Polytope of Type {12,80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,80}*1920a
Also Known As : {12,80|2}. if this polytope has another name.
Group : SmallGroup(1920,41747)
Rank : 3
Schlafli Type : {12,80}
Number of vertices, edges, etc : 12, 480, 80
Order of s0s1s2 : 240
Order of s0s1s2s1 : 2
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 : {6,80}*960, {12,40}*960a
3-fold quotients : {4,80}*640a
4-fold quotients : {6,40}*480, {12,20}*480
5-fold quotients : {12,16}*384a
6-fold quotients : {4,40}*320a, {2,80}*320
8-fold quotients : {12,10}*240, {6,20}*240a
10-fold quotients : {12,8}*192a, {6,16}*192
12-fold quotients : {4,20}*160, {2,40}*160
15-fold quotients : {4,16}*128a
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, {2,16}*64
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)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)(192,427)
(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)(208,443)
(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)(216,461)
(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)(224,459)
(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)(232,477)
(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)(240,475)
(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)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)(608,853)
(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)(624,869)
(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)(640,885)
(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)(656,891)
(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)(672,907)
(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)(688,923)
(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)(696,941)
(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)(704,939)
(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)(712,957)
(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)(720,955);;
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)(721,906)(722,910)
(723,909)(724,908)(725,907)(726,901)(727,905)(728,904)(729,903)(730,902)
(731,911)(732,915)(733,914)(734,913)(735,912)(736,921)(737,925)(738,924)
(739,923)(740,922)(741,916)(742,920)(743,919)(744,918)(745,917)(746,926)
(747,930)(748,929)(749,928)(750,927)(751,951)(752,955)(753,954)(754,953)
(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)(762,960)
(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)(770,937)
(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)(778,944)
(779,943)(780,942)(781,846)(782,850)(783,849)(784,848)(785,847)(786,841)
(787,845)(788,844)(789,843)(790,842)(791,851)(792,855)(793,854)(794,853)
(795,852)(796,861)(797,865)(798,864)(799,863)(800,862)(801,856)(802,860)
(803,859)(804,858)(805,857)(806,866)(807,870)(808,869)(809,868)(810,867)
(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)(818,889)
(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)(826,876)
(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)(834,873)
(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);;
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)( 61,782)( 62,781)( 63,785)( 64,784)
( 65,783)( 66,787)( 67,786)( 68,790)( 69,789)( 70,788)( 71,792)( 72,791)
( 73,795)( 74,794)( 75,793)( 76,797)( 77,796)( 78,800)( 79,799)( 80,798)
( 81,802)( 82,801)( 83,805)( 84,804)( 85,803)( 86,807)( 87,806)( 88,810)
( 89,809)( 90,808)( 91,827)( 92,826)( 93,830)( 94,829)( 95,828)( 96,832)
( 97,831)( 98,835)( 99,834)(100,833)(101,837)(102,836)(103,840)(104,839)
(105,838)(106,812)(107,811)(108,815)(109,814)(110,813)(111,817)(112,816)
(113,820)(114,819)(115,818)(116,822)(117,821)(118,825)(119,824)(120,823)
(121,872)(122,871)(123,875)(124,874)(125,873)(126,877)(127,876)(128,880)
(129,879)(130,878)(131,882)(132,881)(133,885)(134,884)(135,883)(136,887)
(137,886)(138,890)(139,889)(140,888)(141,892)(142,891)(143,895)(144,894)
(145,893)(146,897)(147,896)(148,900)(149,899)(150,898)(151,842)(152,841)
(153,845)(154,844)(155,843)(156,847)(157,846)(158,850)(159,849)(160,848)
(161,852)(162,851)(163,855)(164,854)(165,853)(166,857)(167,856)(168,860)
(169,859)(170,858)(171,862)(172,861)(173,865)(174,864)(175,863)(176,867)
(177,866)(178,870)(179,869)(180,868)(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)(301,542)(302,541)(303,545)(304,544)
(305,543)(306,547)(307,546)(308,550)(309,549)(310,548)(311,552)(312,551)
(313,555)(314,554)(315,553)(316,557)(317,556)(318,560)(319,559)(320,558)
(321,562)(322,561)(323,565)(324,564)(325,563)(326,567)(327,566)(328,570)
(329,569)(330,568)(331,587)(332,586)(333,590)(334,589)(335,588)(336,592)
(337,591)(338,595)(339,594)(340,593)(341,597)(342,596)(343,600)(344,599)
(345,598)(346,572)(347,571)(348,575)(349,574)(350,573)(351,577)(352,576)
(353,580)(354,579)(355,578)(356,582)(357,581)(358,585)(359,584)(360,583)
(361,632)(362,631)(363,635)(364,634)(365,633)(366,637)(367,636)(368,640)
(369,639)(370,638)(371,642)(372,641)(373,645)(374,644)(375,643)(376,647)
(377,646)(378,650)(379,649)(380,648)(381,652)(382,651)(383,655)(384,654)
(385,653)(386,657)(387,656)(388,660)(389,659)(390,658)(391,602)(392,601)
(393,605)(394,604)(395,603)(396,607)(397,606)(398,610)(399,609)(400,608)
(401,612)(402,611)(403,615)(404,614)(405,613)(406,617)(407,616)(408,620)
(409,619)(410,618)(411,622)(412,621)(413,625)(414,624)(415,623)(416,627)
(417,626)(418,630)(419,629)(420,628)(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, s0*s1*s2*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,
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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)
(192,427)(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)
(208,443)(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,461)(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)
(224,459)(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)
(232,477)(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)
(240,475)(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)(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)
(608,853)(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)
(624,869)(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)
(640,885)(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)
(656,891)(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)
(672,907)(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)
(688,923)(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,941)(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)
(704,939)(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)
(712,957)(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)
(720,955);
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)(721,906)
(722,910)(723,909)(724,908)(725,907)(726,901)(727,905)(728,904)(729,903)
(730,902)(731,911)(732,915)(733,914)(734,913)(735,912)(736,921)(737,925)
(738,924)(739,923)(740,922)(741,916)(742,920)(743,919)(744,918)(745,917)
(746,926)(747,930)(748,929)(749,928)(750,927)(751,951)(752,955)(753,954)
(754,953)(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)
(762,960)(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)
(770,937)(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)
(778,944)(779,943)(780,942)(781,846)(782,850)(783,849)(784,848)(785,847)
(786,841)(787,845)(788,844)(789,843)(790,842)(791,851)(792,855)(793,854)
(794,853)(795,852)(796,861)(797,865)(798,864)(799,863)(800,862)(801,856)
(802,860)(803,859)(804,858)(805,857)(806,866)(807,870)(808,869)(809,868)
(810,867)(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)
(818,889)(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)
(826,876)(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)
(834,873)(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);
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)( 61,782)( 62,781)( 63,785)
( 64,784)( 65,783)( 66,787)( 67,786)( 68,790)( 69,789)( 70,788)( 71,792)
( 72,791)( 73,795)( 74,794)( 75,793)( 76,797)( 77,796)( 78,800)( 79,799)
( 80,798)( 81,802)( 82,801)( 83,805)( 84,804)( 85,803)( 86,807)( 87,806)
( 88,810)( 89,809)( 90,808)( 91,827)( 92,826)( 93,830)( 94,829)( 95,828)
( 96,832)( 97,831)( 98,835)( 99,834)(100,833)(101,837)(102,836)(103,840)
(104,839)(105,838)(106,812)(107,811)(108,815)(109,814)(110,813)(111,817)
(112,816)(113,820)(114,819)(115,818)(116,822)(117,821)(118,825)(119,824)
(120,823)(121,872)(122,871)(123,875)(124,874)(125,873)(126,877)(127,876)
(128,880)(129,879)(130,878)(131,882)(132,881)(133,885)(134,884)(135,883)
(136,887)(137,886)(138,890)(139,889)(140,888)(141,892)(142,891)(143,895)
(144,894)(145,893)(146,897)(147,896)(148,900)(149,899)(150,898)(151,842)
(152,841)(153,845)(154,844)(155,843)(156,847)(157,846)(158,850)(159,849)
(160,848)(161,852)(162,851)(163,855)(164,854)(165,853)(166,857)(167,856)
(168,860)(169,859)(170,858)(171,862)(172,861)(173,865)(174,864)(175,863)
(176,867)(177,866)(178,870)(179,869)(180,868)(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)(301,542)(302,541)(303,545)
(304,544)(305,543)(306,547)(307,546)(308,550)(309,549)(310,548)(311,552)
(312,551)(313,555)(314,554)(315,553)(316,557)(317,556)(318,560)(319,559)
(320,558)(321,562)(322,561)(323,565)(324,564)(325,563)(326,567)(327,566)
(328,570)(329,569)(330,568)(331,587)(332,586)(333,590)(334,589)(335,588)
(336,592)(337,591)(338,595)(339,594)(340,593)(341,597)(342,596)(343,600)
(344,599)(345,598)(346,572)(347,571)(348,575)(349,574)(350,573)(351,577)
(352,576)(353,580)(354,579)(355,578)(356,582)(357,581)(358,585)(359,584)
(360,583)(361,632)(362,631)(363,635)(364,634)(365,633)(366,637)(367,636)
(368,640)(369,639)(370,638)(371,642)(372,641)(373,645)(374,644)(375,643)
(376,647)(377,646)(378,650)(379,649)(380,648)(381,652)(382,651)(383,655)
(384,654)(385,653)(386,657)(387,656)(388,660)(389,659)(390,658)(391,602)
(392,601)(393,605)(394,604)(395,603)(396,607)(397,606)(398,610)(399,609)
(400,608)(401,612)(402,611)(403,615)(404,614)(405,613)(406,617)(407,616)
(408,620)(409,619)(410,618)(411,622)(412,621)(413,625)(414,624)(415,623)
(416,627)(417,626)(418,630)(419,629)(420,628)(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, s0*s1*s2*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,
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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope