Polytope of Type {6,16,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16,10}*1920
Also Known As : {{6,16|2},{16,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,203901)
Rank : 4
Schlafli Type : {6,16,10}
Number of vertices, edges, etc : 6, 48, 80, 10
Order of s0s1s2s3 : 240
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 : {6,8,10}*960
3-fold quotients : {2,16,10}*640
4-fold quotients : {6,4,10}*480
5-fold quotients : {6,16,2}*384
6-fold quotients : {2,8,10}*320
8-fold quotients : {6,2,10}*240
10-fold quotients : {6,8,2}*192
12-fold quotients : {2,4,10}*160
15-fold quotients : {2,16,2}*128
16-fold quotients : {3,2,10}*120, {6,2,5}*120
20-fold quotients : {6,4,2}*96a
24-fold quotients : {2,2,10}*80
30-fold quotients : {2,8,2}*64
32-fold quotients : {3,2,5}*60
40-fold quotients : {6,2,2}*48
48-fold quotients : {2,2,5}*40
60-fold quotients : {2,4,2}*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 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)( 8,253)
( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)( 72,307)
( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)( 88,323)
( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,341)
( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)(104,339)
(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)(120,355)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)(192,427)
(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)(208,443)
(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)(216,461)
(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)(224,459)
(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)(232,477)
(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)(240,475)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)(552,787)
(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)(568,803)
(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)(576,821)
(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)(584,819)
(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)(592,837)
(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)(600,835)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)(608,853)
(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)(624,869)
(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)(640,885)
(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)(656,891)
(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)(672,907)
(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)(688,923)
(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)(696,941)
(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)(704,939)
(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)(712,957)
(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)(720,955);;
s1 := ( 1,246)( 2,247)( 3,248)( 4,249)( 5,250)( 6,241)( 7,242)( 8,243)
( 9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,261)
( 17,262)( 18,263)( 19,264)( 20,265)( 21,256)( 22,257)( 23,258)( 24,259)
( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,291)( 32,292)
( 33,293)( 34,294)( 35,295)( 36,286)( 37,287)( 38,288)( 39,289)( 40,290)
( 41,296)( 42,297)( 43,298)( 44,299)( 45,300)( 46,276)( 47,277)( 48,278)
( 49,279)( 50,280)( 51,271)( 52,272)( 53,273)( 54,274)( 55,275)( 56,281)
( 57,282)( 58,283)( 59,284)( 60,285)( 61,336)( 62,337)( 63,338)( 64,339)
( 65,340)( 66,331)( 67,332)( 68,333)( 69,334)( 70,335)( 71,341)( 72,342)
( 73,343)( 74,344)( 75,345)( 76,351)( 77,352)( 78,353)( 79,354)( 80,355)
( 81,346)( 82,347)( 83,348)( 84,349)( 85,350)( 86,356)( 87,357)( 88,358)
( 89,359)( 90,360)( 91,306)( 92,307)( 93,308)( 94,309)( 95,310)( 96,301)
( 97,302)( 98,303)( 99,304)(100,305)(101,311)(102,312)(103,313)(104,314)
(105,315)(106,321)(107,322)(108,323)(109,324)(110,325)(111,316)(112,317)
(113,318)(114,319)(115,320)(116,326)(117,327)(118,328)(119,329)(120,330)
