Polytope of Type {8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*1920d
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 : {8,15}*960a
   4-fold quotients : {4,30}*480
   5-fold quotients : {8,6}*384e
   8-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {8,3}*192
   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 := (  1,577)(  2,580)(  3,579)(  4,578)(  5,590)(  6,591)(  7,592)(  8,589)
(  9,585)( 10,588)( 11,587)( 12,586)( 13,584)( 14,581)( 15,582)( 16,583)
( 17,561)( 18,564)( 19,563)( 20,562)( 21,574)( 22,575)( 23,576)( 24,573)
( 25,569)( 26,572)( 27,571)( 28,570)( 29,568)( 30,565)( 31,566)( 32,567)
( 33,625)( 34,628)( 35,627)( 36,626)( 37,638)( 38,639)( 39,640)( 40,637)
( 41,633)( 42,636)( 43,635)( 44,634)( 45,632)( 46,629)( 47,630)( 48,631)
( 49,609)( 50,612)( 51,611)( 52,610)( 53,622)( 54,623)( 55,624)( 56,621)
( 57,617)( 58,620)( 59,619)( 60,618)( 61,616)( 62,613)( 63,614)( 64,615)
( 65,593)( 66,596)( 67,595)( 68,594)( 69,606)( 70,607)( 71,608)( 72,605)
( 73,601)( 74,604)( 75,603)( 76,602)( 77,600)( 78,597)( 79,598)( 80,599)
( 81,497)( 82,500)( 83,499)( 84,498)( 85,510)( 86,511)( 87,512)( 88,509)
( 89,505)( 90,508)( 91,507)( 92,506)( 93,504)( 94,501)( 95,502)( 96,503)
( 97,481)( 98,484)( 99,483)(100,482)(101,494)(102,495)(103,496)(104,493)
(105,489)(106,492)(107,491)(108,490)(109,488)(110,485)(111,486)(112,487)
(113,545)(114,548)(115,547)(116,546)(117,558)(118,559)(119,560)(120,557)
(121,553)(122,556)(123,555)(124,554)(125,552)(126,549)(127,550)(128,551)
(129,529)(130,532)(131,531)(132,530)(133,542)(134,543)(135,544)(136,541)
(137,537)(138,540)(139,539)(140,538)(141,536)(142,533)(143,534)(144,535)
(145,513)(146,516)(147,515)(148,514)(149,526)(150,527)(151,528)(152,525)
(153,521)(154,524)(155,523)(156,522)(157,520)(158,517)(159,518)(160,519)
(161,657)(162,660)(163,659)(164,658)(165,670)(166,671)(167,672)(168,669)
(169,665)(170,668)(171,667)(172,666)(173,664)(174,661)(175,662)(176,663)
(177,641)(178,644)(179,643)(180,642)(181,654)(182,655)(183,656)(184,653)
(185,649)(186,652)(187,651)(188,650)(189,648)(190,645)(191,646)(192,647)
(193,705)(194,708)(195,707)(196,706)(197,718)(198,719)(199,720)(200,717)
(201,713)(202,716)(203,715)(204,714)(205,712)(206,709)(207,710)(208,711)
(209,689)(210,692)(211,691)(212,690)(213,702)(214,703)(215,704)(216,701)
(217,697)(218,700)(219,699)(220,698)(221,696)(222,693)(223,694)(224,695)
(225,673)(226,676)(227,675)(228,674)(229,686)(230,687)(231,688)(232,685)
(233,681)(234,684)(235,683)(236,682)(237,680)(238,677)(239,678)(240,679)
(241,817)(242,820)(243,819)(244,818)(245,830)(246,831)(247,832)(248,829)
(249,825)(250,828)(251,827)(252,826)(253,824)(254,821)(255,822)(256,823)
(257,801)(258,804)(259,803)(260,802)(261,814)(262,815)(263,816)(264,813)
(265,809)(266,812)(267,811)(268,810)(269,808)(270,805)(271,806)(272,807)
(273,865)(274,868)(275,867)(276,866)(277,878)(278,879)(279,880)(280,877)
(281,873)(282,876)(283,875)(284,874)(285,872)(286,869)(287,870)(288,871)
(289,849)(290,852)(291,851)(292,850)(293,862)(294,863)(295,864)(296,861)
(297,857)(298,860)(299,859)(300,858)(301,856)(302,853)(303,854)(304,855)
(305,833)(306,836)(307,835)(308,834)(309,846)(310,847)(311,848)(312,845)
(313,841)(314,844)(315,843)(316,842)(317,840)(318,837)(319,838)(320,839)
(321,737)(322,740)(323,739)(324,738)(325,750)(326,751)(327,752)(328,749)
(329,745)(330,748)(331,747)(332,746)(333,744)(334,741)(335,742)(336,743)
(337,721)(338,724)(339,723)(340,722)(341,734)(342,735)(343,736)(344,733)
(345,729)(346,732)(347,731)(348,730)(349,728)(350,725)(351,726)(352,727)
(353,785)(354,788)(355,787)(356,786)(357,798)(358,799)(359,800)(360,797)
(361,793)(362,796)(363,795)(364,794)(365,792)(366,789)(367,790)(368,791)
(369,769)(370,772)(371,771)(372,770)(373,782)(374,783)(375,784)(376,781)
(377,777)(378,780)(379,779)(380,778)(381,776)(382,773)(383,774)(384,775)
(385,753)(386,756)(387,755)(388,754)(389,766)(390,767)(391,768)(392,765)
(393,761)(394,764)(395,763)(396,762)(397,760)(398,757)(399,758)(400,759)
(401,897)(402,900)(403,899)(404,898)(405,910)(406,911)(407,912)(408,909)
(409,905)(410,908)(411,907)(412,906)(413,904)(414,901)(415,902)(416,903)
(417,881)(418,884)(419,883)(420,882)(421,894)(422,895)(423,896)(424,893)
(425,889)(426,892)(427,891)(428,890)(429,888)(430,885)(431,886)(432,887)
(433,945)(434,948)(435,947)(436,946)(437,958)(438,959)(439,960)(440,957)
(441,953)(442,956)(443,955)(444,954)(445,952)(446,949)(447,950)(448,951)
(449,929)(450,932)(451,931)(452,930)(453,942)(454,943)(455,944)(456,941)
(457,937)(458,940)(459,939)(460,938)(461,936)(462,933)(463,934)(464,935)
(465,913)(466,916)(467,915)(468,914)(469,926)(470,927)(471,928)(472,925)
(473,921)(474,924)(475,923)(476,922)(477,920)(478,917)(479,918)(480,919);;
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*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*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)!(  1,577)(  2,580)(  3,579)(  4,578)(  5,590)(  6,591)(  7,592)
(  8,589)(  9,585)( 10,588)( 11,587)( 12,586)( 13,584)( 14,581)( 15,582)
( 16,583)( 17,561)( 18,564)( 19,563)( 20,562)( 21,574)( 22,575)( 23,576)
( 24,573)( 25,569)( 26,572)( 27,571)( 28,570)( 29,568)( 30,565)( 31,566)
( 32,567)( 33,625)( 34,628)( 35,627)( 36,626)( 37,638)( 38,639)( 39,640)
( 40,637)( 41,633)( 42,636)( 43,635)( 44,634)( 45,632)( 46,629)( 47,630)
( 48,631)( 49,609)( 50,612)( 51,611)( 52,610)( 53,622)( 54,623)( 55,624)
( 56,621)( 57,617)( 58,620)( 59,619)( 60,618)( 61,616)( 62,613)( 63,614)
( 64,615)( 65,593)( 66,596)( 67,595)( 68,594)( 69,606)( 70,607)( 71,608)
( 72,605)( 73,601)( 74,604)( 75,603)( 76,602)( 77,600)( 78,597)( 79,598)
( 80,599)( 81,497)( 82,500)( 83,499)( 84,498)( 85,510)( 86,511)( 87,512)
( 88,509)( 89,505)( 90,508)( 91,507)( 92,506)( 93,504)( 94,501)( 95,502)
( 96,503)( 97,481)( 98,484)( 99,483)(100,482)(101,494)(102,495)(103,496)
(104,493)(105,489)(106,492)(107,491)(108,490)(109,488)(110,485)(111,486)
(112,487)(113,545)(114,548)(115,547)(116,546)(117,558)(118,559)(119,560)
(120,557)(121,553)(122,556)(123,555)(124,554)(125,552)(126,549)(127,550)
(128,551)(129,529)(130,532)(131,531)(132,530)(133,542)(134,543)(135,544)
(136,541)(137,537)(138,540)(139,539)(140,538)(141,536)(142,533)(143,534)
(144,535)(145,513)(146,516)(147,515)(148,514)(149,526)(150,527)(151,528)
(152,525)(153,521)(154,524)(155,523)(156,522)(157,520)(158,517)(159,518)
(160,519)(161,657)(162,660)(163,659)(164,658)(165,670)(166,671)(167,672)
(168,669)(169,665)(170,668)(171,667)(172,666)(173,664)(174,661)(175,662)
(176,663)(177,641)(178,644)(179,643)(180,642)(181,654)(182,655)(183,656)
(184,653)(185,649)(186,652)(187,651)(188,650)(189,648)(190,645)(191,646)
(192,647)(193,705)(194,708)(195,707)(196,706)(197,718)(198,719)(199,720)
(200,717)(201,713)(202,716)(203,715)(204,714)(205,712)(206,709)(207,710)
(208,711)(209,689)(210,692)(211,691)(212,690)(213,702)(214,703)(215,704)
(216,701)(217,697)(218,700)(219,699)(220,698)(221,696)(222,693)(223,694)
(224,695)(225,673)(226,676)(227,675)(228,674)(229,686)(230,687)(231,688)
(232,685)(233,681)(234,684)(235,683)(236,682)(237,680)(238,677)(239,678)
(240,679)(241,817)(242,820)(243,819)(244,818)(245,830)(246,831)(247,832)
(248,829)(249,825)(250,828)(251,827)(252,826)(253,824)(254,821)(255,822)
(256,823)(257,801)(258,804)(259,803)(260,802)(261,814)(262,815)(263,816)
(264,813)(265,809)(266,812)(267,811)(268,810)(269,808)(270,805)(271,806)
(272,807)(273,865)(274,868)(275,867)(276,866)(277,878)(278,879)(279,880)
(280,877)(281,873)(282,876)(283,875)(284,874)(285,872)(286,869)(287,870)
(288,871)(289,849)(290,852)(291,851)(292,850)(293,862)(294,863)(295,864)
(296,861)(297,857)(298,860)(299,859)(300,858)(301,856)(302,853)(303,854)
(304,855)(305,833)(306,836)(307,835)(308,834)(309,846)(310,847)(311,848)
(312,845)(313,841)(314,844)(315,843)(316,842)(317,840)(318,837)(319,838)
(320,839)(321,737)(322,740)(323,739)(324,738)(325,750)(326,751)(327,752)
(328,749)(329,745)(330,748)(331,747)(332,746)(333,744)(334,741)(335,742)
(336,743)(337,721)(338,724)(339,723)(340,722)(341,734)(342,735)(343,736)
(344,733)(345,729)(346,732)(347,731)(348,730)(349,728)(350,725)(351,726)
(352,727)(353,785)(354,788)(355,787)(356,786)(357,798)(358,799)(359,800)
(360,797)(361,793)(362,796)(363,795)(364,794)(365,792)(366,789)(367,790)
(368,791)(369,769)(370,772)(371,771)(372,770)(373,782)(374,783)(375,784)
(376,781)(377,777)(378,780)(379,779)(380,778)(381,776)(382,773)(383,774)
(384,775)(385,753)(386,756)(387,755)(388,754)(389,766)(390,767)(391,768)
(392,765)(393,761)(394,764)(395,763)(396,762)(397,760)(398,757)(399,758)
(400,759)(401,897)(402,900)(403,899)(404,898)(405,910)(406,911)(407,912)
(408,909)(409,905)(410,908)(411,907)(412,906)(413,904)(414,901)(415,902)
(416,903)(417,881)(418,884)(419,883)(420,882)(421,894)(422,895)(423,896)
(424,893)(425,889)(426,892)(427,891)(428,890)(429,888)(430,885)(431,886)
(432,887)(433,945)(434,948)(435,947)(436,946)(437,958)(438,959)(439,960)
(440,957)(441,953)(442,956)(443,955)(444,954)(445,952)(446,949)(447,950)
(448,951)(449,929)(450,932)(451,931)(452,930)(453,942)(454,943)(455,944)
(456,941)(457,937)(458,940)(459,939)(460,938)(461,936)(462,933)(463,934)
(464,935)(465,913)(466,916)(467,915)(468,914)(469,926)(470,927)(471,928)
(472,925)(473,921)(474,924)(475,923)(476,922)(477,920)(478,917)(479,918)
(480,919);
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*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*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