Polytope of Type {4,120}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239568)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 8, 480, 240
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,60}*960c
4-fold quotients : {4,30}*480
5-fold quotients : {4,24}*384e
8-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
10-fold quotients : {4,12}*192c
16-fold quotients : {4,15}*120, {2,30}*120
20-fold quotients : {4,6}*96
32-fold quotients : {2,15}*60
40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {2,10}*40
80-fold quotients : {4,3}*24, {2,6}*24
96-fold quotients : {2,5}*20
160-fold quotients : {2,3}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,485)( 2,486)( 3,488)( 4,487)( 5,482)( 6,481)( 7,483)( 8,484)
( 9,493)( 10,494)( 11,496)( 12,495)( 13,490)( 14,489)( 15,491)( 16,492)
( 17,501)( 18,502)( 19,504)( 20,503)( 21,498)( 22,497)( 23,499)( 24,500)
( 25,509)( 26,510)( 27,512)( 28,511)( 29,506)( 30,505)( 31,507)( 32,508)
( 33,517)( 34,518)( 35,520)( 36,519)( 37,514)( 38,513)( 39,515)( 40,516)
( 41,525)( 42,526)( 43,528)( 44,527)( 45,522)( 46,521)( 47,523)( 48,524)
( 49,533)( 50,534)( 51,536)( 52,535)( 53,530)( 54,529)( 55,531)( 56,532)
( 57,541)( 58,542)( 59,544)( 60,543)( 61,538)( 62,537)( 63,539)( 64,540)
( 65,549)( 66,550)( 67,552)( 68,551)( 69,546)( 70,545)( 71,547)( 72,548)
( 73,557)( 74,558)( 75,560)( 76,559)( 77,554)( 78,553)( 79,555)( 80,556)
( 81,565)( 82,566)( 83,568)( 84,567)( 85,562)( 86,561)( 87,563)( 88,564)
( 89,573)( 90,574)( 91,576)( 92,575)( 93,570)( 94,569)( 95,571)( 96,572)
( 97,581)( 98,582)( 99,584)(100,583)(101,578)(102,577)(103,579)(104,580)
(105,589)(106,590)(107,592)(108,591)(109,586)(110,585)(111,587)(112,588)
(113,597)(114,598)(115,600)(116,599)(117,594)(118,593)(119,595)(120,596)
(121,606)(122,605)(123,607)(124,608)(125,601)(126,602)(127,604)(128,603)
(129,614)(130,613)(131,615)(132,616)(133,609)(134,610)(135,612)(136,611)
(137,622)(138,621)(139,623)(140,624)(141,617)(142,618)(143,620)(144,619)
(145,630)(146,629)(147,631)(148,632)(149,625)(150,626)(151,628)(152,627)
(153,638)(154,637)(155,639)(156,640)(157,633)(158,634)(159,636)(160,635)
(161,646)(162,645)(163,647)(164,648)(165,641)(166,642)(167,644)(168,643)
(169,654)(170,653)(171,655)(172,656)(173,649)(174,650)(175,652)(176,651)
(177,662)(178,661)(179,663)(180,664)(181,657)(182,658)(183,660)(184,659)
(185,670)(186,669)(187,671)(188,672)(189,665)(190,666)(191,668)(192,667)
(193,678)(194,677)(195,679)(196,680)(197,673)(198,674)(199,676)(200,675)
(201,686)(202,685)(203,687)(204,688)(205,681)(206,682)(207,684)(208,683)
(209,694)(210,693)(211,695)(212,696)(213,689)(214,690)(215,692)(216,691)
(217,702)(218,701)(219,703)(220,704)(221,697)(222,698)(223,700)(224,699)
(225,710)(226,709)(227,711)(228,712)(229,705)(230,706)(231,708)(232,707)
(233,718)(234,717)(235,719)(236,720)(237,713)(238,714)(239,716)(240,715)
(241,845)(242,846)(243,848)(244,847)(245,842)(246,841)(247,843)(248,844)
(249,853)(250,854)(251,856)(252,855)(253,850)(254,849)(255,851)(256,852)
(257,861)(258,862)(259,864)(260,863)(261,858)(262,857)(263,859)(264,860)
(265,869)(266,870)(267,872)(268,871)(269,866)(270,865)(271,867)(272,868)
(273,877)(274,878)(275,880)(276,879)(277,874)(278,873)(279,875)(280,876)
(281,885)(282,886)(283,888)(284,887)(285,882)(286,881)(287,883)(288,884)
(289,893)(290,894)(291,896)(292,895)(293,890)(294,889)(295,891)(296,892)
(297,901)(298,902)(299,904)(300,903)(301,898)(302,897)(303,899)(304,900)
(305,909)(306,910)(307,912)(308,911)(309,906)(310,905)(311,907)(312,908)
(313,917)(314,918)(315,920)(316,919)(317,914)(318,913)(319,915)(320,916)
(321,925)(322,926)(323,928)(324,927)(325,922)(326,921)(327,923)(328,924)
(329,933)(330,934)(331,936)(332,935)(333,930)(334,929)(335,931)(336,932)
(337,941)(338,942)(339,944)(340,943)(341,938)(342,937)(343,939)(344,940)
(345,949)(346,950)(347,952)(348,951)(349,946)(350,945)(351,947)(352,948)
(353,957)(354,958)(355,960)(356,959)(357,954)(358,953)(359,955)(360,956)
(361,725)(362,726)(363,728)(364,727)(365,722)(366,721)(367,723)(368,724)
(369,733)(370,734)(371,736)(372,735)(373,730)(374,729)(375,731)(376,732)
(377,741)(378,742)(379,744)(380,743)(381,738)(382,737)(383,739)(384,740)
(385,749)(386,750)(387,752)(388,751)(389,746)(390,745)(391,747)(392,748)
(393,757)(394,758)(395,760)(396,759)(397,754)(398,753)(399,755)(400,756)
(401,765)(402,766)(403,768)(404,767)(405,762)(406,761)(407,763)(408,764)
(409,773)(410,774)(411,776)(412,775)(413,770)(414,769)(415,771)(416,772)
(417,781)(418,782)(419,784)(420,783)(421,778)(422,777)(423,779)(424,780)
(425,789)(426,790)(427,792)(428,791)(429,786)(430,785)(431,787)(432,788)
(433,797)(434,798)(435,800)(436,799)(437,794)(438,793)(439,795)(440,796)
(441,805)(442,806)(443,808)(444,807)(445,802)(446,801)(447,803)(448,804)
(449,813)(450,814)(451,816)(452,815)(453,810)(454,809)(455,811)(456,812)
(457,821)(458,822)(459,824)(460,823)(461,818)(462,817)(463,819)(464,820)
(465,829)(466,830)(467,832)(468,831)(469,826)(470,825)(471,827)(472,828)
(473,837)(474,838)(475,840)(476,839)(477,834)(478,833)(479,835)(480,836);;
s1 := ( 1,241)( 2,242)( 3,244)( 4,243)( 5,247)( 6,248)( 7,245)( 8,246)
( 9,273)( 10,274)( 11,276)( 12,275)( 13,279)( 14,280)( 15,277)( 16,278)
( 17,265)( 18,266)( 19,268)( 20,267)( 21,271)( 22,272)( 23,269)( 24,270)
( 25,257)( 26,258)( 27,260)( 28,259)( 29,263)( 30,264)( 31,261)( 32,262)
( 33,249)( 34,250)( 35,252)( 36,251)( 37,255)( 38,256)( 39,253)( 40,254)
( 41,321)( 42,322)( 43,324)( 44,323)( 45,327)( 46,328)( 47,325)( 48,326)
( 49,353)( 50,354)( 51,356)( 52,355)( 53,359)( 54,360)( 55,357)( 56,358)
( 57,345)( 58,346)( 59,348)( 60,347)( 61,351)( 62,352)( 63,349)( 64,350)
( 65,337)( 66,338)( 67,340)( 68,339)( 69,343)( 70,344)( 71,341)( 72,342)
( 73,329)( 74,330)( 75,332)( 76,331)( 77,335)( 78,336)( 79,333)( 80,334)
( 81,281)( 82,282)( 83,284)( 84,283)( 85,287)( 86,288)( 87,285)( 88,286)
( 89,313)( 90,314)( 91,316)( 92,315)( 93,319)( 94,320)( 95,317)( 96,318)
( 97,305)( 98,306)( 99,308)(100,307)(101,311)(102,312)(103,309)(104,310)
(105,297)(106,298)(107,300)(108,299)(109,303)(110,304)(111,301)(112,302)
(113,289)(114,290)(115,292)(116,291)(117,295)(118,296)(119,293)(120,294)
(121,362)(122,361)(123,363)(124,364)(125,368)(126,367)(127,366)(128,365)
(129,394)(130,393)(131,395)(132,396)(133,400)(134,399)(135,398)(136,397)
(137,386)(138,385)(139,387)(140,388)(141,392)(142,391)(143,390)(144,389)
(145,378)(146,377)(147,379)(148,380)(149,384)(150,383)(151,382)(152,381)
(153,370)(154,369)(155,371)(156,372)(157,376)(158,375)(159,374)(160,373)
(161,442)(162,441)(163,443)(164,444)(165,448)(166,447)(167,446)(168,445)
(169,474)(170,473)(171,475)(172,476)(173,480)(174,479)(175,478)(176,477)
(177,466)(178,465)(179,467)(180,468)(181,472)(182,471)(183,470)(184,469)
(185,458)(186,457)(187,459)(188,460)(189,464)(190,463)(191,462)(192,461)
(193,450)(194,449)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)
(201,402)(202,401)(203,403)(204,404)(205,408)(206,407)(207,406)(208,405)
(209,434)(210,433)(211,435)(212,436)(213,440)(214,439)(215,438)(216,437)
(217,426)(218,425)(219,427)(220,428)(221,432)(222,431)(223,430)(224,429)
(225,418)(226,417)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)
(233,410)(234,409)(235,411)(236,412)(237,416)(238,415)(239,414)(240,413)
(481,722)(482,721)(483,723)(484,724)(485,728)(486,727)(487,726)(488,725)
(489,754)(490,753)(491,755)(492,756)(493,760)(494,759)(495,758)(496,757)
(497,746)(498,745)(499,747)(500,748)(501,752)(502,751)(503,750)(504,749)
(505,738)(506,737)(507,739)(508,740)(509,744)(510,743)(511,742)(512,741)
(513,730)(514,729)(515,731)(516,732)(517,736)(518,735)(519,734)(520,733)
(521,802)(522,801)(523,803)(524,804)(525,808)(526,807)(527,806)(528,805)
(529,834)(530,833)(531,835)(532,836)(533,840)(534,839)(535,838)(536,837)
(537,826)(538,825)(539,827)(540,828)(541,832)(542,831)(543,830)(544,829)
(545,818)(546,817)(547,819)(548,820)(549,824)(550,823)(551,822)(552,821)
(553,810)(554,809)(555,811)(556,812)(557,816)(558,815)(559,814)(560,813)
(561,762)(562,761)(563,763)(564,764)(565,768)(566,767)(567,766)(568,765)
(569,794)(570,793)(571,795)(572,796)(573,800)(574,799)(575,798)(576,797)
(577,786)(578,785)(579,787)(580,788)(581,792)(582,791)(583,790)(584,789)
(585,778)(586,777)(587,779)(588,780)(589,784)(590,783)(591,782)(592,781)
(593,770)(594,769)(595,771)(596,772)(597,776)(598,775)(599,774)(600,773)
(601,841)(602,842)(603,844)(604,843)(605,847)(606,848)(607,845)(608,846)
(609,873)(610,874)(611,876)(612,875)(613,879)(614,880)(615,877)(616,878)
(617,865)(618,866)(619,868)(620,867)(621,871)(622,872)(623,869)(624,870)
(625,857)(626,858)(627,860)(628,859)(629,863)(630,864)(631,861)(632,862)
(633,849)(634,850)(635,852)(636,851)(637,855)(638,856)(639,853)(640,854)
(641,921)(642,922)(643,924)(644,923)(645,927)(646,928)(647,925)(648,926)
(649,953)(650,954)(651,956)(652,955)(653,959)(654,960)(655,957)(656,958)
(657,945)(658,946)(659,948)(660,947)(661,951)(662,952)(663,949)(664,950)
(665,937)(666,938)(667,940)(668,939)(669,943)(670,944)(671,941)(672,942)
(673,929)(674,930)(675,932)(676,931)(677,935)(678,936)(679,933)(680,934)
(681,881)(682,882)(683,884)(684,883)(685,887)(686,888)(687,885)(688,886)
(689,913)(690,914)(691,916)(692,915)(693,919)(694,920)(695,917)(696,918)
(697,905)(698,906)(699,908)(700,907)(701,911)(702,912)(703,909)(704,910)
(705,897)(706,898)(707,900)(708,899)(709,903)(710,904)(711,901)(712,902)
(713,889)(714,890)(715,892)(716,891)(717,895)(718,896)(719,893)(720,894);;
s2 := ( 1,529)( 2,530)( 3,535)( 4,536)( 5,534)( 6,533)( 7,531)( 8,532)
( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)( 16,524)
( 17,553)( 18,554)( 19,559)( 20,560)( 21,558)( 22,557)( 23,555)( 24,556)
( 25,545)( 26,546)( 27,551)( 28,552)( 29,550)( 30,549)( 31,547)( 32,548)
( 33,537)( 34,538)( 35,543)( 36,544)( 37,542)( 38,541)( 39,539)( 40,540)
( 41,489)( 42,490)( 43,495)( 44,496)( 45,494)( 46,493)( 47,491)( 48,492)
( 49,481)( 50,482)( 51,487)( 52,488)( 53,486)( 54,485)( 55,483)( 56,484)
( 57,513)( 58,514)( 59,519)( 60,520)( 61,518)( 62,517)( 63,515)( 64,516)
( 65,505)( 66,506)( 67,511)( 68,512)( 69,510)( 70,509)( 71,507)( 72,508)
( 73,497)( 74,498)( 75,503)( 76,504)( 77,502)( 78,501)( 79,499)( 80,500)
( 81,569)( 82,570)( 83,575)( 84,576)( 85,574)( 86,573)( 87,571)( 88,572)
( 89,561)( 90,562)( 91,567)( 92,568)( 93,566)( 94,565)( 95,563)( 96,564)
( 97,593)( 98,594)( 99,599)(100,600)(101,598)(102,597)(103,595)(104,596)
(105,585)(106,586)(107,591)(108,592)(109,590)(110,589)(111,587)(112,588)
(113,577)(114,578)(115,583)(116,584)(117,582)(118,581)(119,579)(120,580)
(121,650)(122,649)(123,656)(124,655)(125,653)(126,654)(127,652)(128,651)
(129,642)(130,641)(131,648)(132,647)(133,645)(134,646)(135,644)(136,643)
(137,674)(138,673)(139,680)(140,679)(141,677)(142,678)(143,676)(144,675)
(145,666)(146,665)(147,672)(148,671)(149,669)(150,670)(151,668)(152,667)
(153,658)(154,657)(155,664)(156,663)(157,661)(158,662)(159,660)(160,659)
(161,610)(162,609)(163,616)(164,615)(165,613)(166,614)(167,612)(168,611)
(169,602)(170,601)(171,608)(172,607)(173,605)(174,606)(175,604)(176,603)
(177,634)(178,633)(179,640)(180,639)(181,637)(182,638)(183,636)(184,635)
(185,626)(186,625)(187,632)(188,631)(189,629)(190,630)(191,628)(192,627)
(193,618)(194,617)(195,624)(196,623)(197,621)(198,622)(199,620)(200,619)
(201,690)(202,689)(203,696)(204,695)(205,693)(206,694)(207,692)(208,691)
(209,682)(210,681)(211,688)(212,687)(213,685)(214,686)(215,684)(216,683)
(217,714)(218,713)(219,720)(220,719)(221,717)(222,718)(223,716)(224,715)
(225,706)(226,705)(227,712)(228,711)(229,709)(230,710)(231,708)(232,707)
(233,698)(234,697)(235,704)(236,703)(237,701)(238,702)(239,700)(240,699)
(241,890)(242,889)(243,896)(244,895)(245,893)(246,894)(247,892)(248,891)
(249,882)(250,881)(251,888)(252,887)(253,885)(254,886)(255,884)(256,883)
(257,914)(258,913)(259,920)(260,919)(261,917)(262,918)(263,916)(264,915)
(265,906)(266,905)(267,912)(268,911)(269,909)(270,910)(271,908)(272,907)
(273,898)(274,897)(275,904)(276,903)(277,901)(278,902)(279,900)(280,899)
(281,850)(282,849)(283,856)(284,855)(285,853)(286,854)(287,852)(288,851)
(289,842)(290,841)(291,848)(292,847)(293,845)(294,846)(295,844)(296,843)
(297,874)(298,873)(299,880)(300,879)(301,877)(302,878)(303,876)(304,875)
(305,866)(306,865)(307,872)(308,871)(309,869)(310,870)(311,868)(312,867)
(313,858)(314,857)(315,864)(316,863)(317,861)(318,862)(319,860)(320,859)
(321,930)(322,929)(323,936)(324,935)(325,933)(326,934)(327,932)(328,931)
(329,922)(330,921)(331,928)(332,927)(333,925)(334,926)(335,924)(336,923)
(337,954)(338,953)(339,960)(340,959)(341,957)(342,958)(343,956)(344,955)
(345,946)(346,945)(347,952)(348,951)(349,949)(350,950)(351,948)(352,947)
(353,938)(354,937)(355,944)(356,943)(357,941)(358,942)(359,940)(360,939)
(361,770)(362,769)(363,776)(364,775)(365,773)(366,774)(367,772)(368,771)
(369,762)(370,761)(371,768)(372,767)(373,765)(374,766)(375,764)(376,763)
(377,794)(378,793)(379,800)(380,799)(381,797)(382,798)(383,796)(384,795)
(385,786)(386,785)(387,792)(388,791)(389,789)(390,790)(391,788)(392,787)
(393,778)(394,777)(395,784)(396,783)(397,781)(398,782)(399,780)(400,779)
(401,730)(402,729)(403,736)(404,735)(405,733)(406,734)(407,732)(408,731)
(409,722)(410,721)(411,728)(412,727)(413,725)(414,726)(415,724)(416,723)
(417,754)(418,753)(419,760)(420,759)(421,757)(422,758)(423,756)(424,755)
(425,746)(426,745)(427,752)(428,751)(429,749)(430,750)(431,748)(432,747)
(433,738)(434,737)(435,744)(436,743)(437,741)(438,742)(439,740)(440,739)
(441,810)(442,809)(443,816)(444,815)(445,813)(446,814)(447,812)(448,811)
(449,802)(450,801)(451,808)(452,807)(453,805)(454,806)(455,804)(456,803)
(457,834)(458,833)(459,840)(460,839)(461,837)(462,838)(463,836)(464,835)
(465,826)(466,825)(467,832)(468,831)(469,829)(470,830)(471,828)(472,827)
(473,818)(474,817)(475,824)(476,823)(477,821)(478,822)(479,820)(480,819);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*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*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*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,485)( 2,486)( 3,488)( 4,487)( 5,482)( 6,481)( 7,483)
( 8,484)( 9,493)( 10,494)( 11,496)( 12,495)( 13,490)( 14,489)( 15,491)
( 16,492)( 17,501)( 18,502)( 19,504)( 20,503)( 21,498)( 22,497)( 23,499)
( 24,500)( 25,509)( 26,510)( 27,512)( 28,511)( 29,506)( 30,505)( 31,507)
( 32,508)( 33,517)( 34,518)( 35,520)( 36,519)( 37,514)( 38,513)( 39,515)
( 40,516)( 41,525)( 42,526)( 43,528)( 44,527)( 45,522)( 46,521)( 47,523)
( 48,524)( 49,533)( 50,534)( 51,536)( 52,535)( 53,530)( 54,529)( 55,531)
( 56,532)( 57,541)( 58,542)( 59,544)( 60,543)( 61,538)( 62,537)( 63,539)
( 64,540)( 65,549)( 66,550)( 67,552)( 68,551)( 69,546)( 70,545)( 71,547)
( 72,548)( 73,557)( 74,558)( 75,560)( 76,559)( 77,554)( 78,553)( 79,555)
( 80,556)( 81,565)( 82,566)( 83,568)( 84,567)( 85,562)( 86,561)( 87,563)
( 88,564)( 89,573)( 90,574)( 91,576)( 92,575)( 93,570)( 94,569)( 95,571)
( 96,572)( 97,581)( 98,582)( 99,584)(100,583)(101,578)(102,577)(103,579)
(104,580)(105,589)(106,590)(107,592)(108,591)(109,586)(110,585)(111,587)
(112,588)(113,597)(114,598)(115,600)(116,599)(117,594)(118,593)(119,595)
(120,596)(121,606)(122,605)(123,607)(124,608)(125,601)(126,602)(127,604)
(128,603)(129,614)(130,613)(131,615)(132,616)(133,609)(134,610)(135,612)
(136,611)(137,622)(138,621)(139,623)(140,624)(141,617)(142,618)(143,620)
(144,619)(145,630)(146,629)(147,631)(148,632)(149,625)(150,626)(151,628)
(152,627)(153,638)(154,637)(155,639)(156,640)(157,633)(158,634)(159,636)
(160,635)(161,646)(162,645)(163,647)(164,648)(165,641)(166,642)(167,644)
(168,643)(169,654)(170,653)(171,655)(172,656)(173,649)(174,650)(175,652)
(176,651)(177,662)(178,661)(179,663)(180,664)(181,657)(182,658)(183,660)
(184,659)(185,670)(186,669)(187,671)(188,672)(189,665)(190,666)(191,668)
(192,667)(193,678)(194,677)(195,679)(196,680)(197,673)(198,674)(199,676)
(200,675)(201,686)(202,685)(203,687)(204,688)(205,681)(206,682)(207,684)
(208,683)(209,694)(210,693)(211,695)(212,696)(213,689)(214,690)(215,692)
(216,691)(217,702)(218,701)(219,703)(220,704)(221,697)(222,698)(223,700)
(224,699)(225,710)(226,709)(227,711)(228,712)(229,705)(230,706)(231,708)
(232,707)(233,718)(234,717)(235,719)(236,720)(237,713)(238,714)(239,716)
(240,715)(241,845)(242,846)(243,848)(244,847)(245,842)(246,841)(247,843)
(248,844)(249,853)(250,854)(251,856)(252,855)(253,850)(254,849)(255,851)
(256,852)(257,861)(258,862)(259,864)(260,863)(261,858)(262,857)(263,859)
(264,860)(265,869)(266,870)(267,872)(268,871)(269,866)(270,865)(271,867)
(272,868)(273,877)(274,878)(275,880)(276,879)(277,874)(278,873)(279,875)
(280,876)(281,885)(282,886)(283,888)(284,887)(285,882)(286,881)(287,883)
(288,884)(289,893)(290,894)(291,896)(292,895)(293,890)(294,889)(295,891)
(296,892)(297,901)(298,902)(299,904)(300,903)(301,898)(302,897)(303,899)
(304,900)(305,909)(306,910)(307,912)(308,911)(309,906)(310,905)(311,907)
(312,908)(313,917)(314,918)(315,920)(316,919)(317,914)(318,913)(319,915)
(320,916)(321,925)(322,926)(323,928)(324,927)(325,922)(326,921)(327,923)
(328,924)(329,933)(330,934)(331,936)(332,935)(333,930)(334,929)(335,931)
(336,932)(337,941)(338,942)(339,944)(340,943)(341,938)(342,937)(343,939)
(344,940)(345,949)(346,950)(347,952)(348,951)(349,946)(350,945)(351,947)
(352,948)(353,957)(354,958)(355,960)(356,959)(357,954)(358,953)(359,955)
(360,956)(361,725)(362,726)(363,728)(364,727)(365,722)(366,721)(367,723)
(368,724)(369,733)(370,734)(371,736)(372,735)(373,730)(374,729)(375,731)
(376,732)(377,741)(378,742)(379,744)(380,743)(381,738)(382,737)(383,739)
(384,740)(385,749)(386,750)(387,752)(388,751)(389,746)(390,745)(391,747)
(392,748)(393,757)(394,758)(395,760)(396,759)(397,754)(398,753)(399,755)
(400,756)(401,765)(402,766)(403,768)(404,767)(405,762)(406,761)(407,763)
(408,764)(409,773)(410,774)(411,776)(412,775)(413,770)(414,769)(415,771)
(416,772)(417,781)(418,782)(419,784)(420,783)(421,778)(422,777)(423,779)
(424,780)(425,789)(426,790)(427,792)(428,791)(429,786)(430,785)(431,787)
(432,788)(433,797)(434,798)(435,800)(436,799)(437,794)(438,793)(439,795)
(440,796)(441,805)(442,806)(443,808)(444,807)(445,802)(446,801)(447,803)
(448,804)(449,813)(450,814)(451,816)(452,815)(453,810)(454,809)(455,811)
(456,812)(457,821)(458,822)(459,824)(460,823)(461,818)(462,817)(463,819)
(464,820)(465,829)(466,830)(467,832)(468,831)(469,826)(470,825)(471,827)
(472,828)(473,837)(474,838)(475,840)(476,839)(477,834)(478,833)(479,835)
(480,836);
s1 := Sym(960)!( 1,241)( 2,242)( 3,244)( 4,243)( 5,247)( 6,248)( 7,245)
( 8,246)( 9,273)( 10,274)( 11,276)( 12,275)( 13,279)( 14,280)( 15,277)
( 16,278)( 17,265)( 18,266)( 19,268)( 20,267)( 21,271)( 22,272)( 23,269)
( 24,270)( 25,257)( 26,258)( 27,260)( 28,259)( 29,263)( 30,264)( 31,261)
( 32,262)( 33,249)( 34,250)( 35,252)( 36,251)( 37,255)( 38,256)( 39,253)
( 40,254)( 41,321)( 42,322)( 43,324)( 44,323)( 45,327)( 46,328)( 47,325)
( 48,326)( 49,353)( 50,354)( 51,356)( 52,355)( 53,359)( 54,360)( 55,357)
( 56,358)( 57,345)( 58,346)( 59,348)( 60,347)( 61,351)( 62,352)( 63,349)
( 64,350)( 65,337)( 66,338)( 67,340)( 68,339)( 69,343)( 70,344)( 71,341)
( 72,342)( 73,329)( 74,330)( 75,332)( 76,331)( 77,335)( 78,336)( 79,333)
( 80,334)( 81,281)( 82,282)( 83,284)( 84,283)( 85,287)( 86,288)( 87,285)
( 88,286)( 89,313)( 90,314)( 91,316)( 92,315)( 93,319)( 94,320)( 95,317)
( 96,318)( 97,305)( 98,306)( 99,308)(100,307)(101,311)(102,312)(103,309)
(104,310)(105,297)(106,298)(107,300)(108,299)(109,303)(110,304)(111,301)
(112,302)(113,289)(114,290)(115,292)(116,291)(117,295)(118,296)(119,293)
(120,294)(121,362)(122,361)(123,363)(124,364)(125,368)(126,367)(127,366)
(128,365)(129,394)(130,393)(131,395)(132,396)(133,400)(134,399)(135,398)
(136,397)(137,386)(138,385)(139,387)(140,388)(141,392)(142,391)(143,390)
(144,389)(145,378)(146,377)(147,379)(148,380)(149,384)(150,383)(151,382)
(152,381)(153,370)(154,369)(155,371)(156,372)(157,376)(158,375)(159,374)
(160,373)(161,442)(162,441)(163,443)(164,444)(165,448)(166,447)(167,446)
(168,445)(169,474)(170,473)(171,475)(172,476)(173,480)(174,479)(175,478)
(176,477)(177,466)(178,465)(179,467)(180,468)(181,472)(182,471)(183,470)
(184,469)(185,458)(186,457)(187,459)(188,460)(189,464)(190,463)(191,462)
(192,461)(193,450)(194,449)(195,451)(196,452)(197,456)(198,455)(199,454)
(200,453)(201,402)(202,401)(203,403)(204,404)(205,408)(206,407)(207,406)
(208,405)(209,434)(210,433)(211,435)(212,436)(213,440)(214,439)(215,438)
(216,437)(217,426)(218,425)(219,427)(220,428)(221,432)(222,431)(223,430)
(224,429)(225,418)(226,417)(227,419)(228,420)(229,424)(230,423)(231,422)
(232,421)(233,410)(234,409)(235,411)(236,412)(237,416)(238,415)(239,414)
(240,413)(481,722)(482,721)(483,723)(484,724)(485,728)(486,727)(487,726)
(488,725)(489,754)(490,753)(491,755)(492,756)(493,760)(494,759)(495,758)
(496,757)(497,746)(498,745)(499,747)(500,748)(501,752)(502,751)(503,750)
(504,749)(505,738)(506,737)(507,739)(508,740)(509,744)(510,743)(511,742)
(512,741)(513,730)(514,729)(515,731)(516,732)(517,736)(518,735)(519,734)
(520,733)(521,802)(522,801)(523,803)(524,804)(525,808)(526,807)(527,806)
(528,805)(529,834)(530,833)(531,835)(532,836)(533,840)(534,839)(535,838)
(536,837)(537,826)(538,825)(539,827)(540,828)(541,832)(542,831)(543,830)
(544,829)(545,818)(546,817)(547,819)(548,820)(549,824)(550,823)(551,822)
(552,821)(553,810)(554,809)(555,811)(556,812)(557,816)(558,815)(559,814)
(560,813)(561,762)(562,761)(563,763)(564,764)(565,768)(566,767)(567,766)
(568,765)(569,794)(570,793)(571,795)(572,796)(573,800)(574,799)(575,798)
(576,797)(577,786)(578,785)(579,787)(580,788)(581,792)(582,791)(583,790)
(584,789)(585,778)(586,777)(587,779)(588,780)(589,784)(590,783)(591,782)
(592,781)(593,770)(594,769)(595,771)(596,772)(597,776)(598,775)(599,774)
(600,773)(601,841)(602,842)(603,844)(604,843)(605,847)(606,848)(607,845)
(608,846)(609,873)(610,874)(611,876)(612,875)(613,879)(614,880)(615,877)
(616,878)(617,865)(618,866)(619,868)(620,867)(621,871)(622,872)(623,869)
(624,870)(625,857)(626,858)(627,860)(628,859)(629,863)(630,864)(631,861)
(632,862)(633,849)(634,850)(635,852)(636,851)(637,855)(638,856)(639,853)
(640,854)(641,921)(642,922)(643,924)(644,923)(645,927)(646,928)(647,925)
(648,926)(649,953)(650,954)(651,956)(652,955)(653,959)(654,960)(655,957)
(656,958)(657,945)(658,946)(659,948)(660,947)(661,951)(662,952)(663,949)
(664,950)(665,937)(666,938)(667,940)(668,939)(669,943)(670,944)(671,941)
(672,942)(673,929)(674,930)(675,932)(676,931)(677,935)(678,936)(679,933)
(680,934)(681,881)(682,882)(683,884)(684,883)(685,887)(686,888)(687,885)
(688,886)(689,913)(690,914)(691,916)(692,915)(693,919)(694,920)(695,917)
(696,918)(697,905)(698,906)(699,908)(700,907)(701,911)(702,912)(703,909)
(704,910)(705,897)(706,898)(707,900)(708,899)(709,903)(710,904)(711,901)
(712,902)(713,889)(714,890)(715,892)(716,891)(717,895)(718,896)(719,893)
(720,894);
s2 := Sym(960)!( 1,529)( 2,530)( 3,535)( 4,536)( 5,534)( 6,533)( 7,531)
( 8,532)( 9,521)( 10,522)( 11,527)( 12,528)( 13,526)( 14,525)( 15,523)
( 16,524)( 17,553)( 18,554)( 19,559)( 20,560)( 21,558)( 22,557)( 23,555)
( 24,556)( 25,545)( 26,546)( 27,551)( 28,552)( 29,550)( 30,549)( 31,547)
( 32,548)( 33,537)( 34,538)( 35,543)( 36,544)( 37,542)( 38,541)( 39,539)
( 40,540)( 41,489)( 42,490)( 43,495)( 44,496)( 45,494)( 46,493)( 47,491)
( 48,492)( 49,481)( 50,482)( 51,487)( 52,488)( 53,486)( 54,485)( 55,483)
( 56,484)( 57,513)( 58,514)( 59,519)( 60,520)( 61,518)( 62,517)( 63,515)
( 64,516)( 65,505)( 66,506)( 67,511)( 68,512)( 69,510)( 70,509)( 71,507)
( 72,508)( 73,497)( 74,498)( 75,503)( 76,504)( 77,502)( 78,501)( 79,499)
( 80,500)( 81,569)( 82,570)( 83,575)( 84,576)( 85,574)( 86,573)( 87,571)
( 88,572)( 89,561)( 90,562)( 91,567)( 92,568)( 93,566)( 94,565)( 95,563)
( 96,564)( 97,593)( 98,594)( 99,599)(100,600)(101,598)(102,597)(103,595)
(104,596)(105,585)(106,586)(107,591)(108,592)(109,590)(110,589)(111,587)
(112,588)(113,577)(114,578)(115,583)(116,584)(117,582)(118,581)(119,579)
(120,580)(121,650)(122,649)(123,656)(124,655)(125,653)(126,654)(127,652)
(128,651)(129,642)(130,641)(131,648)(132,647)(133,645)(134,646)(135,644)
(136,643)(137,674)(138,673)(139,680)(140,679)(141,677)(142,678)(143,676)
(144,675)(145,666)(146,665)(147,672)(148,671)(149,669)(150,670)(151,668)
(152,667)(153,658)(154,657)(155,664)(156,663)(157,661)(158,662)(159,660)
(160,659)(161,610)(162,609)(163,616)(164,615)(165,613)(166,614)(167,612)
(168,611)(169,602)(170,601)(171,608)(172,607)(173,605)(174,606)(175,604)
(176,603)(177,634)(178,633)(179,640)(180,639)(181,637)(182,638)(183,636)
(184,635)(185,626)(186,625)(187,632)(188,631)(189,629)(190,630)(191,628)
(192,627)(193,618)(194,617)(195,624)(196,623)(197,621)(198,622)(199,620)
(200,619)(201,690)(202,689)(203,696)(204,695)(205,693)(206,694)(207,692)
(208,691)(209,682)(210,681)(211,688)(212,687)(213,685)(214,686)(215,684)
(216,683)(217,714)(218,713)(219,720)(220,719)(221,717)(222,718)(223,716)
(224,715)(225,706)(226,705)(227,712)(228,711)(229,709)(230,710)(231,708)
(232,707)(233,698)(234,697)(235,704)(236,703)(237,701)(238,702)(239,700)
(240,699)(241,890)(242,889)(243,896)(244,895)(245,893)(246,894)(247,892)
(248,891)(249,882)(250,881)(251,888)(252,887)(253,885)(254,886)(255,884)
(256,883)(257,914)(258,913)(259,920)(260,919)(261,917)(262,918)(263,916)
(264,915)(265,906)(266,905)(267,912)(268,911)(269,909)(270,910)(271,908)
(272,907)(273,898)(274,897)(275,904)(276,903)(277,901)(278,902)(279,900)
(280,899)(281,850)(282,849)(283,856)(284,855)(285,853)(286,854)(287,852)
(288,851)(289,842)(290,841)(291,848)(292,847)(293,845)(294,846)(295,844)
(296,843)(297,874)(298,873)(299,880)(300,879)(301,877)(302,878)(303,876)
(304,875)(305,866)(306,865)(307,872)(308,871)(309,869)(310,870)(311,868)
(312,867)(313,858)(314,857)(315,864)(316,863)(317,861)(318,862)(319,860)
(320,859)(321,930)(322,929)(323,936)(324,935)(325,933)(326,934)(327,932)
(328,931)(329,922)(330,921)(331,928)(332,927)(333,925)(334,926)(335,924)
(336,923)(337,954)(338,953)(339,960)(340,959)(341,957)(342,958)(343,956)
(344,955)(345,946)(346,945)(347,952)(348,951)(349,949)(350,950)(351,948)
(352,947)(353,938)(354,937)(355,944)(356,943)(357,941)(358,942)(359,940)
(360,939)(361,770)(362,769)(363,776)(364,775)(365,773)(366,774)(367,772)
(368,771)(369,762)(370,761)(371,768)(372,767)(373,765)(374,766)(375,764)
(376,763)(377,794)(378,793)(379,800)(380,799)(381,797)(382,798)(383,796)
(384,795)(385,786)(386,785)(387,792)(388,791)(389,789)(390,790)(391,788)
(392,787)(393,778)(394,777)(395,784)(396,783)(397,781)(398,782)(399,780)
(400,779)(401,730)(402,729)(403,736)(404,735)(405,733)(406,734)(407,732)
(408,731)(409,722)(410,721)(411,728)(412,727)(413,725)(414,726)(415,724)
(416,723)(417,754)(418,753)(419,760)(420,759)(421,757)(422,758)(423,756)
(424,755)(425,746)(426,745)(427,752)(428,751)(429,749)(430,750)(431,748)
(432,747)(433,738)(434,737)(435,744)(436,743)(437,741)(438,742)(439,740)
(440,739)(441,810)(442,809)(443,816)(444,815)(445,813)(446,814)(447,812)
(448,811)(449,802)(450,801)(451,808)(452,807)(453,805)(454,806)(455,804)
(456,803)(457,834)(458,833)(459,840)(460,839)(461,837)(462,838)(463,836)
(464,835)(465,826)(466,825)(467,832)(468,831)(469,829)(470,830)(471,828)
(472,827)(473,818)(474,817)(475,824)(476,823)(477,821)(478,822)(479,820)
(480,819);
poly := sub<Sym(960)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*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*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*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope