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