,809)(430,810)(431,801)(432,802)
(433,803)(434,804)(435,805)(436,781)(437,782)(438,783)(439,784)(440,785)
(441,791)(442,792)(443,793)(444,794)(445,795)(446,786)(447,787)(448,788)
(449,789)(450,790)(451,826)(452,827)(453,828)(454,829)(455,830)(456,836)
(457,837)(458,838)(459,839)(460,840)(461,831)(462,832)(463,833)(464,834)
(465,835)(466,811)(467,812)(468,813)(469,814)(470,815)(471,821)(472,822)
(473,823)(474,824)(475,825)(476,816)(477,817)(478,818)(479,819)(480,820);;
s1 := (  1,246)(  2,250)(  3,249)(  4,248)(  5,247)(  6,241)(  7,245)(  8,244)
(  9,243)( 10,242)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,261)
( 17,265)( 18,264)( 19,263)( 20,262)( 21,256)( 22,260)( 23,259)( 24,258)
( 25,257)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,276)( 32,280)
( 33,279)( 34,278)( 35,277)( 36,271)( 37,275)( 38,274)( 39,273)( 40,272)
( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,291)( 47,295)( 48,294)
( 49,293)( 50,292)( 51,286)( 52,290)( 53,289)( 54,288)( 55,287)( 56,296)
( 57,300)( 58,299)( 59,298)( 60,297)( 61,306)( 62,310)( 63,309)( 64,308)
( 65,307)( 66,301)( 67,305)( 68,304)( 69,303)( 70,302)( 71,311)( 72,315)
( 73,314)( 74,313)( 75,312)( 76,321)( 77,325)( 78,324)( 79,323)( 80,322)
( 81,316)( 82,320)( 83,319)( 84,318)( 85,317)( 86,326)( 87,330)( 88,329)
( 89,328)( 90,327)( 91,336)( 92,340)( 93,339)( 94,338)( 95,337)( 96,331)
( 97,335)( 98,334)( 99,333)(100,332)(101,341)(102,345)(103,344)(104,343)
(105,342)(106,351)(107,355)(108,354)(109,353)(110,352)(111,346)(112,350)
(113,349)(114,348)(115,347)(116,356)(117,360)(118,359)(119,358)(120,357)
(121,366)(122,370)(123,369)(124,368)(125,367)(126,361)(127,365)(128,364)
(129,363)(130,362)(131,371)(132,375)(133,374)(134,373)(135,372)(136,381)
(137,385)(138,384)(139,383)(140,382)(141,376)(142,380)(143,379)(144,378)
(145,377)(146,386)(147,390)(148,389)(149,388)(150,387)(151,396)(152,400)
(153,399)(154,398)(155,397)(156,391)(157,395)(158,394)(159,393)(160,392)
(161,401)(162,405)(163,404)(164,403)(165,402)(166,411)(167,415)(168,414)
(169,413)(170,412)(171,406)(172,410)(173,409)(174,408)(175,407)(176,416)
(177,420)(178,419)(179,418)(180,417)(181,426)(182,430)(183,429)(184,428)
(185,427)(186,421)(187,425)(188,424)(189,423)(190,422)(191,431)(192,435)
(193,434)(194,433)(195,432)(196,441)(197,445)(198,444)(199,443)(200,442)
(201,436)(202,440)(203,439)(204,438)(205,437)(206,446)(207,450)(208,449)
(209,448)(210,447)(211,456)(212,460)(213,459)(214,458)(215,457)(216,451)
(217,455)(218,454)(219,453)(220,452)(221,461)(222,465)(223,464)(224,463)
(225,462)(226,471)(227,475)(228,474)(229,473)(230,472)(231,466)(232,470)
(233,469)(234,468)(235,467)(236,476)(237,480)(238,479)(239,478)(240,477)
(481,726)(482,730)(483,729)(484,728)(485,727)(486,721)(487,725)(488,724)
(489,723)(490,722)(491,731)(492,735)(493,734)(494,733)(495,732)(496,741)
(497,745)(498,744)(499,743)(500,742)(501,736)(502,740)(503,739)(504,738)
(505,737)(506,746)(507,750)(508,749)(509,748)(510,747)(511,756)(512,760)
(513,759)(514,758)(515,757)(516,751)(517,755)(518,754)(519,753)(520,752)
(521,761)(522,765)(523,764)(524,763)(525,762)(526,771)(527,775)(528,774)
(529,773)(530,772)(531,766)(532,770)(533,769)(534,768)(535,767)(536,776)
(537,780)(538,779)(539,778)(540,777)(541,786)(542,790)(543,789)(544,788)
(545,787)(546,781)(547,785)(548,784)(549,783)(550,782)(551,791)(552,795)
(553,794)(554,793)(555,792)(556,801)(557,805)(558,804)(559,803)(560,802)
(561,796)(562,800)(563,799)(564,798)(565,797)(566,806)(567,810)(568,809)
(569,808)(570,807)(571,816)(572,820)(573,819)(574,818)(575,817)(576,811)
(577,815)(578,814)(579,813)(580,812)(581,821)(582,825)(583,824)(584,823)
(585,822)(586,831)(587,835)(588,834)(589,833)(590,832)(591,826)(592,830)
(593,829)(594,828)(595,827)(596,836)(597,840)(598,839)(599,838)(600,837)
(601,846)(602,850)(603,849)(604,848)(605,847)(606,841)(607,845)(608,844)
(609,843)(610,842)(611,851)(612,855)(613,854)(614,853)(615,852)(616,861)
(617,865)(618,864)(619,863)(620,862)(621,856)(622,860)(623,859)(624,858)
(625,857)(626,866)(627,870)(628,869)(629,868)(630,867)(631,876)(632,880)
(633,879)(634,878)(635,877)(636,871)(637,875)(638,874)(639,873)(640,872)
(641,881)(642,885)(643,884)(644,883)(645,882)(646,891)(647,895)(648,894)
(649,893)(650,892)(651,886)(652,890)(653,889)(654,888)(655,887)(656,896)
(657,900)(658,899)(659,898)(660,897)(661,906)(662,910)(663,909)(664,908)
(665,907)(666,901)(667,905)(668,904)(669,903)(670,902)(671,911)(672,915)
(673,914)(674,913)(675,912)(676,921)(677,925)(678,924)(679,923)(680,922)
(681,916)(682,920)(683,919)(684,918)(685,917)(686,926)(687,930)(688,929)
(689,928)(690,927)(691,936)(692,940)(693,939)(694,938)(695,937)(696,931)
(697,935)(698,934)(699,933)(700,932)(701,941)(702,945)(703,944)(704,943)
(705,942)(706,951)(707,955)(708,954)(709,953)(710,952)(711,946)(712,950)
(713,949)(714,948)(715,947)(716,956)(717,960)(718,959)(719,958)(720,957);;
s2 := (  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)
(121,542)(122,541)(123,545)(124,544)(125,543)(126,547)(127,546)(128,550)
(129,549)(130,548)(131,552)(132,551)(133,555)(134,554)(135,553)(136,557)
(137,556)(138,560)(139,559)(140,558)(141,562)(142,561)(143,565)(144,564)
(145,563)(146,567)(147,566)(148,570)(149,569)(150,568)(151,572)(152,571)
(153,575)(154,574)(155,573)(156,577)(157,576)(158,580)(159,579)(160,578)
(161,582)(162,581)(163,585)(164,584)(165,583)(166,587)(167,586)(168,590)
(169,589)(170,588)(171,592)(172,591)(173,595)(174,594)(175,593)(176,597)
(177,596)(178,600)(179,599)(180,598)(181,482)(182,481)(183,485)(184,484)
