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