Polytope of Type {120,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,14512)
Rank : 3
Schlafli Type : {120,8}
Number of vertices, edges, etc : 120, 480, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {120,4}*960b, {60,8}*960a
3-fold quotients : {40,8}*640d
4-fold quotients : {60,4}*480a, {30,8}*480
5-fold quotients : {24,8}*384d
6-fold quotients : {40,4}*320b, {20,8}*320a
8-fold quotients : {60,2}*240, {30,4}*240a
10-fold quotients : {24,4}*192b, {12,8}*192a
12-fold quotients : {20,4}*160, {10,8}*160
15-fold quotients : {8,8}*128a
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, {8,4}*64b
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)( 61,316)( 62,320)( 63,319)( 64,318)
( 65,317)( 66,326)( 67,330)( 68,329)( 69,328)( 70,327)( 71,321)( 72,325)
( 73,324)( 74,323)( 75,322)( 76,301)( 77,305)( 78,304)( 79,303)( 80,302)
( 81,311)( 82,315)( 83,314)( 84,313)( 85,312)( 86,306)( 87,310)( 88,309)
( 89,308)( 90,307)( 91,346)( 92,350)( 93,349)( 94,348)( 95,347)( 96,356)
( 97,360)( 98,359)( 99,358)(100,357)(101,351)(102,355)(103,354)(104,353)
(105,352)(106,331)(107,335)(108,334)(109,333)(110,332)(111,341)(112,345)
(113,344)(114,343)(115,342)(116,336)(117,340)(118,339)(119,338)(120,337)
(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)(181,421)(182,425)(183,424)(184,423)
(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)(192,430)
(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)(200,437)
(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)(208,444)
(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)(216,461)
(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)(224,458)
(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)(232,480)
(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)(240,472)
(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)(541,796)(542,800)(543,799)(544,798)
(545,797)(546,806)(547,810)(548,809)(549,808)(550,807)(551,801)(552,805)
(553,804)(554,803)(555,802)(556,781)(557,785)(558,784)(559,783)(560,782)
(561,791)(562,795)(563,794)(564,793)(565,792)(566,786)(567,790)(568,789)
(569,788)(570,787)(571,826)(572,830)(573,829)(574,828)(575,827)(576,836)
(577,840)(578,839)(579,838)(580,837)(581,831)(582,835)(583,834)(584,833)
(585,832)(586,811)(587,815)(588,814)(589,813)(590,812)(591,821)(592,825)
(593,824)(594,823)(595,822)(596,816)(597,820)(598,819)(599,818)(600,817)
(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)(661,901)(662,905)(663,904)(664,903)
(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)(672,910)
(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)(680,917)
(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)(688,924)
(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)(696,941)
(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)(704,938)
(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)(712,960)
(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)(720,952);;
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, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)( 64, 84)
( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)
( 73, 90)( 74, 89)( 75, 88)( 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)
(181,232)(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)
(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)
(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)
(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(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)(271,337)(272,336)(273,340)(274,339)
(275,338)(276,332)(277,331)(278,335)(279,334)(280,333)(281,342)(282,341)
(283,345)(284,344)(285,343)(286,352)(287,351)(288,355)(289,354)(290,353)
(291,347)(292,346)(293,350)(294,349)(295,348)(296,357)(297,356)(298,360)
(299,359)(300,358)(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)(511,637)(512,636)(513,640)(514,639)
(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)
(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)
(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)
(539,659)(540,658)(541,682)(542,681)(543,685)(544,684)(545,683)(546,677)
(547,676)(548,680)(549,679)(550,678)(551,687)(552,686)(553,690)(554,689)
(555,688)(556,667)(557,666)(558,670)(559,669)(560,668)(561,662)(562,661)
(563,665)(564,664)(565,663)(566,672)(567,671)(568,675)(569,674)(570,673)
(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)(751,952)(752,951)(753,955)(754,954)
(755,953)(756,947)(757,946)(758,950)(759,949)(760,948)(761,957)(762,956)
(763,960)(764,959)(765,958)(766,937)(767,936)(768,940)(769,939)(770,938)
(771,932)(772,931)(773,935)(774,934)(775,933)(776,942)(777,941)(778,945)
(779,944)(780,943)(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)
(811,892)(812,891)(813,895)(814,894)(815,893)(816,887)(817,886)(818,890)
(819,889)(820,888)(821,897)(822,896)(823,900)(824,899)(825,898)(826,877)
(827,876)(828,880)(829,879)(830,878)(831,872)(832,871)(833,875)(834,874)
(835,873)(836,882)(837,881)(838,885)(839,884)(840,883);;
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)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(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)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(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,
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*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*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)( 61,316)( 62,320)( 63,319)
( 64,318)( 65,317)( 66,326)( 67,330)( 68,329)( 69,328)( 70,327)( 71,321)
( 72,325)( 73,324)( 74,323)( 75,322)( 76,301)( 77,305)( 78,304)( 79,303)
( 80,302)( 81,311)( 82,315)( 83,314)( 84,313)( 85,312)( 86,306)( 87,310)
( 88,309)( 89,308)( 90,307)( 91,346)( 92,350)( 93,349)( 94,348)( 95,347)
( 96,356)( 97,360)( 98,359)( 99,358)(100,357)(101,351)(102,355)(103,354)
(104,353)(105,352)(106,331)(107,335)(108,334)(109,333)(110,332)(111,341)
(112,345)(113,344)(114,343)(115,342)(116,336)(117,340)(118,339)(119,338)
(120,337)(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)(181,421)(182,425)(183,424)
(184,423)(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)
(192,430)(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)
(200,437)(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)
(208,444)(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)
(216,461)(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)
(224,458)(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)
(232,480)(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)
(240,472)(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)(541,796)(542,800)(543,799)
(544,798)(545,797)(546,806)(547,810)(548,809)(549,808)(550,807)(551,801)
(552,805)(553,804)(554,803)(555,802)(556,781)(557,785)(558,784)(559,783)
(560,782)(561,791)(562,795)(563,794)(564,793)(565,792)(566,786)(567,790)
(568,789)(569,788)(570,787)(571,826)(572,830)(573,829)(574,828)(575,827)
(576,836)(577,840)(578,839)(579,838)(580,837)(581,831)(582,835)(583,834)
(584,833)(585,832)(586,811)(587,815)(588,814)(589,813)(590,812)(591,821)
(592,825)(593,824)(594,823)(595,822)(596,816)(597,820)(598,819)(599,818)
(600,817)(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)(661,901)(662,905)(663,904)
(664,903)(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)
(672,910)(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)
(680,917)(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)
(688,924)(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)
(696,941)(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)
(704,938)(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)
(712,960)(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)
(720,952);
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, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)
( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)
( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 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)(181,232)(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)
(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)
(196,217)(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)
(204,214)(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(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)(271,337)(272,336)(273,340)
(274,339)(275,338)(276,332)(277,331)(278,335)(279,334)(280,333)(281,342)
(282,341)(283,345)(284,344)(285,343)(286,352)(287,351)(288,355)(289,354)
(290,353)(291,347)(292,346)(293,350)(294,349)(295,348)(296,357)(297,356)
(298,360)(299,359)(300,358)(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)(511,637)(512,636)(513,640)
(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)
(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)
(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)
(538,660)(539,659)(540,658)(541,682)(542,681)(543,685)(544,684)(545,683)
(546,677)(547,676)(548,680)(549,679)(550,678)(551,687)(552,686)(553,690)
(554,689)(555,688)(556,667)(557,666)(558,670)(559,669)(560,668)(561,662)
(562,661)(563,665)(564,664)(565,663)(566,672)(567,671)(568,675)(569,674)
(570,673)(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)(751,952)(752,951)(753,955)
(754,954)(755,953)(756,947)(757,946)(758,950)(759,949)(760,948)(761,957)
(762,956)(763,960)(764,959)(765,958)(766,937)(767,936)(768,940)(769,939)
(770,938)(771,932)(772,931)(773,935)(774,934)(775,933)(776,942)(777,941)
(778,945)(779,944)(780,943)(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)(811,892)(812,891)(813,895)(814,894)(815,893)(816,887)(817,886)
(818,890)(819,889)(820,888)(821,897)(822,896)(823,900)(824,899)(825,898)
(826,877)(827,876)(828,880)(829,879)(830,878)(831,872)(832,871)(833,875)
(834,874)(835,873)(836,882)(837,881)(838,885)(839,884)(840,883);
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)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(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)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(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,
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*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*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