(185,483)(186,487)(187,486)(188,490)(189,489)(190,488)(191,492)(192,491)
(193,495)(194,494)(195,493)(196,497)(197,496)(198,500)(199,499)(200,498)
(201,502)(202,501)(203,505)(204,504)(205,503)(206,507)(207,506)(208,510)
(209,509)(210,508)(211,512)(212,511)(213,515)(214,514)(215,513)(216,517)
(217,516)(218,520)(219,519)(220,518)(221,522)(222,521)(223,525)(224,524)
(225,523)(226,527)(227,526)(228,530)(229,529)(230,528)(231,532)(232,531)
(233,535)(234,534)(235,533)(236,537)(237,536)(238,540)(239,539)(240,538)
(241,887)(242,886)(243,890)(244,889)(245,888)(246,892)(247,891)(248,895)
(249,894)(250,893)(251,897)(252,896)(253,900)(254,899)(255,898)(256,872)
(257,871)(258,875)(259,874)(260,873)(261,877)(262,876)(263,880)(264,879)
(265,878)(266,882)(267,881)(268,885)(269,884)(270,883)(271,857)(272,856)
(273,860)(274,859)(275,858)(276,862)(277,861)(278,865)(279,864)(280,863)
(281,867)(282,866)(283,870)(284,869)(285,868)(286,842)(287,841)(288,845)
(289,844)(290,843)(291,847)(292,846)(293,850)(294,849)(295,848)(296,852)
(297,851)(298,855)(299,854)(300,853)(301,947)(302,946)(303,950)(304,949)
(305,948)(306,952)(307,951)(308,955)(309,954)(310,953)(311,957)(312,956)
(313,960)(314,959)(315,958)(316,932)(317,931)(318,935)(319,934)(320,933)
(321,937)(322,936)(323,940)(324,939)(325,938)(326,942)(327,941)(328,945)
(329,944)(330,943)(331,917)(332,916)(333,920)(334,919)(335,918)(336,922)
(337,921)(338,925)(339,924)(340,923)(341,927)(342,926)(343,930)(344,929)
(345,928)(346,902)(347,901)(348,905)(349,904)(350,903)(351,907)(352,906)
(353,910)(354,909)(355,908)(356,912)(357,911)(358,915)(359,914)(360,913)
(361,827)(362,826)(363,830)(364,829)(365,828)(366,832)(367,831)(368,835)
(369,834)(370,833)(371,837)(372,836)(373,840)(374,839)(375,838)(376,812)
(377,811)(378,815)(379,814)(380,813)(381,817)(382,816)(383,820)(384,819)
(385,818)(386,822)(387,821)(388,825)(389,824)(390,823)(391,797)(392,796)
(393,800)(394,799)(395,798)(396,802)(397,801)(398,805)(399,804)(400,803)
(401,807)(402,806)(403,810)(404,809)(405,808)(406,782)(407,781)(408,785)
(409,784)(410,783)(411,787)(412,786)(413,790)(414,789)(415,788)(416,792)
(417,791)(418,795)(419,794)(420,793)(421,767)(422,766)(423,770)(424,769)
(425,768)(426,772)(427,771)(428,775)(429,774)(430,773)(431,777)(432,776)
(433,780)(434,779)(435,778)(436,752)(437,751)(438,755)(439,754)(440,753)
(441,757)(442,756)(443,760)(444,759)(445,758)(446,762)(447,761)(448,765)
(449,764)(450,763)(451,737)(452,736)(453,740)(454,739)(455,738)(456,742)
(457,741)(458,745)(459,744)(460,743)(461,747)(462,746)(463,750)(464,749)
(465,748)(466,722)(467,721)(468,725)(469,724)(470,723)(471,727)(472,726)
(473,730)(474,729)(475,728)(476,732)(477,731)(478,735)(479,734)(480,733);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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)(121,481)(122,482)(123,483)(124,484)(125,485)(126,491)(127,492)
(128,493)(129,494)(130,495)(131,486)(132,487)(133,488)(134,489)(135,490)
(136,496)(137,497)(138,498)(139,499)(140,500)(141,506)(142,507)(143,508)
(144,509)(145,510)(146,501)(147,502)(148,503)(149,504)(150,505)(151,511)
(152,512)(153,513)(154,514)(155,515)(156,521)(157,522)(158,523)(159,524)
(160,525)(161,516)(162,517)(163,518)(164,519)(165,520)(166,526)(167,527)
(168,528)(169,529)(170,530)(171,536)(172,537)(173,538)(174,539)(175,540)
(176,531)(177,532)(178,533)(179,534)(180,535)(181,541)(182,542)(183,543)
(184,544)(185,545)(186,551)(187,552)(188,553)(189,554)(190,555)(191,546)
(192,547)(193,548)(194,549)(195,550)(196,556)(197,557)(198,558)(199,559)
(200,560)(201,566)(202,567)(203,568)(204,569)(205,570)(206,561)(207,562)
(208,563)(209,564)(210,565)(211,571)(212,572)(213,573)(214,574)(215,575)
(216,581)(217,582)(218,583)(219,584)(220,585)(221,576)(222,577)(223,578)
(224,579)(225,580)(226,586)(227,587)(228,588)(229,589)(230,590)(231,596)
(232,597)(233,598)(234,599)(235,600)(236,591)(237,592)(238,593)(239,594)
(240,595)(241,856)(242,857)(243,858)(244,859)(245,860)(246,866)(247,867)
(248,868)(249,869)(250,870)(251,861)(252,862)(253,863)(254,864)(255,865)
(256,841)(257,842)(258,843)(259,844)(260,845)(261,851)(262,852)(263,853)
(264,854)(265,855)(266,846)(267,847)(268,848)(269,849)(270,850)(271,886)
(272,887)(273,888)(274,889)(275,890)(276,896)(277,897)(278,898)(279,899)
(280,900)(281,891)(282,892)(283,893)(284,894)(285,895)(286,871)(287,872)
(288,873)(289,874)(290,875)(291,881)(292,882)(293,883)(294,884)(295,885)
(296,876)(297,877)(298,878)(299,879)(300,880)(301,916)(302,917)(303,918)
(304,919)(305,920)(306,926)(307,927)(308,928)(309,929)(310,930)(311,921)
(312,922)(313,923)(314,924)(315,925)(316,901)(317,902)(318,903)(319,904)
(320,905)(321,911)(322,912)(323,913)(324,914)(325,915)(326,906)(327,907)
(328,908)(329,909)(330,910)(331,946)(332,947)(333,948)(334,949)(335,950)
(336,956)(337,957)(338,958)(339,959)(340,960)(341,951)(342,952)(343,953)
(344,954)(345,955)(346,931)(347,932)(348,933)(349,934)(350,935)(351,941)
(352,942)(353,943)(354,944)(355,945)(356,936)(357,937)(358,938)(359,939)
(360,940)(361,736)(362,737)(363,738)(364,739)(365,740)(366,746)(367,747)
(368,748)(369,749)(370,750)(371,741)(372,742)(373,743)(374,744)(375,745)
(376,721)(377,722)(378,723)(379,724)(380,725)(381,731)(382,732)(383,733)
(384,734)(385,735)(386,726)(387,727)(388,728)(389,729)(390,730)(391,766)
(392,767)(393,768)(394,769)(395,770)(396,776)(397,777)(398,778)(399,779)
(400,780)(401,771)(402,772)(403,773)(404,774)(405,775)(406,751)(407,752)
(408,753)(409,754)(410,755)(411,761)(412,762)(413,763)(414,764)(415,765)
(416,756)(417,757)(418,758)(419,759)(420,760)(421,796)(422,797)(423,798)
(424,799)(425,800)(426,806)(427,807)(428,808)(429,809)(430,810)(431,801)
(432,802)(433,803)(434,804)(435,805)(436,781)(437,782)(438,783)(439,784)
(440,785)(441,791)(442,792)(443,793)(444,794)(445,795)(446,786)(447,787)
(448,788)(449,789)(450,790)(451,826)(452,827)(453,828)(454,829)(455,830)
(456,836)(457,837)(458,838)(459,839)(460,840)(461,831)(462,832)(463,833)
(464,834)(465,835)(466,811)(467,812)(468,813)(469,814)(470,815)(471,821)
(472,822)(473,823)(474,824)(475,825)(476,816)(477,817)(478,818)(479,819)
(480,820);
s1 := Sym(960)!(  1,246)(  2,250)(  3,249)(  4,248)(  5,247)(  6,241)(  7,245)
(  8,244)(  9,243)( 10,242)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)
( 16,261)( 17,265)( 18,264)( 19,263)( 20,262)( 21,256)( 22,260)( 23,259)
( 24,258)( 25,257)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,276)
( 32,280)( 33,279)( 34,278)( 35,277)( 36,271)( 37,275)( 38,274)( 39,273)
( 40,272)( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,291)( 47,295)
( 48,294)( 49,293)( 50,292)( 51,286)( 52,290)( 53,289)( 54,288)( 55,287)
( 56,296)( 57,300)( 58,299)( 59,298)( 60,297)( 61,306)( 62,310)( 63,309)
( 64,308)( 65,307)( 66,301)( 67,305)( 68,304)( 69,303)( 70,302)( 71,311)
( 72,315)( 73,314)( 74,313)( 75,312)( 76,321)( 77,325)( 78,324)( 79,323)
( 80,322)( 81,316)( 82,320)( 83,319)( 84,318)( 85,317)( 86,326)( 87,330)
( 88,329)( 89,328)( 90,327)( 91,336)( 92,340)( 93,339)( 94,338)( 95,337)
( 96,331)( 97,335)( 98,334)( 99,333)(100,332)(101,341)(102,345)(103,344)
(104,343)(105,342)(106,351)(107,355)(108,354)(109,353)(110,352)(111,346)
(112,350)(113,349)(114,348)(115,347)(116,356)(117,360)(118,359)(119,358)
(120,357)(121,366)(122,370)(123,369)(124,368)(125,367)(126,361)(127,365)
(128,364)(129,363)(130,362)(131,371)(132,375)(133,374)(134,373)(135,372)
(136,381)(137,385)(138,384)(139,383)(140,382)(141,376)(142,380)(143,379)
(144,378)(145,377)(146,386)(147,390)(148,389)(149,388)(150,387)(151,396)
(152,400)(153,399)(154,398)(155,397)(156,391)(157,395)(158,394)(159,393)
(160,392)(161,401)(162,405)(163,404)(164,403)(165,402)(166,411)(167,415)
(168,414)(169,413)(170,412)(171,406)(172,410)(173,409)(174,408)(175,407)
(176,416)(177,420)(178,419)(179,418)(180,417)(181,426)(182,430)(183,429)
(184,428)(185,427)(186,421)(187,425)(188,424)(189,423)(190,422)(191,431)
(192,435)(193,434)(194,433)(195,432)(196,441)(197,445)(198,444)(199,443)
(200,442)(201,436)(202,440)(203,439)(204,438)(205,437)(206,446)(207,450)
(208,449)(209,448)(210,447)(211,456)(212,460)(213,459)(214,458)(215,457)
(216,451)(217,455)(218,454)(219,453)(220,452)(221,461)(222,465)(223,464)
(224,463)(225,462)(226,471)(227,475)(228,474)(229,473)(230,472)(231,466)
(232,470)(233,469)(234,468)(235,467)(236,476)(237,480)(238,479)(239,478)
(240,477)(481,726)(482,730)(483,729)(484,728)(485,727)(486,721)(487,725)
(488,724)(489,723)(490,722)(491,731)(492,735)(493,734)(494,733)(495,732)
(496,741)(497,745)(498,744)(499,743)(500,742)(501,736)(502,740)(503,739)
(504,738)(505,737)(506,746)(507,750)(508,749)(509,748)(510,747)(511,756)
(512,760)(513,759)(514,758)(515,757)(516,751)(517,755)(518,754)(519,753)
(520,752)(521,761)(522,765)(523,764)(524,763)(525,762)(526,771)(527,775)
(528,774)(529,773)(530,772)(531,766)(532,770)(533,769)(534,768)(535,767)
(536,776)(537,780)(538,779)(539,778)(540,777)(541,786)(542,790)(543,789)
(544,788)(545,787)(546,781)(547,785)(548,784)(549,783)(550,782)(551,791)
(552,795)(553,794)(554,793)(555,792)(556,801)(557,805)(558,804)(559,803)
(560,802)(561,796)(562,800)(563,799)(564,798)(565,797)(566,806)(567,810)
(568,809)(569,808)(570,807)(571,816)(572,820)(573,819)(574,818)(575,817)
(576,811)(577,815)(578,814)(579,813)(580,812)(581,821)(582,825)(583,824)
(584,823)(585,822)(586,831)(587,835)(588,834)(589,833)(590,832)(591,826)
(592,830)(593,829)(594,828)(595,827)(596,836)(597,840)(598,839)(599,838)
(600,837)(601,846)(602,850)(603,849)(604,848)(605,847)(606,841)(607,845)
(608,844)(609,843)(610,842)(611,851)(612,855)(613,854)(614,853)(615,852)
(616,861)(617,865)(618,864)(619,863)(620,862)(621,856)(622,860)(623,859)
(624,858)(625,857)(626,866)(627,870)(628,869)(629,868)(630,867)(631,876)
(632,880)(633,879)(634,878)(635,877)(636,871)(637,875)(638,874)(639,873)
(640,872)(641,881)(642,885)(643,884)(644,883)(645,882)(646,891)(647,895)
(648,894)(649,893)(650,892)(651,886)(652,890)(653,889)(654,888)(655,887)
(656,896)(657,900)(658,899)(659,898)(660,897)(661,906)(662,910)(663,909)
(664,908)(665,907)(666,901)(667,905)(668,904)(669,903)(670,902)(671,911)
(672,915)(673,914)(674,913)(675,912)(676,921)(677,925)(678,924)(679,923)
(680,922)(681,916)(682,920)(683,919)(684,918)(685,917)(686,926)(687,930)
(688,929)(689,928)(690,927)(691,936)(692,940)(693,939)(694,938)(695,937)
(696,931)(697,935)(698,934)(699,933)(700,932)(701,941)(702,945)(703,944)
(704,943)(705,942)(706,951)(707,955)(708,954)(709,953)(710,952)(711,946)
(712,950)(713,949)(714,948)(715,947)(716,956)(717,960)(718,959)(719,958)
(720,957);
s2 := 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)(121,542)(122,541)(123,545)(124,544)(125,543)(126,547)(127,546)
(128,550)(129,549)(130,548)(131,552)(132,551)(133,555)(134,554)(135,553)
(136,557)(137,556)(138,560)(139,559)(140,558)(141,562)(142,561)(143,565)
(144,564)(145,563)(146,567)(147,566)(148,570)(149,569)(150,568)(151,572)
(152,571)(153,575)(154,574)(155,573)(156,577)(157,576)(158,580)(159,579)
(160,578)(161,582)(162,581)(163,585)(164,584)(165,583)(166,587)(167,586)
(168,590)(169,589)(170,588)(171,592)(172,591)(173,595)(174,594)(175,593)
(176,597)(177,596)(178,600)(179,599)(180,598)(181,482)(182,481)(183,485)
(184,484)(185,483)(186,487)(187,486)(188,490)(189,489)(190,488)(191,492)
(192,491)(193,495)(194,494)(195,493)(196,497)(197,496)(198,500)(199,499)
(200,498)(201,502)(202,501)(203,505)(204,504)(205,503)(206,507)(207,506)
(208,510)(209,509)(210,508)(211,512)(212,511)(213,515)(214,514)(215,513)
(216,517)(217,516)(218,520)(219,519)(220,518)(221,522)(222,521)(223,525)
(224,524)(225,523)(226,527)(227,526)(228,530)(229,529)(230,528)(231,532)
(232,531)(233,535)(234,534)(235,533)(236,537)(237,536)(238,540)(239,539)
(240,538)(241,887)(242,886)(243,890)(244,889)(245,888)(246,892)(247,891)
(248,895)(249,894)(250,893)(251,897)(252,896)(253,900)(254,899)(255,898)
(256,872)(257,871)(258,875)(259,874)(260,873)(261,877)(262,876)(263,880)
(264,879)(265,878)(266,882)(267,881)(268,885)(269,884)(270,883)(271,857)
(272,856)(273,860)(274,859)(275,858)(276,862)(277,861)(278,865)(279,864)
(280,863)(281,867)(282,866)(283,870)(284,869)(285,868)(286,842)(287,841)
(288,845)(289,844)(290,843)(291,847)(292,846)(293,850)(294,849)(295,848)
(296,852)(297,851)(298,855)(299,854)(300,853)(301,947)(302,946)(303,950)
(304,949)(305,948)(306,952)(307,951)(308,955)(309,954)(310,953)(311,957)
(312,956)(313,960)(314,959)(315,958)(316,932)(317,931)(318,935)(319,934)
(320,933)(321,937)(322,936)(323,940)(324,939)(325,938)(326,942)(327,941)
(328,945)(329,944)(330,943)(331,917)(332,916)(333,920)(334,919)(335,918)
(336,922)(337,921)(338,925)(339,924)(340,923)(341,927)(342,926)(343,930)
(344,929)(345,928)(346,902)(347,901)(348,905)(349,904)(350,903)(351,907)
(352,906)(353,910)(354,909)(355,908)(356,912)(357,911)(358,915)(359,914)
(360,913)(361,827)(362,826)(363,830)(364,829)(365,828)(366,832)(367,831)
(368,835)(369,834)(370,833)(371,837)(372,836)(373,840)(374,839)(375,838)
(376,812)(377,811)(378,815)(379,814)(380,813)(381,817)(382,816)(383,820)
(384,819)(385,818)(386,822)(387,821)(388,825)(389,824)(390,823)(391,797)
(392,796)(393,800)(394,799)(395,798)(396,802)(397,801)(398,805)(399,804)
(400,803)(401,807)(402,806)(403,810)(404,809)(405,808)(406,782)(407,781)
(408,785)(409,784)(410,783)(411,787)(412,786)(413,790)(414,789)(415,788)
(416,792)(417,791)(418,795)(419,794)(420,793)(421,767)(422,766)(423,770)
(424,769)(425,768)(426,772)(427,771)(428,775)(429,774)(430,773)(431,777)
(432,776)(433,780)(434,779)(435,778)(436,752)(437,751)(438,755)(439,754)
(440,753)(441,757)(442,756)(443,760)(444,759)(445,758)(446,762)(447,761)
(448,765)(449,764)(450,763)(451,737)(452,736)(453,740)(454,739)(455,738)
(456,742)(457,741)(458,745)(459,744)(460,743)(461,747)(462,746)(463,750)
(464,749)(465,748)(466,722)(467,721)(468,725)(469,724)(470,723)(471,727)
(472,726)(473,730)(474,729)(475,728)(476,732)(477,731)(478,735)(479,734)
(480,733);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope