Polytope of Type {8,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*1920j
if this polytope has a name.
Group : SmallGroup(1920,240269)
Rank : 3
Schlafli Type : {8,30}
Number of vertices, edges, etc : 32, 480, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {8,15}*960c, {4,30}*960d
3-fold quotients : {8,10}*640c
4-fold quotients : {4,15}*480
6-fold quotients : {8,5}*320a, {4,10}*320b
12-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,483)( 2,484)( 3,481)( 4,482)( 5,487)( 6,488)( 7,485)( 8,486)
( 9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)( 16,494)
( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)( 24,502)
( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)( 32,510)
( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)( 40,518)
( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)( 48,526)
( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)( 56,534)
( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)( 64,542)
( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)( 72,550)
( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)( 80,558)
( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)( 88,566)
( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)( 96,574)
( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)(104,582)
(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)(112,590)
(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)(120,598)
(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)(128,606)
(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)(136,614)
(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)(144,622)
(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)(152,630)
(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)(160,638)
(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)(168,646)
(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)(176,654)
(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)(184,662)
(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)(192,670)
(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)(200,678)
(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)(208,686)
(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)(216,694)
(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)(224,702)
(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)(232,710)
(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)(240,718)
(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)(248,726)
(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)(256,734)
(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)(264,742)
(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)(272,750)
(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)(280,758)
(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)(288,766)
(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)(296,774)
(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)(304,782)
(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)(312,790)
(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)(320,798)
(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)(328,806)
(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)(336,814)
(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)(344,822)
(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)(352,830)
(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)(360,838)
(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)(368,846)
(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)(376,854)
(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)(384,862)
(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)(392,870)
(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)(400,878)
