Polytope of Type {60,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,16}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42007)
Rank : 3
Schlafli Type : {60,16}
Number of vertices, edges, etc : 60, 480, 16
Order of s0s1s2 : 240
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {60,8}*960a
3-fold quotients : {20,16}*640b
4-fold quotients : {60,4}*480a, {30,8}*480
5-fold quotients : {12,16}*384b
6-fold quotients : {20,8}*320a
8-fold quotients : {60,2}*240, {30,4}*240a
10-fold quotients : {12,8}*192a
12-fold quotients : {20,4}*160, {10,8}*160
15-fold quotients : {4,16}*128b
16-fold quotients : {30,2}*120
20-fold quotients : {12,4}*96a, {6,8}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {4,8}*64a
32-fold quotients : {15,2}*60
40-fold quotients : {12,2}*48, {6,4}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {2,8}*32
80-fold quotients : {6,2}*24
96-fold quotients : {5,2}*20
120-fold quotients : {2,4}*16, {4,2}*16
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,251)( 7,255)( 8,254)
( 9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)( 24,268)
( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)( 48,289)
( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)( 56,291)
( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)( 72,310)
( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)( 88,324)
( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,341)
( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)(104,338)
(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)(112,360)
(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)(120,352)
(121,376)(122,380)(123,379)(124,378)(125,377)(126,386)(127,390)(128,389)
(129,388)(130,387)(131,381)(132,385)(133,384)(134,383)(135,382)(136,361)
(137,365)(138,364)(139,363)(140,362)(141,371)(142,375)(143,374)(144,373)
(145,372)(146,366)(147,370)(148,369)(149,368)(150,367)(151,406)(152,410)
(153,409)(154,408)(155,407)(156,416)(157,420)(158,419)(159,418)(160,417)
(161,411)(162,415)(163,414)(164,413)(165,412)(166,391)(167,395)(168,394)
(169,393)(170,392)(171,401)(172,405)(173,404)(174,403)(175,402)(176,396)
(177,400)(178,399)(179,398)(180,397)(181,436)(182,440)(183,439)(184,438)
(185,437)(186,446)(187,450)(188,449)(189,448)(190,447)(191,441)(192,445)
(193,444)(194,443)(195,442)(196,421)(197,425)(198,424)(199,423)(200,422)
(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)(208,429)
(209,428)(210,427)(211,466)(212,470)(213,469)(214,468)(215,467)(216,476)
(217,480)(218,479)(219,478)(220,477)(221,471)(222,475)(223,474)(224,473)
(225,472)(226,451)(227,455)(228,454)(229,453)(230,452)(231,461)(232,465)
(233,464)(234,463)(235,462)(236,456)(237,460)(238,459)(239,458)(240,457)
(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)(488,734)
(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)(496,736)
(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)(504,748)
(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)(512,755)
(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)(520,762)
(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)(528,769)
(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)(536,771)
(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)(544,783)
(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)(552,790)
(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)(560,797)
(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)(568,804)
(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)(576,821)
(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)(584,818)
(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)(592,840)
(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)(600,832)
(601,856)(602,860)(603,859)(604,858)(605,857)(606,866)(607,870)(608,869)
(609,868)(610,867)(611,861)(612,865)(613,864)(614,863)(615,862)(616,841)
(617,845)(618,844)(619,843)(620,842)(621,851)(622,855)(623,854)(624,853)
(625,852)(626,846)(627,850)(628,849)(629,848)(630,847)(631,886)(632,890)
(633,889)(634,888)(635,887)(636,896)(637,900)(638,899)(639,898)(640,897)
(641,891)(642,895)(643,894)(644,893)(645,892)(646,871)(647,875)(648,874)
(649,873)(650,872)(651,881)(652,885)(653,884)(654,883)(655,882)(656,876)
(657,880)(658,879)(659,878)(660,877)(661,916)(662,920)(663,919)(664,918)
(665,917)(666,926)(667,930)(668,929)(669,928)(670,927)(671,921)(672,925)
(673,924)(674,923)(675,922)(676,901)(677,905)(678,904)(679,903)(680,902)
(681,911)(682,915)(683,914)(684,913)(685,912)(686,906)(687,910)(688,909)
(689,908)(690,907)(691,946)(692,950)(693,949)(694,948)(695,947)(696,956)
(697,960)(698,959)(699,958)(700,957)(701,951)(702,955)(703,954)(704,953)
(705,952)(706,931)(707,935)(708,934)(709,933)(710,932)(711,941)(712,945)
(713,944)(714,943)(715,942)(716,936)(717,940)(718,939)(719,938)(720,937);;
s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)
( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)
(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)
(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)
(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)(142,166)
(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)(150,178)
(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)(188,215)
(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)(196,232)
(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)(204,229)
(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)(242,306)
(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)
(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)(258,325)
(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)(266,327)
(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)(274,354)
(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)(282,356)
(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)(290,338)
(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)(298,345)
(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)(366,452)
(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)(374,464)
(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)(382,466)
(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)(390,478)
(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)(398,425)
(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)(406,442)
(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)(414,439)
(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)(482,606)
(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)
(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)
(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)
(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)(514,654)
(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)(522,656)
(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)(530,638)
(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)(538,645)
(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)
(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)
(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)
(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)
(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)(578,710)
(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)(586,697)
(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)(594,694)
(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,922)(722,921)
(723,925)(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)
(731,927)(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)
(739,909)(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)
(747,911)(748,915)(749,914)(750,913)(751,937)(752,936)(753,940)(754,939)
(755,938)(756,932)(757,931)(758,935)(759,934)(760,933)(761,942)(762,941)
(763,945)(764,944)(765,943)(766,952)(767,951)(768,955)(769,954)(770,953)
(771,947)(772,946)(773,950)(774,949)(775,948)(776,957)(777,956)(778,960)
(779,959)(780,958)(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)
(787,856)(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)
(795,868)(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)
(803,845)(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)
(811,877)(812,876)(813,880)(814,879)(815,878)(816,872)(817,871)(818,875)
(819,874)(820,873)(821,882)(822,881)(823,885)(824,884)(825,883)(826,892)
(827,891)(828,895)(829,894)(830,893)(831,887)(832,886)(833,890)(834,889)
(835,888)(836,897)(837,896)(838,900)(839,899)(840,898);;
s2 := ( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)
( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)( 32,527)
( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)( 40,535)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)( 48,513)
( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)( 96,576)
( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)(112,592)
(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)(120,600)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,706)(182,707)(183,708)(184,709)
(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)(192,717)
(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)(200,695)
(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)(208,703)
(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)(216,681)
(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)(224,689)
(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)(240,675)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)(272,767)
(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)(280,775)
(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)(288,753)
(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)(296,761)
(297,762)(298,763)(299,764)(300,765)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,811)(332,812)(333,813)(334,814)(335,815)(336,816)
(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)(344,824)
(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)(352,832)
(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)(360,840)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,946)(422,947)(423,948)(424,949)
(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)(432,957)
(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)(440,935)
(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)(448,943)
(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)(456,921)
(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)(464,929)
(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)(472,907)
(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)(480,915);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,251)( 7,255)
( 8,254)( 9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)
( 24,268)( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)
( 48,289)( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)
( 56,291)( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)
( 72,310)( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)
( 88,324)( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,341)( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)
(104,338)(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)
(112,360)(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)
(120,352)(121,376)(122,380)(123,379)(124,378)(125,377)(126,386)(127,390)
(128,389)(129,388)(130,387)(131,381)(132,385)(133,384)(134,383)(135,382)
(136,361)(137,365)(138,364)(139,363)(140,362)(141,371)(142,375)(143,374)
(144,373)(145,372)(146,366)(147,370)(148,369)(149,368)(150,367)(151,406)
(152,410)(153,409)(154,408)(155,407)(156,416)(157,420)(158,419)(159,418)
(160,417)(161,411)(162,415)(163,414)(164,413)(165,412)(166,391)(167,395)
(168,394)(169,393)(170,392)(171,401)(172,405)(173,404)(174,403)(175,402)
(176,396)(177,400)(178,399)(179,398)(180,397)(181,436)(182,440)(183,439)
(184,438)(185,437)(186,446)(187,450)(188,449)(189,448)(190,447)(191,441)
(192,445)(193,444)(194,443)(195,442)(196,421)(197,425)(198,424)(199,423)
(200,422)(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)
(208,429)(209,428)(210,427)(211,466)(212,470)(213,469)(214,468)(215,467)
(216,476)(217,480)(218,479)(219,478)(220,477)(221,471)(222,475)(223,474)
(224,473)(225,472)(226,451)(227,455)(228,454)(229,453)(230,452)(231,461)
(232,465)(233,464)(234,463)(235,462)(236,456)(237,460)(238,459)(239,458)
(240,457)(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)
(488,734)(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)
(496,736)(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)
(504,748)(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)
(512,755)(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)
(520,762)(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)
(528,769)(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)
(536,771)(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)
(544,783)(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)
(552,790)(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)
(560,797)(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)
(568,804)(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)
(576,821)(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)
(584,818)(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)
(592,840)(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)
(600,832)(601,856)(602,860)(603,859)(604,858)(605,857)(606,866)(607,870)
(608,869)(609,868)(610,867)(611,861)(612,865)(613,864)(614,863)(615,862)
(616,841)(617,845)(618,844)(619,843)(620,842)(621,851)(622,855)(623,854)
(624,853)(625,852)(626,846)(627,850)(628,849)(629,848)(630,847)(631,886)
(632,890)(633,889)(634,888)(635,887)(636,896)(637,900)(638,899)(639,898)
(640,897)(641,891)(642,895)(643,894)(644,893)(645,892)(646,871)(647,875)
(648,874)(649,873)(650,872)(651,881)(652,885)(653,884)(654,883)(655,882)
(656,876)(657,880)(658,879)(659,878)(660,877)(661,916)(662,920)(663,919)
(664,918)(665,917)(666,926)(667,930)(668,929)(669,928)(670,927)(671,921)
(672,925)(673,924)(674,923)(675,922)(676,901)(677,905)(678,904)(679,903)
(680,902)(681,911)(682,915)(683,914)(684,913)(685,912)(686,906)(687,910)
(688,909)(689,908)(690,907)(691,946)(692,950)(693,949)(694,948)(695,947)
(696,956)(697,960)(698,959)(699,958)(700,957)(701,951)(702,955)(703,954)
(704,953)(705,952)(706,931)(707,935)(708,934)(709,933)(710,932)(711,941)
(712,945)(713,944)(714,943)(715,942)(716,936)(717,940)(718,939)(719,938)
(720,937);
s1 := Sym(960)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)
( 63, 70)( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)
( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)
(103,120)(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)
(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)
(134,164)(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)
(142,166)(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)
(150,178)(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)
(188,215)(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)
(196,232)(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)
(204,229)(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)
(242,306)(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)
(250,303)(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)
(258,325)(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)
(266,327)(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)
(274,354)(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)
(282,356)(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)
(290,338)(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)
(298,345)(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)
(366,452)(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)
(374,464)(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)
(382,466)(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)
(390,478)(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)
(398,425)(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)
(406,442)(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)
(414,439)(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)
(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)
(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)
(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)
(506,627)(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)
(514,654)(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)
(522,656)(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)
(530,638)(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)
(538,645)(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)
(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)
(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)
(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)
(570,688)(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)
(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)
(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)
(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,922)
(722,921)(723,925)(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)
(730,918)(731,927)(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)
(738,910)(739,909)(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)
(746,912)(747,911)(748,915)(749,914)(750,913)(751,937)(752,936)(753,940)
(754,939)(755,938)(756,932)(757,931)(758,935)(759,934)(760,933)(761,942)
(762,941)(763,945)(764,944)(765,943)(766,952)(767,951)(768,955)(769,954)
(770,953)(771,947)(772,946)(773,950)(774,949)(775,948)(776,957)(777,956)
(778,960)(779,959)(780,958)(781,862)(782,861)(783,865)(784,864)(785,863)
(786,857)(787,856)(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)
(794,869)(795,868)(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)
(802,841)(803,845)(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)
(810,853)(811,877)(812,876)(813,880)(814,879)(815,878)(816,872)(817,871)
(818,875)(819,874)(820,873)(821,882)(822,881)(823,885)(824,884)(825,883)
(826,892)(827,891)(828,895)(829,894)(830,893)(831,887)(832,886)(833,890)
(834,889)(835,888)(836,897)(837,896)(838,900)(839,899)(840,898);
s2 := Sym(960)!( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)
( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)
( 32,527)( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)
( 40,535)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)
( 48,513)( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)
( 96,576)( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)
(112,592)(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)
(120,600)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,706)(182,707)(183,708)
(184,709)(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)
(192,717)(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)
(200,695)(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)
(208,703)(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)
(216,681)(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)
(224,689)(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)
(232,667)(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)
(240,675)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)
(272,767)(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)
(280,775)(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)
(288,753)(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)
(296,761)(297,762)(298,763)(299,764)(300,765)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,811)(332,812)(333,813)(334,814)(335,815)
(336,816)(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)
(344,824)(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)
(352,832)(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)
(360,840)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,946)(422,947)(423,948)
(424,949)(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)
(432,957)(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)
(440,935)(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)
(448,943)(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)
(456,921)(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)
(464,929)(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)
(472,907)(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)
(480,915);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope