Polytope of Type {12,80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,80}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42029)
Rank : 3
Schlafli Type : {12,80}
Number of vertices, edges, etc : 12, 480, 80
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 : {12,40}*960a
3-fold quotients : {4,80}*640b
4-fold quotients : {6,40}*480, {12,20}*480
5-fold quotients : {12,16}*384b
6-fold quotients : {4,40}*320a
8-fold quotients : {12,10}*240, {6,20}*240a
10-fold quotients : {12,8}*192a
12-fold quotients : {4,20}*160, {2,40}*160
15-fold quotients : {4,16}*128b
16-fold quotients : {6,10}*120
20-fold quotients : {12,4}*96a, {6,8}*96
24-fold quotients : {2,20}*80, {4,10}*80
30-fold quotients : {4,8}*64a
40-fold quotients : {12,2}*48, {6,4}*48a
48-fold quotients : {2,10}*40
60-fold quotients : {4,4}*32, {2,8}*32
80-fold quotients : {6,2}*24
96-fold quotients : {2,5}*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)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)( 8,253)
( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)( 72,307)
( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)( 88,323)
( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,341)
( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)(104,339)
(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)(120,355)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,386)(127,387)(128,388)
(129,389)(130,390)(131,381)(132,382)(133,383)(134,384)(135,385)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,371)(142,372)(143,373)(144,374)
(145,375)(146,366)(147,367)(148,368)(149,369)(150,370)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,416)(157,417)(158,418)(159,419)(160,420)
(161,411)(162,412)(163,413)(164,414)(165,415)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,401)(172,402)(173,403)(174,404)(175,405)(176,396)
(177,397)(178,398)(179,399)(180,400)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,446)(187,447)(188,448)(189,449)(190,450)(191,441)(192,442)
(193,443)(194,444)(195,445)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)(208,428)
(209,429)(210,430)(211,466)(212,467)(213,468)(214,469)(215,470)(216,476)
(217,477)(218,478)(219,479)(220,480)(221,471)(222,472)(223,473)(224,474)
(225,475)(226,451)(227,452)(228,453)(229,454)(230,455)(231,461)(232,462)
(233,463)(234,464)(235,465)(236,456)(237,457)(238,458)(239,459)(240,460)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)(552,787)
(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)(568,803)
(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)(576,821)
(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)(584,819)
(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)(592,837)
(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)(600,835)
(601,856)(602,857)(603,858)(604,859)(605,860)(606,866)(607,867)(608,868)
(609,869)(610,870)(611,861)(612,862)(613,863)(614,864)(615,865)(616,841)
(617,842)(618,843)(619,844)(620,845)(621,851)(622,852)(623,853)(624,854)
(625,855)(626,846)(627,847)(628,848)(629,849)(630,850)(631,886)(632,887)
(633,888)(634,889)(635,890)(636,896)(637,897)(638,898)(639,899)(640,900)
(641,891)(642,892)(643,893)(644,894)(645,895)(646,871)(647,872)(648,873)
(649,874)(650,875)(651,881)(652,882)(653,883)(654,884)(655,885)(656,876)
(657,877)(658,878)(659,879)(660,880)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,926)(667,927)(668,928)(669,929)(670,930)(671,921)(672,922)
(673,923)(674,924)(675,925)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,911)(682,912)(683,913)(684,914)(685,915)(686,906)(687,907)(688,908)
(689,909)(690,910)(691,946)(692,947)(693,948)(694,949)(695,950)(696,956)
(697,957)(698,958)(699,959)(700,960)(701,951)(702,952)(703,953)(704,954)
(705,955)(706,931)(707,932)(708,933)(709,934)(710,935)(711,941)(712,942)
(713,943)(714,944)(715,945)(716,936)(717,937)(718,938)(719,939)(720,940);;
s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)( 32, 55)
( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)
( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)( 63, 69)
( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)
( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)
(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)(134,163)
(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)
(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)(150,177)
(181,216)(182,220)(183,219)(184,218)(185,217)(186,211)(187,215)(188,214)
(189,213)(190,212)(191,221)(192,225)(193,224)(194,223)(195,222)(196,231)
(197,235)(198,234)(199,233)(200,232)(201,226)(202,230)(203,229)(204,228)
(205,227)(206,236)(207,240)(208,239)(209,238)(210,237)(241,306)(242,310)
(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)
(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)(258,324)
(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)(266,326)
(267,330)(268,329)(269,328)(270,327)(271,351)(272,355)(273,354)(274,353)
(275,352)(276,346)(277,350)(278,349)(279,348)(280,347)(281,356)(282,360)
(283,359)(284,358)(285,357)(286,336)(287,340)(288,339)(289,338)(290,337)
(291,331)(292,335)(293,334)(294,333)(295,332)(296,341)(297,345)(298,344)
(299,343)(300,342)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)
(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)(374,463)
(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)(382,470)
(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)(390,477)
(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)(398,424)
(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)(406,441)
(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)(414,438)
(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)(482,610)
(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)(490,602)
(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)(498,624)
(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)(506,626)
(507,630)(508,629)(509,628)(510,627)(511,651)(512,655)(513,654)(514,653)
(515,652)(516,646)(517,650)(518,649)(519,648)(520,647)(521,656)(522,660)
(523,659)(524,658)(525,657)(526,636)(527,640)(528,639)(529,638)(530,637)
(531,631)(532,635)(533,634)(534,633)(535,632)(536,641)(537,645)(538,644)
(539,643)(540,642)(541,666)(542,670)(543,669)(544,668)(545,667)(546,661)
(547,665)(548,664)(549,663)(550,662)(551,671)(552,675)(553,674)(554,673)
(555,672)(556,681)(557,685)(558,684)(559,683)(560,682)(561,676)(562,680)
(563,679)(564,678)(565,677)(566,686)(567,690)(568,689)(569,688)(570,687)
(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)(578,709)
(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)(586,696)
(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)(594,693)
(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,921)(722,925)
(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)(730,917)
(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)(738,909)
(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)(746,911)
(747,915)(748,914)(749,913)(750,912)(751,936)(752,940)(753,939)(754,938)
(755,937)(756,931)(757,935)(758,934)(759,933)(760,932)(761,941)(762,945)
(763,944)(764,943)(765,942)(766,951)(767,955)(768,954)(769,953)(770,952)
(771,946)(772,950)(773,949)(774,948)(775,947)(776,956)(777,960)(778,959)
(779,958)(780,957)(781,861)(782,865)(783,864)(784,863)(785,862)(786,856)
(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)(794,868)
(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)(802,845)
(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)(810,852)
(811,876)(812,880)(813,879)(814,878)(815,877)(816,871)(817,875)(818,874)
(819,873)(820,872)(821,881)(822,885)(823,884)(824,883)(825,882)(826,891)
(827,895)(828,894)(829,893)(830,892)(831,886)(832,890)(833,889)(834,888)
(835,887)(836,896)(837,900)(838,899)(839,898)(840,897);;
s2 := ( 1,722)( 2,721)( 3,725)( 4,724)( 5,723)( 6,727)( 7,726)( 8,730)
( 9,729)( 10,728)( 11,732)( 12,731)( 13,735)( 14,734)( 15,733)( 16,737)
( 17,736)( 18,740)( 19,739)( 20,738)( 21,742)( 22,741)( 23,745)( 24,744)
( 25,743)( 26,747)( 27,746)( 28,750)( 29,749)( 30,748)( 31,767)( 32,766)
( 33,770)( 34,769)( 35,768)( 36,772)( 37,771)( 38,775)( 39,774)( 40,773)
( 41,777)( 42,776)( 43,780)( 44,779)( 45,778)( 46,752)( 47,751)( 48,755)
( 49,754)( 50,753)( 51,757)( 52,756)( 53,760)( 54,759)( 55,758)( 56,762)
( 57,761)( 58,765)( 59,764)( 60,763)( 61,797)( 62,796)( 63,800)( 64,799)
( 65,798)( 66,802)( 67,801)( 68,805)( 69,804)( 70,803)( 71,807)( 72,806)
( 73,810)( 74,809)( 75,808)( 76,782)( 77,781)( 78,785)( 79,784)( 80,783)
( 81,787)( 82,786)( 83,790)( 84,789)( 85,788)( 86,792)( 87,791)( 88,795)
( 89,794)( 90,793)( 91,812)( 92,811)( 93,815)( 94,814)( 95,813)( 96,817)
( 97,816)( 98,820)( 99,819)(100,818)(101,822)(102,821)(103,825)(104,824)
(105,823)(106,827)(107,826)(108,830)(109,829)(110,828)(111,832)(112,831)
(113,835)(114,834)(115,833)(116,837)(117,836)(118,840)(119,839)(120,838)
(121,887)(122,886)(123,890)(124,889)(125,888)(126,892)(127,891)(128,895)
(129,894)(130,893)(131,897)(132,896)(133,900)(134,899)(135,898)(136,872)
(137,871)(138,875)(139,874)(140,873)(141,877)(142,876)(143,880)(144,879)
(145,878)(146,882)(147,881)(148,885)(149,884)(150,883)(151,857)(152,856)
(153,860)(154,859)(155,858)(156,862)(157,861)(158,865)(159,864)(160,863)
(161,867)(162,866)(163,870)(164,869)(165,868)(166,842)(167,841)(168,845)
(169,844)(170,843)(171,847)(172,846)(173,850)(174,849)(175,848)(176,852)
(177,851)(178,855)(179,854)(180,853)(181,932)(182,931)(183,935)(184,934)
(185,933)(186,937)(187,936)(188,940)(189,939)(190,938)(191,942)(192,941)
(193,945)(194,944)(195,943)(196,947)(197,946)(198,950)(199,949)(200,948)
(201,952)(202,951)(203,955)(204,954)(205,953)(206,957)(207,956)(208,960)
(209,959)(210,958)(211,902)(212,901)(213,905)(214,904)(215,903)(216,907)
(217,906)(218,910)(219,909)(220,908)(221,912)(222,911)(223,915)(224,914)
(225,913)(226,917)(227,916)(228,920)(229,919)(230,918)(231,922)(232,921)
(233,925)(234,924)(235,923)(236,927)(237,926)(238,930)(239,929)(240,928)
(241,482)(242,481)(243,485)(244,484)(245,483)(246,487)(247,486)(248,490)
(249,489)(250,488)(251,492)(252,491)(253,495)(254,494)(255,493)(256,497)
(257,496)(258,500)(259,499)(260,498)(261,502)(262,501)(263,505)(264,504)
(265,503)(266,507)(267,506)(268,510)(269,509)(270,508)(271,527)(272,526)
(273,530)(274,529)(275,528)(276,532)(277,531)(278,535)(279,534)(280,533)
(281,537)(282,536)(283,540)(284,539)(285,538)(286,512)(287,511)(288,515)
(289,514)(290,513)(291,517)(292,516)(293,520)(294,519)(295,518)(296,522)
(297,521)(298,525)(299,524)(300,523)(301,557)(302,556)(303,560)(304,559)
(305,558)(306,562)(307,561)(308,565)(309,564)(310,563)(311,567)(312,566)
(313,570)(314,569)(315,568)(316,542)(317,541)(318,545)(319,544)(320,543)
(321,547)(322,546)(323,550)(324,549)(325,548)(326,552)(327,551)(328,555)
(329,554)(330,553)(331,572)(332,571)(333,575)(334,574)(335,573)(336,577)
(337,576)(338,580)(339,579)(340,578)(341,582)(342,581)(343,585)(344,584)
(345,583)(346,587)(347,586)(348,590)(349,589)(350,588)(351,592)(352,591)
(353,595)(354,594)(355,593)(356,597)(357,596)(358,600)(359,599)(360,598)
(361,647)(362,646)(363,650)(364,649)(365,648)(366,652)(367,651)(368,655)
(369,654)(370,653)(371,657)(372,656)(373,660)(374,659)(375,658)(376,632)
(377,631)(378,635)(379,634)(380,633)(381,637)(382,636)(383,640)(384,639)
(385,638)(386,642)(387,641)(388,645)(389,644)(390,643)(391,617)(392,616)
(393,620)(394,619)(395,618)(396,622)(397,621)(398,625)(399,624)(400,623)
(401,627)(402,626)(403,630)(404,629)(405,628)(406,602)(407,601)(408,605)
(409,604)(410,603)(411,607)(412,606)(413,610)(414,609)(415,608)(416,612)
(417,611)(418,615)(419,614)(420,613)(421,692)(422,691)(423,695)(424,694)
(425,693)(426,697)(427,696)(428,700)(429,699)(430,698)(431,702)(432,701)
(433,705)(434,704)(435,703)(436,707)(437,706)(438,710)(439,709)(440,708)
(441,712)(442,711)(443,715)(444,714)(445,713)(446,717)(447,716)(448,720)
(449,719)(450,718)(451,662)(452,661)(453,665)(454,664)(455,663)(456,667)
(457,666)(458,670)(459,669)(460,668)(461,672)(462,671)(463,675)(464,674)
(465,673)(466,677)(467,676)(468,680)(469,679)(470,678)(471,682)(472,681)
(473,685)(474,684)(475,683)(476,687)(477,686)(478,690)(479,689)(480,688);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)
( 8,253)( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)
( 72,307)( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)
( 88,323)( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,341)( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)
(104,339)(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)
(120,355)(121,376)(122,377)(123,378)(124,379)(125,380)(126,386)(127,387)
(128,388)(129,389)(130,390)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,371)(142,372)(143,373)
(144,374)(145,375)(146,366)(147,367)(148,368)(149,369)(150,370)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,416)(157,417)(158,418)(159,419)
(160,420)(161,411)(162,412)(163,413)(164,414)(165,415)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,401)(172,402)(173,403)(174,404)(175,405)
(176,396)(177,397)(178,398)(179,399)(180,400)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,446)(187,447)(188,448)(189,449)(190,450)(191,441)
(192,442)(193,443)(194,444)(195,445)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)
(208,428)(209,429)(210,430)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,476)(217,477)(218,478)(219,479)(220,480)(221,471)(222,472)(223,473)
(224,474)(225,475)(226,451)(227,452)(228,453)(229,454)(230,455)(231,461)
(232,462)(233,463)(234,464)(235,465)(236,456)(237,457)(238,458)(239,459)
(240,460)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)
(552,787)(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)
(568,803)(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,821)(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)
(584,819)(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)
(592,837)(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)
(600,835)(601,856)(602,857)(603,858)(604,859)(605,860)(606,866)(607,867)
(608,868)(609,869)(610,870)(611,861)(612,862)(613,863)(614,864)(615,865)
(616,841)(617,842)(618,843)(619,844)(620,845)(621,851)(622,852)(623,853)
(624,854)(625,855)(626,846)(627,847)(628,848)(629,849)(630,850)(631,886)
(632,887)(633,888)(634,889)(635,890)(636,896)(637,897)(638,898)(639,899)
(640,900)(641,891)(642,892)(643,893)(644,894)(645,895)(646,871)(647,872)
(648,873)(649,874)(650,875)(651,881)(652,882)(653,883)(654,884)(655,885)
(656,876)(657,877)(658,878)(659,879)(660,880)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,926)(667,927)(668,928)(669,929)(670,930)(671,921)
(672,922)(673,923)(674,924)(675,925)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,911)(682,912)(683,913)(684,914)(685,915)(686,906)(687,907)
(688,908)(689,909)(690,910)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,956)(697,957)(698,958)(699,959)(700,960)(701,951)(702,952)(703,953)
(704,954)(705,955)(706,931)(707,932)(708,933)(709,934)(710,935)(711,941)
(712,942)(713,943)(714,944)(715,945)(716,936)(717,937)(718,938)(719,939)
(720,940);
s1 := Sym(960)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 12, 15)( 13, 14)
( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)
( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)
( 40, 47)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)
( 63, 69)( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)
( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)
(103,119)(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)
(126,151)(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)
(134,163)(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)
(142,170)(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)
(150,177)(181,216)(182,220)(183,219)(184,218)(185,217)(186,211)(187,215)
(188,214)(189,213)(190,212)(191,221)(192,225)(193,224)(194,223)(195,222)
(196,231)(197,235)(198,234)(199,233)(200,232)(201,226)(202,230)(203,229)
(204,228)(205,227)(206,236)(207,240)(208,239)(209,238)(210,237)(241,306)
(242,310)(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)
(250,302)(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)
(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)
(266,326)(267,330)(268,329)(269,328)(270,327)(271,351)(272,355)(273,354)
(274,353)(275,352)(276,346)(277,350)(278,349)(279,348)(280,347)(281,356)
(282,360)(283,359)(284,358)(285,357)(286,336)(287,340)(288,339)(289,338)
(290,337)(291,331)(292,335)(293,334)(294,333)(295,332)(296,341)(297,345)
(298,344)(299,343)(300,342)(361,456)(362,460)(363,459)(364,458)(365,457)
(366,451)(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)
(374,463)(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)
(382,470)(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)
(390,477)(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)
(398,424)(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)
(406,441)(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)
(414,438)(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)
(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)
(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)
(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)
(506,626)(507,630)(508,629)(509,628)(510,627)(511,651)(512,655)(513,654)
(514,653)(515,652)(516,646)(517,650)(518,649)(519,648)(520,647)(521,656)
(522,660)(523,659)(524,658)(525,657)(526,636)(527,640)(528,639)(529,638)
(530,637)(531,631)(532,635)(533,634)(534,633)(535,632)(536,641)(537,645)
(538,644)(539,643)(540,642)(541,666)(542,670)(543,669)(544,668)(545,667)
(546,661)(547,665)(548,664)(549,663)(550,662)(551,671)(552,675)(553,674)
(554,673)(555,672)(556,681)(557,685)(558,684)(559,683)(560,682)(561,676)
(562,680)(563,679)(564,678)(565,677)(566,686)(567,690)(568,689)(569,688)
(570,687)(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)
(578,709)(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)
(586,696)(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)
(594,693)(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,921)
(722,925)(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)
(730,917)(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)
(738,909)(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)
(746,911)(747,915)(748,914)(749,913)(750,912)(751,936)(752,940)(753,939)
(754,938)(755,937)(756,931)(757,935)(758,934)(759,933)(760,932)(761,941)
(762,945)(763,944)(764,943)(765,942)(766,951)(767,955)(768,954)(769,953)
(770,952)(771,946)(772,950)(773,949)(774,948)(775,947)(776,956)(777,960)
(778,959)(779,958)(780,957)(781,861)(782,865)(783,864)(784,863)(785,862)
(786,856)(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)
(794,868)(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)
(802,845)(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)
(810,852)(811,876)(812,880)(813,879)(814,878)(815,877)(816,871)(817,875)
(818,874)(819,873)(820,872)(821,881)(822,885)(823,884)(824,883)(825,882)
(826,891)(827,895)(828,894)(829,893)(830,892)(831,886)(832,890)(833,889)
(834,888)(835,887)(836,896)(837,900)(838,899)(839,898)(840,897);
s2 := Sym(960)!( 1,722)( 2,721)( 3,725)( 4,724)( 5,723)( 6,727)( 7,726)
( 8,730)( 9,729)( 10,728)( 11,732)( 12,731)( 13,735)( 14,734)( 15,733)
( 16,737)( 17,736)( 18,740)( 19,739)( 20,738)( 21,742)( 22,741)( 23,745)
( 24,744)( 25,743)( 26,747)( 27,746)( 28,750)( 29,749)( 30,748)( 31,767)
( 32,766)( 33,770)( 34,769)( 35,768)( 36,772)( 37,771)( 38,775)( 39,774)
( 40,773)( 41,777)( 42,776)( 43,780)( 44,779)( 45,778)( 46,752)( 47,751)
( 48,755)( 49,754)( 50,753)( 51,757)( 52,756)( 53,760)( 54,759)( 55,758)
( 56,762)( 57,761)( 58,765)( 59,764)( 60,763)( 61,797)( 62,796)( 63,800)
( 64,799)( 65,798)( 66,802)( 67,801)( 68,805)( 69,804)( 70,803)( 71,807)
( 72,806)( 73,810)( 74,809)( 75,808)( 76,782)( 77,781)( 78,785)( 79,784)
( 80,783)( 81,787)( 82,786)( 83,790)( 84,789)( 85,788)( 86,792)( 87,791)
( 88,795)( 89,794)( 90,793)( 91,812)( 92,811)( 93,815)( 94,814)( 95,813)
( 96,817)( 97,816)( 98,820)( 99,819)(100,818)(101,822)(102,821)(103,825)
(104,824)(105,823)(106,827)(107,826)(108,830)(109,829)(110,828)(111,832)
(112,831)(113,835)(114,834)(115,833)(116,837)(117,836)(118,840)(119,839)
(120,838)(121,887)(122,886)(123,890)(124,889)(125,888)(126,892)(127,891)
(128,895)(129,894)(130,893)(131,897)(132,896)(133,900)(134,899)(135,898)
(136,872)(137,871)(138,875)(139,874)(140,873)(141,877)(142,876)(143,880)
(144,879)(145,878)(146,882)(147,881)(148,885)(149,884)(150,883)(151,857)
(152,856)(153,860)(154,859)(155,858)(156,862)(157,861)(158,865)(159,864)
(160,863)(161,867)(162,866)(163,870)(164,869)(165,868)(166,842)(167,841)
(168,845)(169,844)(170,843)(171,847)(172,846)(173,850)(174,849)(175,848)
(176,852)(177,851)(178,855)(179,854)(180,853)(181,932)(182,931)(183,935)
(184,934)(185,933)(186,937)(187,936)(188,940)(189,939)(190,938)(191,942)
(192,941)(193,945)(194,944)(195,943)(196,947)(197,946)(198,950)(199,949)
(200,948)(201,952)(202,951)(203,955)(204,954)(205,953)(206,957)(207,956)
(208,960)(209,959)(210,958)(211,902)(212,901)(213,905)(214,904)(215,903)
(216,907)(217,906)(218,910)(219,909)(220,908)(221,912)(222,911)(223,915)
(224,914)(225,913)(226,917)(227,916)(228,920)(229,919)(230,918)(231,922)
(232,921)(233,925)(234,924)(235,923)(236,927)(237,926)(238,930)(239,929)
(240,928)(241,482)(242,481)(243,485)(244,484)(245,483)(246,487)(247,486)
(248,490)(249,489)(250,488)(251,492)(252,491)(253,495)(254,494)(255,493)
(256,497)(257,496)(258,500)(259,499)(260,498)(261,502)(262,501)(263,505)
(264,504)(265,503)(266,507)(267,506)(268,510)(269,509)(270,508)(271,527)
(272,526)(273,530)(274,529)(275,528)(276,532)(277,531)(278,535)(279,534)
(280,533)(281,537)(282,536)(283,540)(284,539)(285,538)(286,512)(287,511)
(288,515)(289,514)(290,513)(291,517)(292,516)(293,520)(294,519)(295,518)
(296,522)(297,521)(298,525)(299,524)(300,523)(301,557)(302,556)(303,560)
(304,559)(305,558)(306,562)(307,561)(308,565)(309,564)(310,563)(311,567)
(312,566)(313,570)(314,569)(315,568)(316,542)(317,541)(318,545)(319,544)
(320,543)(321,547)(322,546)(323,550)(324,549)(325,548)(326,552)(327,551)
(328,555)(329,554)(330,553)(331,572)(332,571)(333,575)(334,574)(335,573)
(336,577)(337,576)(338,580)(339,579)(340,578)(341,582)(342,581)(343,585)
(344,584)(345,583)(346,587)(347,586)(348,590)(349,589)(350,588)(351,592)
(352,591)(353,595)(354,594)(355,593)(356,597)(357,596)(358,600)(359,599)
(360,598)(361,647)(362,646)(363,650)(364,649)(365,648)(366,652)(367,651)
(368,655)(369,654)(370,653)(371,657)(372,656)(373,660)(374,659)(375,658)
(376,632)(377,631)(378,635)(379,634)(380,633)(381,637)(382,636)(383,640)
(384,639)(385,638)(386,642)(387,641)(388,645)(389,644)(390,643)(391,617)
(392,616)(393,620)(394,619)(395,618)(396,622)(397,621)(398,625)(399,624)
(400,623)(401,627)(402,626)(403,630)(404,629)(405,628)(406,602)(407,601)
(408,605)(409,604)(410,603)(411,607)(412,606)(413,610)(414,609)(415,608)
(416,612)(417,611)(418,615)(419,614)(420,613)(421,692)(422,691)(423,695)
(424,694)(425,693)(426,697)(427,696)(428,700)(429,699)(430,698)(431,702)
(432,701)(433,705)(434,704)(435,703)(436,707)(437,706)(438,710)(439,709)
(440,708)(441,712)(442,711)(443,715)(444,714)(445,713)(446,717)(447,716)
(448,720)(449,719)(450,718)(451,662)(452,661)(453,665)(454,664)(455,663)
(456,667)(457,666)(458,670)(459,669)(460,668)(461,672)(462,671)(463,675)
(464,674)(465,673)(466,677)(467,676)(468,680)(469,679)(470,678)(471,682)
(472,681)(473,685)(474,684)(475,683)(476,687)(477,686)(478,690)(479,689)
(480,688);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*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*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 >;
References : None.
to this polytope