(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)(128,363)
(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)(144,379)
(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,411)(152,412)
(153,413)(154,414)(155,415)(156,406)(157,407)(158,408)(159,409)(160,410)
(161,416)(162,417)(163,418)(164,419)(165,420)(166,396)(167,397)(168,398)
(169,399)(170,400)(171,391)(172,392)(173,393)(174,394)(175,395)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,456)(182,457)(183,458)(184,459)
(185,460)(186,451)(187,452)(188,453)(189,454)(190,455)(191,461)(192,462)
(193,463)(194,464)(195,465)(196,471)(197,472)(198,473)(199,474)(200,475)
(201,466)(202,467)(203,468)(204,469)(205,470)(206,476)(207,477)(208,478)
(209,479)(210,480)(211,426)(212,427)(213,428)(214,429)(215,430)(216,421)
(217,422)(218,423)(219,424)(220,425)(221,431)(222,432)(223,433)(224,434)
(225,435)(226,441)(227,442)(228,443)(229,444)(230,445)(231,436)(232,437)
(233,438)(234,439)(235,440)(236,446)(237,447)(238,448)(239,449)(240,450)
(481,786)(482,787)(483,788)(484,789)(485,790)(486,781)(487,782)(488,783)
(489,784)(490,785)(491,791)(492,792)(493,793)(494,794)(495,795)(496,801)
(497,802)(498,803)(499,804)(500,805)(501,796)(502,797)(503,798)(504,799)
(505,800)(506,806)(507,807)(508,808)(509,809)(510,810)(511,831)(512,832)
(513,833)(514,834)(515,835)(516,826)(517,827)(518,828)(519,829)(520,830)
(521,836)(522,837)(523,838)(524,839)(525,840)(526,816)(527,817)(528,818)
(529,819)(530,820)(531,811)(532,812)(533,813)(534,814)(535,815)(536,821)
(537,822)(538,823)(539,824)(540,825)(541,726)(542,727)(543,728)(544,729)
(545,730)(546,721)(547,722)(548,723)(549,724)(550,725)(551,731)(552,732)
(553,733)(554,734)(555,735)(556,741)(557,742)(558,743)(559,744)(560,745)
(561,736)(562,737)(563,738)(564,739)(565,740)(566,746)(567,747)(568,748)
(569,749)(570,750)(571,771)(572,772)(573,773)(574,774)(575,775)(576,766)
(577,767)(578,768)(579,769)(580,770)(581,776)(582,777)(583,778)(584,779)
(585,780)(586,756)(587,757)(588,758)(589,759)(590,760)(591,751)(592,752)
(593,753)(594,754)(595,755)(596,761)(597,762)(598,763)(599,764)(600,765)
(601,906)(602,907)(603,908)(604,909)(605,910)(606,901)(607,902)(608,903)
(609,904)(610,905)(611,911)(612,912)(613,913)(614,914)(615,915)(616,921)
(617,922)(618,923)(619,924)(620,925)(621,916)(622,917)(623,918)(624,919)
(625,920)(626,926)(627,927)(628,928)(629,929)(630,930)(631,951)(632,952)
(633,953)(634,954)(635,955)(636,946)(637,947)(638,948)(639,949)(640,950)
(641,956)(642,957)(643,958)(644,959)(645,960)(646,936)(647,937)(648,938)
(649,939)(650,940)(651,931)(652,932)(653,933)(654,934)(655,935)(656,941)
(657,942)(658,943)(659,944)(660,945)(661,846)(662,847)(663,848)(664,849)
(665,850)(666,841)(667,842)(668,843)(669,844)(670,845)(671,851)(672,852)
(673,853)(674,854)(675,855)(676,861)(677,862)(678,863)(679,864)(680,865)
(681,856)(682,857)(683,858)(684,859)(685,860)(686,866)(687,867)(688,868)
(689,869)(690,870)(691,891)(692,892)(693,893)(694,894)(695,895)(696,886)
(697,887)(698,888)(699,889)(700,890)(701,896)(702,897)(703,898)(704,899)
(705,900)(706,876)(707,877)(708,878)(709,879)(710,880)(711,871)(712,872)
(713,873)(714,874)(715,875)(716,881)(717,882)(718,883)(719,884)(720,885);;
s2 := ( 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)( 31,646)( 32,650)
( 33,649)( 34,648)( 35,647)( 36,651)( 37,655)( 38,654)( 39,653)( 40,652)
( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,631)( 47,635)( 48,634)
( 49,633)( 50,632)( 51,636)( 52,640)( 53,639)( 54,638)( 55,637)( 56,641)
( 57,645)( 58,644)( 59,643)( 60,642)( 61,691)( 62,695)( 63,694)( 64,693)
( 65,692)( 66,696)( 67,700)( 68,699)( 69,698)( 70,697)( 71,701)( 72,705)
( 73,704)( 74,703)( 75,702)( 76,706)( 77,710)( 78,709)( 79,708)( 80,707)
( 81,711)( 82,715)( 83,714)( 84,713)( 85,712)( 86,716)( 87,720)( 88,719)
( 89,718)( 90,717)( 91,661)( 92,665)( 93,664)( 94,663)( 95,662)( 96,666)
( 97,670)( 98,669)( 99,668)(100,667)(101,671)(102,675)(103,674)(104,673)
(105,672)(106,676)(107,680)(108,679)(109,678)(110,677)(111,681)(112,685)
(113,684)(114,683)(115,682)(116,686)(117,690)(118,689)(119,688)(120,687)
(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)(151,526)(152,530)
(153,529)(154,528)(155,527)(156,531)(157,535)(158,534)(159,533)(160,532)
(161,536)(162,540)(163,539)(164,538)(165,537)(166,511)(167,515)(168,514)
(169,513)(170,512)(171,516)(172,520)(173,519)(174,518)(175,517)(176,521)
(177,525)(178,524)(179,523)(180,522)(181,571)(182,575)(183,574)(184,573)
(185,572)(186,576)(187,580)(188,579)(189,578)(190,577)(191,581)(192,585)
(193,584)(194,583)(195,582)(196,586)(197,590)(198,589)(199,588)(200,587)
(201,591)(202,595)(203,594)(204,593)(205,592)(206,596)(207,600)(208,599)
(209,598)(210,597)(211,541)(212,545)(213,544)(214,543)(215,542)(216,546)
(217,550)(218,549)(219,548)(220,547)(221,551)(222,555)(223,554)(224,553)
(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,561)(232,565)
(233,564)(234,563)(235,562)(236,566)(237,570)(238,569)(239,568)(240,567)
(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)(248,849)
(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)(256,856)
(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)(264,863)
(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(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)(301,931)(302,935)(303,934)(304,933)
(305,932)(306,936)(307,940)(308,939)(309,938)(310,937)(311,941)(312,945)
(313,944)(314,943)(315,942)(316,946)(317,950)(318,949)(319,948)(320,947)
(321,951)(322,955)(323,954)(324,953)(325,952)(326,956)(327,960)(328,959)
(329,958)(330,957)(331,901)(332,905)(333,904)(334,903)(335,902)(336,906)
(337,910)(338,909)(339,908)(340,907)(341,911)(342,915)(343,914)(344,913)
(345,912)(346,916)(347,920)(348,919)(349,918)(350,917)(351,921)(352,925)
(353,924)(354,923)(355,922)(356,926)(357,930)(358,929)(359,928)(360,927)
(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)(368,729)
(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)(376,736)
(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)(384,743)
(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(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)(421,811)(422,815)(423,814)(424,813)
(425,812)(426,816)(427,820)(428,819)(429,818)(430,817)(431,821)(432,825)
(433,824)(434,823)(435,822)(436,826)(437,830)(438,829)(439,828)(440,827)
(441,831)(442,835)(443,834)(444,833)(445,832)(446,836)(447,840)(448,839)
(449,838)(450,837)(451,781)(452,785)(453,784)(454,783)(455,782)(456,786)
(457,790)(458,789)(459,788)(460,787)(461,791)(462,795)(463,794)(464,793)
(465,792)(466,796)(467,800)(468,799)(469,798)(470,797)(471,801)(472,805)
(473,804)(474,803)(475,802)(476,806)(477,810)(478,809)(479,808)(480,807);;
s3 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)
( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)(280,398)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)(304,424)
(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)(320,438)
(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)(328,450)
(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)(336,457)
(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)(344,464)
(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)(352,471)
(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)(360,478)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)(576,697)
(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)(592,711)
(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)(728,850)
(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)(744,864)
(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)(760,878)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)(784,904)
(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)(792,911)
(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)(800,918)
(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)(808,930)
(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)(816,937)
(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)(824,944)
(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)(832,951)
(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)(840,958);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)
( 8,253)( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)
( 72,307)( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)
( 88,323)( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,341)( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)
(104,339)(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)
(120,355)(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)
(192,427)(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)
(208,443)(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,461)(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)
(224,459)(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)
(232,477)(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)
(240,475)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)
(552,787)(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)
(568,803)(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,821)(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)
(584,819)(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)
(592,837)(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)
(600,835)(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)
(608,853)(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)
(624,869)(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)
(640,885)(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)
(656,891)(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)
(672,907)(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)
(688,923)(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,941)(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)
(704,939)(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)
(712,957)(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)
(720,955);
s1 := Sym(960)!( 1,246)( 2,247)( 3,248)( 4,249)( 5,250)( 6,241)( 7,242)
( 8,243)( 9,244)( 10,245)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,261)( 17,262)( 18,263)( 19,264)( 20,265)( 21,256)( 22,257)( 23,258)
( 24,259)( 25,260)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,291)
( 32,292)( 33,293)( 34,294)( 35,295)( 36,286)( 37,287)( 38,288)( 39,289)
( 40,290)( 41,296)( 42,297)( 43,298)( 44,299)( 45,300)( 46,276)( 47,277)
( 48,278)( 49,279)( 50,280)( 51,271)( 52,272)( 53,273)( 54,274)( 55,275)
( 56,281)( 57,282)( 58,283)( 59,284)( 60,285)( 61,336)( 62,337)( 63,338)
( 64,339)( 65,340)( 66,331)( 67,332)( 68,333)( 69,334)( 70,335)( 71,341)
( 72,342)( 73,343)( 74,344)( 75,345)( 76,351)( 77,352)( 78,353)( 79,354)
( 80,355)( 81,346)( 82,347)( 83,348)( 84,349)( 85,350)( 86,356)( 87,357)
( 88,358)( 89,359)( 90,360)( 91,306)( 92,307)( 93,308)( 94,309)( 95,310)
( 96,301)( 97,302)( 98,303)( 99,304)(100,305)(101,311)(102,312)(103,313)
(104,314)(105,315)(106,321)(107,322)(108,323)(109,324)(110,325)(111,316)
(112,317)(113,318)(114,319)(115,320)(116,326)(117,327)(118,328)(119,329)
(120,330)(121,366)(122,367)(123,368)(124,369)(125,370)(126,361)(127,362)
(128,363)(129,364)(130,365)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,376)(142,377)(143,378)
(144,379)(145,380)(146,386)(147,387)(148,388)(149,389)(150,390)(151,411)
(152,412)(153,413)(154,414)(155,415)(156,406)(157,407)(158,408)(159,409)
(160,410)(161,416)(162,417)(163,418)(164,419)(165,420)(166,396)(167,397)
(168,398)(169,399)(170,400)(171,391)(172,392)(173,393)(174,394)(175,395)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,456)(182,457)(183,458)
(184,459)(185,460)(186,451)(187,452)(188,453)(189,454)(190,455)(191,461)
(192,462)(193,463)(194,464)(195,465)(196,471)(197,472)(198,473)(199,474)
(200,475)(201,466)(202,467)(203,468)(204,469)(205,470)(206,476)(207,477)
(208,478)(209,479)(210,480)(211,426)(212,427)(213,428)(214,429)(215,430)
(216,421)(217,422)(218,423)(219,424)(220,425)(221,431)(222,432)(223,433)
(224,434)(225,435)(226,441)(227,442)(228,443)(229,444)(230,445)(231,436)
(232,437)(233,438)(234,439)(235,440)(236,446)(237,447)(238,448)(239,449)
(240,450)(481,786)(482,787)(483,788)(484,789)(485,790)(486,781)(487,782)
(488,783)(489,784)(490,785)(491,791)(492,792)(493,793)(494,794)(495,795)
(496,801)(497,802)(498,803)(499,804)(500,805)(501,796)(502,797)(503,798)
(504,799)(505,800)(506,806)(507,807)(508,808)(509,809)(510,810)(511,831)
(512,832)(513,833)(514,834)(515,835)(516,826)(517,827)(518,828)(519,829)
(520,830)(521,836)(522,837)(523,838)(524,839)(525,840)(526,816)(527,817)
(528,818)(529,819)(530,820)(531,811)(532,812)(533,813)(534,814)(535,815)
(536,821)(537,822)(538,823)(539,824)(540,825)(541,726)(542,727)(543,728)
(544,729)(545,730)(546,721)(547,722)(548,723)(549,724)(550,725)(551,731)
(552,732)(553,733)(554,734)(555,735)(556,741)(557,742)(558,743)(559,744)
(560,745)(561,736)(562,737)(563,738)(564,739)(565,740)(566,746)(567,747)
(568,748)(569,749)(570,750)(571,771)(572,772)(573,773)(574,774)(575,775)
(576,766)(577,767)(578,768)(579,769)(580,770)(581,776)(582,777)(583,778)
(584,779)(585,780)(586,756)(587,757)(588,758)(589,759)(590,760)(591,751)
(592,752)(593,753)(594,754)(595,755)(596,761)(597,762)(598,763)(599,764)
(600,765)(601,906)(602,907)(603,908)(604,909)(605,910)(606,901)(607,902)
(608,903)(609,904)(610,905)(611,911)(612,912)(613,913)(614,914)(615,915)
(616,921)(617,922)(618,923)(619,924)(620,925)(621,916)(622,917)(623,918)
(624,919)(625,920)(626,926)(627,927)(628,928)(629,929)(630,930)(631,951)
(632,952)(633,953)(634,954)(635,955)(636,946)(637,947)(638,948)(639,949)
(640,950)(641,956)(642,957)(643,958)(644,959)(645,960)(646,936)(647,937)
(648,938)(649,939)(650,940)(651,931)(652,932)(653,933)(654,934)(655,935)
(656,941)(657,942)(658,943)(659,944)(660,945)(661,846)(662,847)(663,848)
(664,849)(665,850)(666,841)(667,842)(668,843)(669,844)(670,845)(671,851)
(672,852)(673,853)(674,854)(675,855)(676,861)(677,862)(678,863)(679,864)
(680,865)(681,856)(682,857)(683,858)(684,859)(685,860)(686,866)(687,867)
(688,868)(689,869)(690,870)(691,891)(692,892)(693,893)(694,894)(695,895)
(696,886)(697,887)(698,888)(699,889)(700,890)(701,896)(702,897)(703,898)
(704,899)(705,900)(706,876)(707,877)(708,878)(709,879)(710,880)(711,871)
(712,872)(713,873)(714,874)(715,875)(716,881)(717,882)(718,883)(719,884)
(720,885);
s2 := 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)( 31,646)
( 32,650)( 33,649)( 34,648)( 35,647)( 36,651)( 37,655)( 38,654)( 39,653)
( 40,652)( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,631)( 47,635)
( 48,634)( 49,633)( 50,632)( 51,636)( 52,640)( 53,639)( 54,638)( 55,637)
( 56,641)( 57,645)( 58,644)( 59,643)( 60,642)( 61,691)( 62,695)( 63,694)
( 64,693)( 65,692)( 66,696)( 67,700)( 68,699)( 69,698)( 70,697)( 71,701)
( 72,705)( 73,704)( 74,703)( 75,702)( 76,706)( 77,710)( 78,709)( 79,708)
( 80,707)( 81,711)( 82,715)( 83,714)( 84,713)( 85,712)( 86,716)( 87,720)
( 88,719)( 89,718)( 90,717)( 91,661)( 92,665)( 93,664)( 94,663)( 95,662)
( 96,666)( 97,670)( 98,669)( 99,668)(100,667)(101,671)(102,675)(103,674)
(104,673)(105,672)(106,676)(107,680)(108,679)(109,678)(110,677)(111,681)
(112,685)(113,684)(114,683)(115,682)(116,686)(117,690)(118,689)(119,688)
(120,687)(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)(151,526)
(152,530)(153,529)(154,528)(155,527)(156,531)(157,535)(158,534)(159,533)
(160,532)(161,536)(162,540)(163,539)(164,538)(165,537)(166,511)(167,515)
(168,514)(169,513)(170,512)(171,516)(172,520)(173,519)(174,518)(175,517)
(176,521)(177,525)(178,524)(179,523)(180,522)(181,571)(182,575)(183,574)
(184,573)(185,572)(186,576)(187,580)(188,579)(189,578)(190,577)(191,581)
(192,585)(193,584)(194,583)(195,582)(196,586)(197,590)(198,589)(199,588)
(200,587)(201,591)(202,595)(203,594)(204,593)(205,592)(206,596)(207,600)
(208,599)(209,598)(210,597)(211,541)(212,545)(213,544)(214,543)(215,542)
(216,546)(217,550)(218,549)(219,548)(220,547)(221,551)(222,555)(223,554)
(224,553)(225,552)(226,556)(227,560)(228,559)(229,558)(230,557)(231,561)
(232,565)(233,564)(234,563)(235,562)(236,566)(237,570)(238,569)(239,568)
(240,567)(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)
(248,849)(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)
(256,856)(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)
(264,863)(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(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)(301,931)(302,935)(303,934)
(304,933)(305,932)(306,936)(307,940)(308,939)(309,938)(310,937)(311,941)
(312,945)(313,944)(314,943)(315,942)(316,946)(317,950)(318,949)(319,948)
(320,947)(321,951)(322,955)(323,954)(324,953)(325,952)(326,956)(327,960)
(328,959)(329,958)(330,957)(331,901)(332,905)(333,904)(334,903)(335,902)
(336,906)(337,910)(338,909)(339,908)(340,907)(341,911)(342,915)(343,914)
(344,913)(345,912)(346,916)(347,920)(348,919)(349,918)(350,917)(351,921)
(352,925)(353,924)(354,923)(355,922)(356,926)(357,930)(358,929)(359,928)
(360,927)(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)
(368,729)(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)
(376,736)(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)
(384,743)(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(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)(421,811)(422,815)(423,814)
(424,813)(425,812)(426,816)(427,820)(428,819)(429,818)(430,817)(431,821)
(432,825)(433,824)(434,823)(435,822)(436,826)(437,830)(438,829)(439,828)
(440,827)(441,831)(442,835)(443,834)(444,833)(445,832)(446,836)(447,840)
(448,839)(449,838)(450,837)(451,781)(452,785)(453,784)(454,783)(455,782)
(456,786)(457,790)(458,789)(459,788)(460,787)(461,791)(462,795)(463,794)
(464,793)(465,792)(466,796)(467,800)(468,799)(469,798)(470,797)(471,801)
(472,805)(473,804)(474,803)(475,802)(476,806)(477,810)(478,809)(479,808)
(480,807);
s3 := Sym(960)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)
( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)
(280,398)(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)
(304,424)(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)
(320,438)(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)
(328,450)(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)
(336,457)(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)
(344,464)(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)
(352,471)(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)
(360,478)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,697)(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)
(592,711)(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)
(728,850)(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)
(744,864)(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)
(760,878)(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)
(784,904)(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)
(792,911)(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)
(800,918)(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)
(808,930)(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)
(816,937)(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)
(824,944)(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)
(832,951)(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)
(840,958);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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