Polytope of Type {8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239473)
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
   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 : {8,30}*960a
   4-fold quotients : {4,30}*480
   5-fold quotients : {8,6}*384d
   8-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {8,6}*192a
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,6}*96
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope