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