Polytope of Type {4,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240412)
Rank : 4
Schlafli Type : {4,30,4}
Number of vertices, edges, etc : 4, 120, 120, 8
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Non-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 : {4,15,4}*960a, {4,30,4}*960f, {4,30,4}*960g
4-fold quotients : {4,30,2}*480c, {4,15,4}*480
5-fold quotients : {4,6,4}*384f
8-fold quotients : {4,15,2}*240
10-fold quotients : {4,3,4}*192a, {4,6,4}*192f, {4,6,4}*192g
20-fold quotients : {4,6,2}*96b, {4,3,4}*96
40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)
( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)
( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)( 24,512)
( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)
( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)
( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)
( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)
( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)
( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)
( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)
( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)
( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)
( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)
(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)
(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)
(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)
(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)
(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)
(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)
(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)
(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)
(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)
(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)
(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)
(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)
(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)
(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)
(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)
(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)
(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)
(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)
(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)
(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)
(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)
(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)
(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)
(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)
(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)
(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)
(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)
(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)
(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)
(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)
(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)
(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)
(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)
(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)
(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)
(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)
(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)
(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)
(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)
(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)
(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)
(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)
(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)
(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)
(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)
(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)
(473,945)(474,946)(475,947)(476,948)(477,949)(478,950)(479,951)(480,952);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)( 26, 78)
( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)( 42, 62)
( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)
( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)
(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)
(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)(122,222)
(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)
(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)(138,206)
(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)
(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)(154,190)
(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)
(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)(268,319)
(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)
(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)(284,303)
(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)
(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)(348,479)
(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)
(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)(364,463)
(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)
(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)(380,447)
(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)
(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)(396,431)
(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)(490,494)
(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)
(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)
(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)
(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)
(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)(566,646)
(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)
(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)(582,710)
(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)
(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)(598,694)
(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)
(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)(614,678)
(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)
(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)(630,662)
(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)
(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)(732,735)
(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)(744,791)
(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)
(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)(760,775)
(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)
(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)(808,887)
(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)
(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)(824,951)
(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)
(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)(840,935)
(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)
(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)(856,919)
(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)
(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)(872,903)
(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);;
s2 := ( 1,577)( 2,580)( 3,579)( 4,578)( 5,589)( 6,592)( 7,591)( 8,590)
( 9,585)( 10,588)( 11,587)( 12,586)( 13,581)( 14,584)( 15,583)( 16,582)
( 17,561)( 18,564)( 19,563)( 20,562)( 21,573)( 22,576)( 23,575)( 24,574)
( 25,569)( 26,572)( 27,571)( 28,570)( 29,565)( 30,568)( 31,567)( 32,566)
( 33,625)( 34,628)( 35,627)( 36,626)( 37,637)( 38,640)( 39,639)( 40,638)
( 41,633)( 42,636)( 43,635)( 44,634)( 45,629)( 46,632)( 47,631)( 48,630)
( 49,609)( 50,612)( 51,611)( 52,610)( 53,621)( 54,624)( 55,623)( 56,622)
( 57,617)( 58,620)( 59,619)( 60,618)( 61,613)( 62,616)( 63,615)( 64,614)
( 65,593)( 66,596)( 67,595)( 68,594)( 69,605)( 70,608)( 71,607)( 72,606)
( 73,601)( 74,604)( 75,603)( 76,602)( 77,597)( 78,600)( 79,599)( 80,598)
( 81,497)( 82,500)( 83,499)( 84,498)( 85,509)( 86,512)( 87,511)( 88,510)
( 89,505)( 90,508)( 91,507)( 92,506)( 93,501)( 94,504)( 95,503)( 96,502)
( 97,481)( 98,484)( 99,483)(100,482)(101,493)(102,496)(103,495)(104,494)
(105,489)(106,492)(107,491)(108,490)(109,485)(110,488)(111,487)(112,486)
(113,545)(114,548)(115,547)(116,546)(117,557)(118,560)(119,559)(120,558)
(121,553)(122,556)(123,555)(124,554)(125,549)(126,552)(127,551)(128,550)
(129,529)(130,532)(131,531)(132,530)(133,541)(134,544)(135,543)(136,542)
(137,537)(138,540)(139,539)(140,538)(141,533)(142,536)(143,535)(144,534)
(145,513)(146,516)(147,515)(148,514)(149,525)(150,528)(151,527)(152,526)
(153,521)(154,524)(155,523)(156,522)(157,517)(158,520)(159,519)(160,518)
(161,657)(162,660)(163,659)(164,658)(165,669)(166,672)(167,671)(168,670)
(169,665)(170,668)(171,667)(172,666)(173,661)(174,664)(175,663)(176,662)
(177,641)(178,644)(179,643)(180,642)(181,653)(182,656)(183,655)(184,654)
(185,649)(186,652)(187,651)(188,650)(189,645)(190,648)(191,647)(192,646)
(193,705)(194,708)(195,707)(196,706)(197,717)(198,720)(199,719)(200,718)
(201,713)(202,716)(203,715)(204,714)(205,709)(206,712)(207,711)(208,710)
(209,689)(210,692)(211,691)(212,690)(213,701)(214,704)(215,703)(216,702)
(217,697)(218,700)(219,699)(220,698)(221,693)(222,696)(223,695)(224,694)
(225,673)(226,676)(227,675)(228,674)(229,685)(230,688)(231,687)(232,686)
(233,681)(234,684)(235,683)(236,682)(237,677)(238,680)(239,679)(240,678)
(241,817)(242,820)(243,819)(244,818)(245,829)(246,832)(247,831)(248,830)
(249,825)(250,828)(251,827)(252,826)(253,821)(254,824)(255,823)(256,822)
(257,801)(258,804)(259,803)(260,802)(261,813)(262,816)(263,815)(264,814)
(265,809)(266,812)(267,811)(268,810)(269,805)(270,808)(271,807)(272,806)
(273,865)(274,868)(275,867)(276,866)(277,877)(278,880)(279,879)(280,878)
(281,873)(282,876)(283,875)(284,874)(285,869)(286,872)(287,871)(288,870)
(289,849)(290,852)(291,851)(292,850)(293,861)(294,864)(295,863)(296,862)
(297,857)(298,860)(299,859)(300,858)(301,853)(302,856)(303,855)(304,854)
(305,833)(306,836)(307,835)(308,834)(309,845)(310,848)(311,847)(312,846)
(313,841)(314,844)(315,843)(316,842)(317,837)(318,840)(319,839)(320,838)
(321,737)(322,740)(323,739)(324,738)(325,749)(326,752)(327,751)(328,750)
(329,745)(330,748)(331,747)(332,746)(333,741)(334,744)(335,743)(336,742)
(337,721)(338,724)(339,723)(340,722)(341,733)(342,736)(343,735)(344,734)
(345,729)(346,732)(347,731)(348,730)(349,725)(350,728)(351,727)(352,726)
(353,785)(354,788)(355,787)(356,786)(357,797)(358,800)(359,799)(360,798)
(361,793)(362,796)(363,795)(364,794)(365,789)(366,792)(367,791)(368,790)
(369,769)(370,772)(371,771)(372,770)(373,781)(374,784)(375,783)(376,782)
(377,777)(378,780)(379,779)(380,778)(381,773)(382,776)(383,775)(384,774)
(385,753)(386,756)(387,755)(388,754)(389,765)(390,768)(391,767)(392,766)
(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)(400,758)
(401,897)(402,900)(403,899)(404,898)(405,909)(406,912)(407,911)(408,910)
(409,905)(410,908)(411,907)(412,906)(413,901)(414,904)(415,903)(416,902)
(417,881)(418,884)(419,883)(420,882)(421,893)(422,896)(423,895)(424,894)
(425,889)(426,892)(427,891)(428,890)(429,885)(430,888)(431,887)(432,886)
(433,945)(434,948)(435,947)(436,946)(437,957)(438,960)(439,959)(440,958)
(441,953)(442,956)(443,955)(444,954)(445,949)(446,952)(447,951)(448,950)
(449,929)(450,932)(451,931)(452,930)(453,941)(454,944)(455,943)(456,942)
(457,937)(458,940)(459,939)(460,938)(461,933)(462,936)(463,935)(464,934)
(465,913)(466,916)(467,915)(468,914)(469,925)(470,928)(471,927)(472,926)
(473,921)(474,924)(475,923)(476,922)(477,917)(478,920)(479,919)(480,918);;
s3 := ( 1,242)( 2,241)( 3,244)( 4,243)( 5,246)( 6,245)( 7,248)( 8,247)
( 9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)
( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)
( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)
( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)
( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)
( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)
( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)
( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)
( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)
( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)
(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)
(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)
(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)(128,367)
(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)(136,375)
(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)(144,383)
(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)(152,391)
(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)(160,399)
(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)(168,407)
(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)(176,415)
(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)(184,423)
(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)(192,431)
(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)(200,439)
(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)(208,447)
(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)(216,455)
(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)(224,463)
(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)(232,471)
(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)(240,479)
(481,722)(482,721)(483,724)(484,723)(485,726)(486,725)(487,728)(488,727)
(489,730)(490,729)(491,732)(492,731)(493,734)(494,733)(495,736)(496,735)
(497,738)(498,737)(499,740)(500,739)(501,742)(502,741)(503,744)(504,743)
(505,746)(506,745)(507,748)(508,747)(509,750)(510,749)(511,752)(512,751)
(513,754)(514,753)(515,756)(516,755)(517,758)(518,757)(519,760)(520,759)
(521,762)(522,761)(523,764)(524,763)(525,766)(526,765)(527,768)(528,767)
(529,770)(530,769)(531,772)(532,771)(533,774)(534,773)(535,776)(536,775)
(537,778)(538,777)(539,780)(540,779)(541,782)(542,781)(543,784)(544,783)
(545,786)(546,785)(547,788)(548,787)(549,790)(550,789)(551,792)(552,791)
(553,794)(554,793)(555,796)(556,795)(557,798)(558,797)(559,800)(560,799)
(561,802)(562,801)(563,804)(564,803)(565,806)(566,805)(567,808)(568,807)
(569,810)(570,809)(571,812)(572,811)(573,814)(574,813)(575,816)(576,815)
(577,818)(578,817)(579,820)(580,819)(581,822)(582,821)(583,824)(584,823)
(585,826)(586,825)(587,828)(588,827)(589,830)(590,829)(591,832)(592,831)
(593,834)(594,833)(595,836)(596,835)(597,838)(598,837)(599,840)(600,839)
(601,842)(602,841)(603,844)(604,843)(605,846)(606,845)(607,848)(608,847)
(609,850)(610,849)(611,852)(612,851)(613,854)(614,853)(615,856)(616,855)
(617,858)(618,857)(619,860)(620,859)(621,862)(622,861)(623,864)(624,863)
(625,866)(626,865)(627,868)(628,867)(629,870)(630,869)(631,872)(632,871)
(633,874)(634,873)(635,876)(636,875)(637,878)(638,877)(639,880)(640,879)
(641,882)(642,881)(643,884)(644,883)(645,886)(646,885)(647,888)(648,887)
(649,890)(650,889)(651,892)(652,891)(653,894)(654,893)(655,896)(656,895)
(657,898)(658,897)(659,900)(660,899)(661,902)(662,901)(663,904)(664,903)
(665,906)(666,905)(667,908)(668,907)(669,910)(670,909)(671,912)(672,911)
(673,914)(674,913)(675,916)(676,915)(677,918)(678,917)(679,920)(680,919)
(681,922)(682,921)(683,924)(684,923)(685,926)(686,925)(687,928)(688,927)
(689,930)(690,929)(691,932)(692,931)(693,934)(694,933)(695,936)(696,935)
(697,938)(698,937)(699,940)(700,939)(701,942)(702,941)(703,944)(704,943)
(705,946)(706,945)(707,948)(708,947)(709,950)(710,949)(711,952)(712,951)
(713,954)(714,953)(715,956)(716,955)(717,958)(718,957)(719,960)(720,959);;
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*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s0*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*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)
( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)
( 16,488)( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)
( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)
( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)
( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)
( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)
( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)
( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)
( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)
( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)
( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)
( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)
(104,592)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)
(112,584)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)
(120,608)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)
(128,600)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)
(136,624)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)
(144,616)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)
(152,640)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)
(160,632)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)
(168,656)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)
(176,648)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)
(184,672)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)
(192,664)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)
(200,688)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)
(208,680)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)
(216,704)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)
(224,696)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)
(232,720)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)
(240,712)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)
(248,736)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)
(256,728)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)
(264,752)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)
(272,744)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)
(280,768)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)
(288,760)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)
(296,784)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)
(304,776)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)
(312,800)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)
(320,792)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)
(328,816)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)
(336,808)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)
(344,832)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)
(352,824)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)
(360,848)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)
(368,840)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)
(376,864)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)
(384,856)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)
(392,880)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)
(400,872)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)
(408,896)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)
(416,888)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)
(424,912)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)
(432,904)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)
(440,928)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)
(448,920)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)
(456,944)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)
(464,936)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)
(472,960)(473,945)(474,946)(475,947)(476,948)(477,949)(478,950)(479,951)
(480,952);
s1 := Sym(960)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)
( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)
( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)
( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)
(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)
(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)
(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)
(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)
(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)
(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)
(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)
(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)
(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)
(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)
(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)
(340,467)(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)
(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)
(356,451)(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)
(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)
(372,435)(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)
(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)
(388,419)(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)
(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)
(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)
(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)
(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)
(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)
(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)
(566,646)(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)
(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)
(582,710)(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)
(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)
(598,694)(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)
(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)
(614,678)(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)
(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)
(630,662)(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)
(638,666)(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)
(732,735)(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)
(744,791)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)
(752,795)(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)
(760,775)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)
(768,779)(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)
(808,887)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)
(816,891)(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)
(824,951)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)
(832,955)(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)
(840,935)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)
(848,939)(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)
(856,919)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)
(864,923)(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)
(872,903)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)
(880,907);
s2 := Sym(960)!( 1,577)( 2,580)( 3,579)( 4,578)( 5,589)( 6,592)( 7,591)
( 8,590)( 9,585)( 10,588)( 11,587)( 12,586)( 13,581)( 14,584)( 15,583)
( 16,582)( 17,561)( 18,564)( 19,563)( 20,562)( 21,573)( 22,576)( 23,575)
( 24,574)( 25,569)( 26,572)( 27,571)( 28,570)( 29,565)( 30,568)( 31,567)
( 32,566)( 33,625)( 34,628)( 35,627)( 36,626)( 37,637)( 38,640)( 39,639)
( 40,638)( 41,633)( 42,636)( 43,635)( 44,634)( 45,629)( 46,632)( 47,631)
( 48,630)( 49,609)( 50,612)( 51,611)( 52,610)( 53,621)( 54,624)( 55,623)
( 56,622)( 57,617)( 58,620)( 59,619)( 60,618)( 61,613)( 62,616)( 63,615)
( 64,614)( 65,593)( 66,596)( 67,595)( 68,594)( 69,605)( 70,608)( 71,607)
( 72,606)( 73,601)( 74,604)( 75,603)( 76,602)( 77,597)( 78,600)( 79,599)
( 80,598)( 81,497)( 82,500)( 83,499)( 84,498)( 85,509)( 86,512)( 87,511)
( 88,510)( 89,505)( 90,508)( 91,507)( 92,506)( 93,501)( 94,504)( 95,503)
( 96,502)( 97,481)( 98,484)( 99,483)(100,482)(101,493)(102,496)(103,495)
(104,494)(105,489)(106,492)(107,491)(108,490)(109,485)(110,488)(111,487)
(112,486)(113,545)(114,548)(115,547)(116,546)(117,557)(118,560)(119,559)
(120,558)(121,553)(122,556)(123,555)(124,554)(125,549)(126,552)(127,551)
(128,550)(129,529)(130,532)(131,531)(132,530)(133,541)(134,544)(135,543)
(136,542)(137,537)(138,540)(139,539)(140,538)(141,533)(142,536)(143,535)
(144,534)(145,513)(146,516)(147,515)(148,514)(149,525)(150,528)(151,527)
(152,526)(153,521)(154,524)(155,523)(156,522)(157,517)(158,520)(159,519)
(160,518)(161,657)(162,660)(163,659)(164,658)(165,669)(166,672)(167,671)
(168,670)(169,665)(170,668)(171,667)(172,666)(173,661)(174,664)(175,663)
(176,662)(177,641)(178,644)(179,643)(180,642)(181,653)(182,656)(183,655)
(184,654)(185,649)(186,652)(187,651)(188,650)(189,645)(190,648)(191,647)
(192,646)(193,705)(194,708)(195,707)(196,706)(197,717)(198,720)(199,719)
(200,718)(201,713)(202,716)(203,715)(204,714)(205,709)(206,712)(207,711)
(208,710)(209,689)(210,692)(211,691)(212,690)(213,701)(214,704)(215,703)
(216,702)(217,697)(218,700)(219,699)(220,698)(221,693)(222,696)(223,695)
(224,694)(225,673)(226,676)(227,675)(228,674)(229,685)(230,688)(231,687)
(232,686)(233,681)(234,684)(235,683)(236,682)(237,677)(238,680)(239,679)
(240,678)(241,817)(242,820)(243,819)(244,818)(245,829)(246,832)(247,831)
(248,830)(249,825)(250,828)(251,827)(252,826)(253,821)(254,824)(255,823)
(256,822)(257,801)(258,804)(259,803)(260,802)(261,813)(262,816)(263,815)
(264,814)(265,809)(266,812)(267,811)(268,810)(269,805)(270,808)(271,807)
(272,806)(273,865)(274,868)(275,867)(276,866)(277,877)(278,880)(279,879)
(280,878)(281,873)(282,876)(283,875)(284,874)(285,869)(286,872)(287,871)
(288,870)(289,849)(290,852)(291,851)(292,850)(293,861)(294,864)(295,863)
(296,862)(297,857)(298,860)(299,859)(300,858)(301,853)(302,856)(303,855)
(304,854)(305,833)(306,836)(307,835)(308,834)(309,845)(310,848)(311,847)
(312,846)(313,841)(314,844)(315,843)(316,842)(317,837)(318,840)(319,839)
(320,838)(321,737)(322,740)(323,739)(324,738)(325,749)(326,752)(327,751)
(328,750)(329,745)(330,748)(331,747)(332,746)(333,741)(334,744)(335,743)
(336,742)(337,721)(338,724)(339,723)(340,722)(341,733)(342,736)(343,735)
(344,734)(345,729)(346,732)(347,731)(348,730)(349,725)(350,728)(351,727)
(352,726)(353,785)(354,788)(355,787)(356,786)(357,797)(358,800)(359,799)
(360,798)(361,793)(362,796)(363,795)(364,794)(365,789)(366,792)(367,791)
(368,790)(369,769)(370,772)(371,771)(372,770)(373,781)(374,784)(375,783)
(376,782)(377,777)(378,780)(379,779)(380,778)(381,773)(382,776)(383,775)
(384,774)(385,753)(386,756)(387,755)(388,754)(389,765)(390,768)(391,767)
(392,766)(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)
(400,758)(401,897)(402,900)(403,899)(404,898)(405,909)(406,912)(407,911)
(408,910)(409,905)(410,908)(411,907)(412,906)(413,901)(414,904)(415,903)
(416,902)(417,881)(418,884)(419,883)(420,882)(421,893)(422,896)(423,895)
(424,894)(425,889)(426,892)(427,891)(428,890)(429,885)(430,888)(431,887)
(432,886)(433,945)(434,948)(435,947)(436,946)(437,957)(438,960)(439,959)
(440,958)(441,953)(442,956)(443,955)(444,954)(445,949)(446,952)(447,951)
(448,950)(449,929)(450,932)(451,931)(452,930)(453,941)(454,944)(455,943)
(456,942)(457,937)(458,940)(459,939)(460,938)(461,933)(462,936)(463,935)
(464,934)(465,913)(466,916)(467,915)(468,914)(469,925)(470,928)(471,927)
(472,926)(473,921)(474,924)(475,923)(476,922)(477,917)(478,920)(479,919)
(480,918);
s3 := Sym(960)!( 1,242)( 2,241)( 3,244)( 4,243)( 5,246)( 6,245)( 7,248)
( 8,247)( 9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)
( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)
( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)
( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)
( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)
( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)
( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)
( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)
( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)
( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)
( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)
(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)
(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)
(120,359)(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)
(128,367)(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)
(136,375)(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)
(144,383)(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)
(152,391)(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)
(160,399)(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)
(168,407)(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)
(176,415)(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)
(184,423)(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)
(192,431)(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)
(200,439)(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)
(208,447)(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)
(216,455)(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)
(224,463)(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)
(232,471)(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)
(240,479)(481,722)(482,721)(483,724)(484,723)(485,726)(486,725)(487,728)
(488,727)(489,730)(490,729)(491,732)(492,731)(493,734)(494,733)(495,736)
(496,735)(497,738)(498,737)(499,740)(500,739)(501,742)(502,741)(503,744)
(504,743)(505,746)(506,745)(507,748)(508,747)(509,750)(510,749)(511,752)
(512,751)(513,754)(514,753)(515,756)(516,755)(517,758)(518,757)(519,760)
(520,759)(521,762)(522,761)(523,764)(524,763)(525,766)(526,765)(527,768)
(528,767)(529,770)(530,769)(531,772)(532,771)(533,774)(534,773)(535,776)
(536,775)(537,778)(538,777)(539,780)(540,779)(541,782)(542,781)(543,784)
(544,783)(545,786)(546,785)(547,788)(548,787)(549,790)(550,789)(551,792)
(552,791)(553,794)(554,793)(555,796)(556,795)(557,798)(558,797)(559,800)
(560,799)(561,802)(562,801)(563,804)(564,803)(565,806)(566,805)(567,808)
(568,807)(569,810)(570,809)(571,812)(572,811)(573,814)(574,813)(575,816)
(576,815)(577,818)(578,817)(579,820)(580,819)(581,822)(582,821)(583,824)
(584,823)(585,826)(586,825)(587,828)(588,827)(589,830)(590,829)(591,832)
(592,831)(593,834)(594,833)(595,836)(596,835)(597,838)(598,837)(599,840)
(600,839)(601,842)(602,841)(603,844)(604,843)(605,846)(606,845)(607,848)
(608,847)(609,850)(610,849)(611,852)(612,851)(613,854)(614,853)(615,856)
(616,855)(617,858)(618,857)(619,860)(620,859)(621,862)(622,861)(623,864)
(624,863)(625,866)(626,865)(627,868)(628,867)(629,870)(630,869)(631,872)
(632,871)(633,874)(634,873)(635,876)(636,875)(637,878)(638,877)(639,880)
(640,879)(641,882)(642,881)(643,884)(644,883)(645,886)(646,885)(647,888)
(648,887)(649,890)(650,889)(651,892)(652,891)(653,894)(654,893)(655,896)
(656,895)(657,898)(658,897)(659,900)(660,899)(661,902)(662,901)(663,904)
(664,903)(665,906)(666,905)(667,908)(668,907)(669,910)(670,909)(671,912)
(672,911)(673,914)(674,913)(675,916)(676,915)(677,918)(678,917)(679,920)
(680,919)(681,922)(682,921)(683,924)(684,923)(685,926)(686,925)(687,928)
(688,927)(689,930)(690,929)(691,932)(692,931)(693,934)(694,933)(695,936)
(696,935)(697,938)(698,937)(699,940)(700,939)(701,942)(702,941)(703,944)
(704,943)(705,946)(706,945)(707,948)(708,947)(709,950)(710,949)(711,952)
(712,951)(713,954)(714,953)(715,956)(716,955)(717,958)(718,957)(719,960)
(720,959);
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*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s0*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*s0*s2*s1*s0 >;
References : None.
to this polytope