Polytope of Type {30,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,12}*960a
if this polytope has a name.
Group : SmallGroup(960,10958)
Rank : 3
Schlafli Type : {30,12}
Number of vertices, edges, etc : 40, 240, 16
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,12,2} of size 1920
Vertex Figure Of :
   {2,30,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,12}*480, {30,6}*480
   4-fold quotients : {15,6}*240
   5-fold quotients : {6,12}*192b
   10-fold quotients : {3,12}*96, {6,6}*96
   20-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {10,2}*40
   40-fold quotients : {3,3}*24
   48-fold quotients : {5,2}*20
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,12}*1920a, {60,12}*1920b, {30,12}*1920
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;

References : None.
to this polytope