(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)(408,886)
(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)(416,894)
(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)(424,902)
(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)(432,910)
(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)(440,918)
(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)(448,926)
(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)(456,934)
(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)(464,942)
(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)(472,950)
(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)(480,958);;
s1 := ( 1, 33)( 2, 34)( 3, 64)( 4, 63)( 5, 44)( 6, 43)( 7, 53)( 8, 54)
( 9, 60)( 10, 59)( 11, 38)( 12, 37)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 51)( 20, 52)( 21, 39)( 22, 40)( 23, 58)( 24, 57)
( 25, 56)( 26, 55)( 27, 42)( 28, 41)( 29, 62)( 30, 61)( 31, 36)( 32, 35)
( 65,129)( 66,130)( 67,160)( 68,159)( 69,140)( 70,139)( 71,149)( 72,150)
( 73,156)( 74,155)( 75,134)( 76,133)( 77,146)( 78,145)( 79,144)( 80,143)
( 81,142)( 82,141)( 83,147)( 84,148)( 85,135)( 86,136)( 87,154)( 88,153)
( 89,152)( 90,151)( 91,138)( 92,137)( 93,158)( 94,157)( 95,132)( 96,131)
( 99,128)(100,127)(101,108)(102,107)(103,117)(104,118)(105,124)(106,123)
(109,114)(110,113)(111,112)(119,122)(120,121)(125,126)(161,353)(162,354)
(163,384)(164,383)(165,364)(166,363)(167,373)(168,374)(169,380)(170,379)
(171,358)(172,357)(173,370)(174,369)(175,368)(176,367)(177,366)(178,365)
(179,371)(180,372)(181,359)(182,360)(183,378)(184,377)(185,376)(186,375)
(187,362)(188,361)(189,382)(190,381)(191,356)(192,355)(193,321)(194,322)
(195,352)(196,351)(197,332)(198,331)(199,341)(200,342)(201,348)(202,347)
(203,326)(204,325)(205,338)(206,337)(207,336)(208,335)(209,334)(210,333)
(211,339)(212,340)(213,327)(214,328)(215,346)(216,345)(217,344)(218,343)
(219,330)(220,329)(221,350)(222,349)(223,324)(224,323)(225,449)(226,450)
(227,480)(228,479)(229,460)(230,459)(231,469)(232,470)(233,476)(234,475)
(235,454)(236,453)(237,466)(238,465)(239,464)(240,463)(241,462)(242,461)
(243,467)(244,468)(245,455)(246,456)(247,474)(248,473)(249,472)(250,471)
(251,458)(252,457)(253,478)(254,477)(255,452)(256,451)(257,417)(258,418)
(259,448)(260,447)(261,428)(262,427)(263,437)(264,438)(265,444)(266,443)
(267,422)(268,421)(269,434)(270,433)(271,432)(272,431)(273,430)(274,429)
(275,435)(276,436)(277,423)(278,424)(279,442)(280,441)(281,440)(282,439)
(283,426)(284,425)(285,446)(286,445)(287,420)(288,419)(289,385)(290,386)
(291,416)(292,415)(293,396)(294,395)(295,405)(296,406)(297,412)(298,411)
(299,390)(300,389)(301,402)(302,401)(303,400)(304,399)(305,398)(306,397)
(307,403)(308,404)(309,391)(310,392)(311,410)(312,409)(313,408)(314,407)
(315,394)(316,393)(317,414)(318,413)(319,388)(320,387)(481,513)(482,514)
(483,544)(484,543)(485,524)(486,523)(487,533)(488,534)(489,540)(490,539)
(491,518)(492,517)(493,530)(494,529)(495,528)(496,527)(497,526)(498,525)
(499,531)(500,532)(501,519)(502,520)(503,538)(504,537)(505,536)(506,535)
(507,522)(508,521)(509,542)(510,541)(511,516)(512,515)(545,609)(546,610)
(547,640)(548,639)(549,620)(550,619)(551,629)(552,630)(553,636)(554,635)
(555,614)(556,613)(557,626)(558,625)(559,624)(560,623)(561,622)(562,621)
(563,627)(564,628)(565,615)(566,616)(567,634)(568,633)(569,632)(570,631)
(571,618)(572,617)(573,638)(574,637)(575,612)(576,611)(579,608)(580,607)
(581,588)(582,587)(583,597)(584,598)(585,604)(586,603)(589,594)(590,593)
(591,592)(599,602)(600,601)(605,606)(641,833)(642,834)(643,864)(644,863)
(645,844)(646,843)(647,853)(648,854)(649,860)(650,859)(651,838)(652,837)
(653,850)(654,849)(655,848)(656,847)(657,846)(658,845)(659,851)(660,852)
(661,839)(662,840)(663,858)(664,857)(665,856)(666,855)(667,842)(668,841)
(669,862)(670,861)(671,836)(672,835)(673,801)(674,802)(675,832)(676,831)
(677,812)(678,811)(679,821)(680,822)(681,828)(682,827)(683,806)(684,805)
(685,818)(686,817)(687,816)(688,815)(689,814)(690,813)(691,819)(692,820)
(693,807)(694,808)(695,826)(696,825)(697,824)(698,823)(699,810)(700,809)
(701,830)(702,829)(703,804)(704,803)(705,929)(706,930)(707,960)(708,959)
(709,940)(710,939)(711,949)(712,950)(713,956)(714,955)(715,934)(716,933)
(717,946)(718,945)(719,944)(720,943)(721,942)(722,941)(723,947)(724,948)
(725,935)(726,936)(727,954)(728,953)(729,952)(730,951)(731,938)(732,937)
(733,958)(734,957)(735,932)(736,931)(737,897)(738,898)(739,928)(740,927)
(741,908)(742,907)(743,917)(744,918)(745,924)(746,923)(747,902)(748,901)
(749,914)(750,913)(751,912)(752,911)(753,910)(754,909)(755,915)(756,916)
(757,903)(758,904)(759,922)(760,921)(761,920)(762,919)(763,906)(764,905)
(765,926)(766,925)(767,900)(768,899)(769,865)(770,866)(771,896)(772,895)
(773,876)(774,875)(775,885)(776,886)(777,892)(778,891)(779,870)(780,869)
(781,882)(782,881)(783,880)(784,879)(785,878)(786,877)(787,883)(788,884)
(789,871)(790,872)(791,890)(792,889)(793,888)(794,887)(795,874)(796,873)
(797,894)(798,893)(799,868)(800,867);;
s2 := ( 1,641)( 2,642)( 3,643)( 4,644)( 5,648)( 6,647)( 7,646)( 8,645)
( 9,650)( 10,649)( 11,652)( 12,651)( 13,655)( 14,656)( 15,653)( 16,654)
( 17,668)( 18,667)( 19,666)( 20,665)( 21,669)( 22,670)( 23,671)( 24,672)
( 25,660)( 26,659)( 27,658)( 28,657)( 29,661)( 30,662)( 31,663)( 32,664)
( 33,769)( 34,770)( 35,771)( 36,772)( 37,776)( 38,775)( 39,774)( 40,773)
( 41,778)( 42,777)( 43,780)( 44,779)( 45,783)( 46,784)( 47,781)( 48,782)
( 49,796)( 50,795)( 51,794)( 52,793)( 53,797)( 54,798)( 55,799)( 56,800)
( 57,788)( 58,787)( 59,786)( 60,785)( 61,789)( 62,790)( 63,791)( 64,792)
( 65,737)( 66,738)( 67,739)( 68,740)( 69,744)( 70,743)( 71,742)( 72,741)
( 73,746)( 74,745)( 75,748)( 76,747)( 77,751)( 78,752)( 79,749)( 80,750)
( 81,764)( 82,763)( 83,762)( 84,761)( 85,765)( 86,766)( 87,767)( 88,768)
( 89,756)( 90,755)( 91,754)( 92,753)( 93,757)( 94,758)( 95,759)( 96,760)
( 97,705)( 98,706)( 99,707)(100,708)(101,712)(102,711)(103,710)(104,709)
(105,714)(106,713)(107,716)(108,715)(109,719)(110,720)(111,717)(112,718)
(113,732)(114,731)(115,730)(116,729)(117,733)(118,734)(119,735)(120,736)
(121,724)(122,723)(123,722)(124,721)(125,725)(126,726)(127,727)(128,728)
(129,673)(130,674)(131,675)(132,676)(133,680)(134,679)(135,678)(136,677)
(137,682)(138,681)(139,684)(140,683)(141,687)(142,688)(143,685)(144,686)
(145,700)(146,699)(147,698)(148,697)(149,701)(150,702)(151,703)(152,704)
(153,692)(154,691)(155,690)(156,689)(157,693)(158,694)(159,695)(160,696)
(161,481)(162,482)(163,483)(164,484)(165,488)(166,487)(167,486)(168,485)
(169,490)(170,489)(171,492)(172,491)(173,495)(174,496)(175,493)(176,494)
(177,508)(178,507)(179,506)(180,505)(181,509)(182,510)(183,511)(184,512)
(185,500)(186,499)(187,498)(188,497)(189,501)(190,502)(191,503)(192,504)
(193,609)(194,610)(195,611)(196,612)(197,616)(198,615)(199,614)(200,613)
(201,618)(202,617)(203,620)(204,619)(205,623)(206,624)(207,621)(208,622)
(209,636)(210,635)(211,634)(212,633)(213,637)(214,638)(215,639)(216,640)
(217,628)(218,627)(219,626)(220,625)(221,629)(222,630)(223,631)(224,632)
(225,577)(226,578)(227,579)(228,580)(229,584)(230,583)(231,582)(232,581)
(233,586)(234,585)(235,588)(236,587)(237,591)(238,592)(239,589)(240,590)
(241,604)(242,603)(243,602)(244,601)(245,605)(246,606)(247,607)(248,608)
(249,596)(250,595)(251,594)(252,593)(253,597)(254,598)(255,599)(256,600)
(257,545)(258,546)(259,547)(260,548)(261,552)(262,551)(263,550)(264,549)
(265,554)(266,553)(267,556)(268,555)(269,559)(270,560)(271,557)(272,558)
(273,572)(274,571)(275,570)(276,569)(277,573)(278,574)(279,575)(280,576)
(281,564)(282,563)(283,562)(284,561)(285,565)(286,566)(287,567)(288,568)
(289,513)(290,514)(291,515)(292,516)(293,520)(294,519)(295,518)(296,517)
(297,522)(298,521)(299,524)(300,523)(301,527)(302,528)(303,525)(304,526)
(305,540)(306,539)(307,538)(308,537)(309,541)(310,542)(311,543)(312,544)
(313,532)(314,531)(315,530)(316,529)(317,533)(318,534)(319,535)(320,536)
(321,801)(322,802)(323,803)(324,804)(325,808)(326,807)(327,806)(328,805)
(329,810)(330,809)(331,812)(332,811)(333,815)(334,816)(335,813)(336,814)
(337,828)(338,827)(339,826)(340,825)(341,829)(342,830)(343,831)(344,832)
(345,820)(346,819)(347,818)(348,817)(349,821)(350,822)(351,823)(352,824)
(353,929)(354,930)(355,931)(356,932)(357,936)(358,935)(359,934)(360,933)
(361,938)(362,937)(363,940)(364,939)(365,943)(366,944)(367,941)(368,942)
(369,956)(370,955)(371,954)(372,953)(373,957)(374,958)(375,959)(376,960)
(377,948)(378,947)(379,946)(380,945)(381,949)(382,950)(383,951)(384,952)
(385,897)(386,898)(387,899)(388,900)(389,904)(390,903)(391,902)(392,901)
(393,906)(394,905)(395,908)(396,907)(397,911)(398,912)(399,909)(400,910)
(401,924)(402,923)(403,922)(404,921)(405,925)(406,926)(407,927)(408,928)
(409,916)(410,915)(411,914)(412,913)(413,917)(414,918)(415,919)(416,920)
(417,865)(418,866)(419,867)(420,868)(421,872)(422,871)(423,870)(424,869)
(425,874)(426,873)(427,876)(428,875)(429,879)(430,880)(431,877)(432,878)
(433,892)(434,891)(435,890)(436,889)(437,893)(438,894)(439,895)(440,896)
(441,884)(442,883)(443,882)(444,881)(445,885)(446,886)(447,887)(448,888)
(449,833)(450,834)(451,835)(452,836)(453,840)(454,839)(455,838)(456,837)
(457,842)(458,841)(459,844)(460,843)(461,847)(462,848)(463,845)(464,846)
(465,860)(466,859)(467,858)(468,857)(469,861)(470,862)(471,863)(472,864)
(473,852)(474,851)(475,850)(476,849)(477,853)(478,854)(479,855)(480,856);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,483)( 2,484)( 3,481)( 4,482)( 5,487)( 6,488)( 7,485)
( 8,486)( 9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)
( 16,494)( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)
( 24,502)( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)
( 32,510)( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)
( 40,518)( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)
( 48,526)( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)
( 56,534)( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)
( 64,542)( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)
( 72,550)( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)
( 80,558)( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)
( 88,566)( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)
( 96,574)( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)
(104,582)(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)
(112,590)(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)
(120,598)(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)
(128,606)(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)
(136,614)(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)
(144,622)(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)
(152,630)(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)
(160,638)(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)
(168,646)(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)
(176,654)(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)
(184,662)(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)
(192,670)(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)
(200,678)(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)
(208,686)(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)
(216,694)(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)
(224,702)(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)
(232,710)(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)
(240,718)(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)
(248,726)(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)
(256,734)(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)
(264,742)(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)
(272,750)(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)
(280,758)(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)
(288,766)(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)
(296,774)(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)
(304,782)(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)
(312,790)(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)
(320,798)(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)
(328,806)(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)
(336,814)(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)
(344,822)(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)
(352,830)(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)
(360,838)(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)
(368,846)(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)
(376,854)(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)
(384,862)(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)
(392,870)(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)
(400,878)(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)
(408,886)(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)
(416,894)(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)
(424,902)(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)
(432,910)(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)
(440,918)(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)
(448,926)(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)
(456,934)(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)
(464,942)(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)
(472,950)(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)
(480,958);
s1 := Sym(960)!( 1, 33)( 2, 34)( 3, 64)( 4, 63)( 5, 44)( 6, 43)( 7, 53)
( 8, 54)( 9, 60)( 10, 59)( 11, 38)( 12, 37)( 13, 50)( 14, 49)( 15, 48)
( 16, 47)( 17, 46)( 18, 45)( 19, 51)( 20, 52)( 21, 39)( 22, 40)( 23, 58)
( 24, 57)( 25, 56)( 26, 55)( 27, 42)( 28, 41)( 29, 62)( 30, 61)( 31, 36)
( 32, 35)( 65,129)( 66,130)( 67,160)( 68,159)( 69,140)( 70,139)( 71,149)
( 72,150)( 73,156)( 74,155)( 75,134)( 76,133)( 77,146)( 78,145)( 79,144)
( 80,143)( 81,142)( 82,141)( 83,147)( 84,148)( 85,135)( 86,136)( 87,154)
( 88,153)( 89,152)( 90,151)( 91,138)( 92,137)( 93,158)( 94,157)( 95,132)
( 96,131)( 99,128)(100,127)(101,108)(102,107)(103,117)(104,118)(105,124)
(106,123)(109,114)(110,113)(111,112)(119,122)(120,121)(125,126)(161,353)
(162,354)(163,384)(164,383)(165,364)(166,363)(167,373)(168,374)(169,380)
(170,379)(171,358)(172,357)(173,370)(174,369)(175,368)(176,367)(177,366)
(178,365)(179,371)(180,372)(181,359)(182,360)(183,378)(184,377)(185,376)
(186,375)(187,362)(188,361)(189,382)(190,381)(191,356)(192,355)(193,321)
(194,322)(195,352)(196,351)(197,332)(198,331)(199,341)(200,342)(201,348)
(202,347)(203,326)(204,325)(205,338)(206,337)(207,336)(208,335)(209,334)
(210,333)(211,339)(212,340)(213,327)(214,328)(215,346)(216,345)(217,344)
(218,343)(219,330)(220,329)(221,350)(222,349)(223,324)(224,323)(225,449)
(226,450)(227,480)(228,479)(229,460)(230,459)(231,469)(232,470)(233,476)
(234,475)(235,454)(236,453)(237,466)(238,465)(239,464)(240,463)(241,462)
(242,461)(243,467)(244,468)(245,455)(246,456)(247,474)(248,473)(249,472)
(250,471)(251,458)(252,457)(253,478)(254,477)(255,452)(256,451)(257,417)
(258,418)(259,448)(260,447)(261,428)(262,427)(263,437)(264,438)(265,444)
(266,443)(267,422)(268,421)(269,434)(270,433)(271,432)(272,431)(273,430)
(274,429)(275,435)(276,436)(277,423)(278,424)(279,442)(280,441)(281,440)
(282,439)(283,426)(284,425)(285,446)(286,445)(287,420)(288,419)(289,385)
(290,386)(291,416)(292,415)(293,396)(294,395)(295,405)(296,406)(297,412)
(298,411)(299,390)(300,389)(301,402)(302,401)(303,400)(304,399)(305,398)
(306,397)(307,403)(308,404)(309,391)(310,392)(311,410)(312,409)(313,408)
(314,407)(315,394)(316,393)(317,414)(318,413)(319,388)(320,387)(481,513)
(482,514)(483,544)(484,543)(485,524)(486,523)(487,533)(488,534)(489,540)
(490,539)(491,518)(492,517)(493,530)(494,529)(495,528)(496,527)(497,526)
(498,525)(499,531)(500,532)(501,519)(502,520)(503,538)(504,537)(505,536)
(506,535)(507,522)(508,521)(509,542)(510,541)(511,516)(512,515)(545,609)
(546,610)(547,640)(548,639)(549,620)(550,619)(551,629)(552,630)(553,636)
(554,635)(555,614)(556,613)(557,626)(558,625)(559,624)(560,623)(561,622)
(562,621)(563,627)(564,628)(565,615)(566,616)(567,634)(568,633)(569,632)
(570,631)(571,618)(572,617)(573,638)(574,637)(575,612)(576,611)(579,608)
(580,607)(581,588)(582,587)(583,597)(584,598)(585,604)(586,603)(589,594)
(590,593)(591,592)(599,602)(600,601)(605,606)(641,833)(642,834)(643,864)
(644,863)(645,844)(646,843)(647,853)(648,854)(649,860)(650,859)(651,838)
(652,837)(653,850)(654,849)(655,848)(656,847)(657,846)(658,845)(659,851)
(660,852)(661,839)(662,840)(663,858)(664,857)(665,856)(666,855)(667,842)
(668,841)(669,862)(670,861)(671,836)(672,835)(673,801)(674,802)(675,832)
(676,831)(677,812)(678,811)(679,821)(680,822)(681,828)(682,827)(683,806)
(684,805)(685,818)(686,817)(687,816)(688,815)(689,814)(690,813)(691,819)
(692,820)(693,807)(694,808)(695,826)(696,825)(697,824)(698,823)(699,810)
(700,809)(701,830)(702,829)(703,804)(704,803)(705,929)(706,930)(707,960)
(708,959)(709,940)(710,939)(711,949)(712,950)(713,956)(714,955)(715,934)
(716,933)(717,946)(718,945)(719,944)(720,943)(721,942)(722,941)(723,947)
(724,948)(725,935)(726,936)(727,954)(728,953)(729,952)(730,951)(731,938)
(732,937)(733,958)(734,957)(735,932)(736,931)(737,897)(738,898)(739,928)
(740,927)(741,908)(742,907)(743,917)(744,918)(745,924)(746,923)(747,902)
(748,901)(749,914)(750,913)(751,912)(752,911)(753,910)(754,909)(755,915)
(756,916)(757,903)(758,904)(759,922)(760,921)(761,920)(762,919)(763,906)
(764,905)(765,926)(766,925)(767,900)(768,899)(769,865)(770,866)(771,896)
(772,895)(773,876)(774,875)(775,885)(776,886)(777,892)(778,891)(779,870)
(780,869)(781,882)(782,881)(783,880)(784,879)(785,878)(786,877)(787,883)
(788,884)(789,871)(790,872)(791,890)(792,889)(793,888)(794,887)(795,874)
(796,873)(797,894)(798,893)(799,868)(800,867);
s2 := Sym(960)!( 1,641)( 2,642)( 3,643)( 4,644)( 5,648)( 6,647)( 7,646)
( 8,645)( 9,650)( 10,649)( 11,652)( 12,651)( 13,655)( 14,656)( 15,653)
( 16,654)( 17,668)( 18,667)( 19,666)( 20,665)( 21,669)( 22,670)( 23,671)
( 24,672)( 25,660)( 26,659)( 27,658)( 28,657)( 29,661)( 30,662)( 31,663)
( 32,664)( 33,769)( 34,770)( 35,771)( 36,772)( 37,776)( 38,775)( 39,774)
( 40,773)( 41,778)( 42,777)( 43,780)( 44,779)( 45,783)( 46,784)( 47,781)
( 48,782)( 49,796)( 50,795)( 51,794)( 52,793)( 53,797)( 54,798)( 55,799)
( 56,800)( 57,788)( 58,787)( 59,786)( 60,785)( 61,789)( 62,790)( 63,791)
( 64,792)( 65,737)( 66,738)( 67,739)( 68,740)( 69,744)( 70,743)( 71,742)
( 72,741)( 73,746)( 74,745)( 75,748)( 76,747)( 77,751)( 78,752)( 79,749)
( 80,750)( 81,764)( 82,763)( 83,762)( 84,761)( 85,765)( 86,766)( 87,767)
( 88,768)( 89,756)( 90,755)( 91,754)( 92,753)( 93,757)( 94,758)( 95,759)
( 96,760)( 97,705)( 98,706)( 99,707)(100,708)(101,712)(102,711)(103,710)
(104,709)(105,714)(106,713)(107,716)(108,715)(109,719)(110,720)(111,717)
(112,718)(113,732)(114,731)(115,730)(116,729)(117,733)(118,734)(119,735)
(120,736)(121,724)(122,723)(123,722)(124,721)(125,725)(126,726)(127,727)
(128,728)(129,673)(130,674)(131,675)(132,676)(133,680)(134,679)(135,678)
(136,677)(137,682)(138,681)(139,684)(140,683)(141,687)(142,688)(143,685)
(144,686)(145,700)(146,699)(147,698)(148,697)(149,701)(150,702)(151,703)
(152,704)(153,692)(154,691)(155,690)(156,689)(157,693)(158,694)(159,695)
(160,696)(161,481)(162,482)(163,483)(164,484)(165,488)(166,487)(167,486)
(168,485)(169,490)(170,489)(171,492)(172,491)(173,495)(174,496)(175,493)
(176,494)(177,508)(178,507)(179,506)(180,505)(181,509)(182,510)(183,511)
(184,512)(185,500)(186,499)(187,498)(188,497)(189,501)(190,502)(191,503)
(192,504)(193,609)(194,610)(195,611)(196,612)(197,616)(198,615)(199,614)
(200,613)(201,618)(202,617)(203,620)(204,619)(205,623)(206,624)(207,621)
(208,622)(209,636)(210,635)(211,634)(212,633)(213,637)(214,638)(215,639)
(216,640)(217,628)(218,627)(219,626)(220,625)(221,629)(222,630)(223,631)
(224,632)(225,577)(226,578)(227,579)(228,580)(229,584)(230,583)(231,582)
(232,581)(233,586)(234,585)(235,588)(236,587)(237,591)(238,592)(239,589)
(240,590)(241,604)(242,603)(243,602)(244,601)(245,605)(246,606)(247,607)
(248,608)(249,596)(250,595)(251,594)(252,593)(253,597)(254,598)(255,599)
(256,600)(257,545)(258,546)(259,547)(260,548)(261,552)(262,551)(263,550)
(264,549)(265,554)(266,553)(267,556)(268,555)(269,559)(270,560)(271,557)
(272,558)(273,572)(274,571)(275,570)(276,569)(277,573)(278,574)(279,575)
(280,576)(281,564)(282,563)(283,562)(284,561)(285,565)(286,566)(287,567)
(288,568)(289,513)(290,514)(291,515)(292,516)(293,520)(294,519)(295,518)
(296,517)(297,522)(298,521)(299,524)(300,523)(301,527)(302,528)(303,525)
(304,526)(305,540)(306,539)(307,538)(308,537)(309,541)(310,542)(311,543)
(312,544)(313,532)(314,531)(315,530)(316,529)(317,533)(318,534)(319,535)
(320,536)(321,801)(322,802)(323,803)(324,804)(325,808)(326,807)(327,806)
(328,805)(329,810)(330,809)(331,812)(332,811)(333,815)(334,816)(335,813)
(336,814)(337,828)(338,827)(339,826)(340,825)(341,829)(342,830)(343,831)
(344,832)(345,820)(346,819)(347,818)(348,817)(349,821)(350,822)(351,823)
(352,824)(353,929)(354,930)(355,931)(356,932)(357,936)(358,935)(359,934)
(360,933)(361,938)(362,937)(363,940)(364,939)(365,943)(366,944)(367,941)
(368,942)(369,956)(370,955)(371,954)(372,953)(373,957)(374,958)(375,959)
(376,960)(377,948)(378,947)(379,946)(380,945)(381,949)(382,950)(383,951)
(384,952)(385,897)(386,898)(387,899)(388,900)(389,904)(390,903)(391,902)
(392,901)(393,906)(394,905)(395,908)(396,907)(397,911)(398,912)(399,909)
(400,910)(401,924)(402,923)(403,922)(404,921)(405,925)(406,926)(407,927)
(408,928)(409,916)(410,915)(411,914)(412,913)(413,917)(414,918)(415,919)
(416,920)(417,865)(418,866)(419,867)(420,868)(421,872)(422,871)(423,870)
(424,869)(425,874)(426,873)(427,876)(428,875)(429,879)(430,880)(431,877)
(432,878)(433,892)(434,891)(435,890)(436,889)(437,893)(438,894)(439,895)
(440,896)(441,884)(442,883)(443,882)(444,881)(445,885)(446,886)(447,887)
(448,888)(449,833)(450,834)(451,835)(452,836)(453,840)(454,839)(455,838)
(456,837)(457,842)(458,841)(459,844)(460,843)(461,847)(462,848)(463,845)
(464,846)(465,860)(466,859)(467,858)(468,857)(469,861)(470,862)(471,863)
(472,864)(473,852)(474,851)(475,850)(476,849)(477,853)(478,854)(479,855)
(480,856);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1 >;
References : None.
to this polytope