Polytope of Type {96,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {96,10}*1920
Also Known As : {96,10|2}. if this polytope has another name.
Group : SmallGroup(1920,44850)
Rank : 3
Schlafli Type : {96,10}
Number of vertices, edges, etc : 96, 480, 10
Order of s0s1s2 : 480
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {48,10}*960
3-fold quotients : {32,10}*640
4-fold quotients : {24,10}*480
5-fold quotients : {96,2}*384
6-fold quotients : {16,10}*320
8-fold quotients : {12,10}*240
10-fold quotients : {48,2}*192
12-fold quotients : {8,10}*160
15-fold quotients : {32,2}*128
16-fold quotients : {6,10}*120
20-fold quotients : {24,2}*96
24-fold quotients : {4,10}*80
30-fold quotients : {16,2}*64
40-fold quotients : {12,2}*48
48-fold quotients : {2,10}*40
60-fold quotients : {8,2}*32
80-fold quotients : {6,2}*24
96-fold quotients : {2,5}*20
120-fold quotients : {4,2}*16
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 56)
( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)( 44, 54)
( 45, 55)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)( 67,102)
( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)( 75,100)
( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)( 83,118)
( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)(121,181)
(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)(129,194)
(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)
(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)(145,210)
(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)(153,228)
(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)(161,231)
(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)(169,214)
(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)(177,217)
(178,218)(179,219)(180,220)(246,251)(247,252)(248,253)(249,254)(250,255)
(261,266)(262,267)(263,268)(264,269)(265,270)(271,286)(272,287)(273,288)
(274,289)(275,290)(276,296)(277,297)(278,298)(279,299)(280,300)(281,291)
(282,292)(283,293)(284,294)(285,295)(301,331)(302,332)(303,333)(304,334)
(305,335)(306,341)(307,342)(308,343)(309,344)(310,345)(311,336)(312,337)
(313,338)(314,339)(315,340)(316,346)(317,347)(318,348)(319,349)(320,350)
(321,356)(322,357)(323,358)(324,359)(325,360)(326,351)(327,352)(328,353)
(329,354)(330,355)(361,421)(362,422)(363,423)(364,424)(365,425)(366,431)
(367,432)(368,433)(369,434)(370,435)(371,426)(372,427)(373,428)(374,429)
(375,430)(376,436)(377,437)(378,438)(379,439)(380,440)(381,446)(382,447)
(383,448)(384,449)(385,450)(386,441)(387,442)(388,443)(389,444)(390,445)
(391,466)(392,467)(393,468)(394,469)(395,470)(396,476)(397,477)(398,478)
(399,479)(400,480)(401,471)(402,472)(403,473)(404,474)(405,475)(406,451)
(407,452)(408,453)(409,454)(410,455)(411,461)(412,462)(413,463)(414,464)
(415,465)(416,456)(417,457)(418,458)(419,459)(420,460)(481,601)(482,602)
(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)(489,614)(490,615)
(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)(497,617)(498,618)
(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)(505,630)(506,621)
(507,622)(508,623)(509,624)(510,625)(511,646)(512,647)(513,648)(514,649)
(515,650)(516,656)(517,657)(518,658)(519,659)(520,660)(521,651)(522,652)
(523,653)(524,654)(525,655)(526,631)(527,632)(528,633)(529,634)(530,635)
(531,641)(532,642)(533,643)(534,644)(535,645)(536,636)(537,637)(538,638)
(539,639)(540,640)(541,691)(542,692)(543,693)(544,694)(545,695)(546,701)
(547,702)(548,703)(549,704)(550,705)(551,696)(552,697)(553,698)(554,699)
(555,700)(556,706)(557,707)(558,708)(559,709)(560,710)(561,716)(562,717)
(563,718)(564,719)(565,720)(566,711)(567,712)(568,713)(569,714)(570,715)
(571,661)(572,662)(573,663)(574,664)(575,665)(576,671)(577,672)(578,673)
(579,674)(580,675)(581,666)(582,667)(583,668)(584,669)(585,670)(586,676)
(587,677)(588,678)(589,679)(590,680)(591,686)(592,687)(593,688)(594,689)
(595,690)(596,681)(597,682)(598,683)(599,684)(600,685)(721,841)(722,842)
(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)(729,854)(730,855)
(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)(737,857)(738,858)
(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)(745,870)(746,861)
(747,862)(748,863)(749,864)(750,865)(751,886)(752,887)(753,888)(754,889)
(755,890)(756,896)(757,897)(758,898)(759,899)(760,900)(761,891)(762,892)
(763,893)(764,894)(765,895)(766,871)(767,872)(768,873)(769,874)(770,875)
(771,881)(772,882)(773,883)(774,884)(775,885)(776,876)(777,877)(778,878)
(779,879)(780,880)(781,931)(782,932)(783,933)(784,934)(785,935)(786,941)
(787,942)(788,943)(789,944)(790,945)(791,936)(792,937)(793,938)(794,939)
(795,940)(796,946)(797,947)(798,948)(799,949)(800,950)(801,956)(802,957)
(803,958)(804,959)(805,960)(806,951)(807,952)(808,953)(809,954)(810,955)
(811,901)(812,902)(813,903)(814,904)(815,905)(816,911)(817,912)(818,913)
(819,914)(820,915)(821,906)(822,907)(823,908)(824,909)(825,910)(826,916)
(827,917)(828,918)(829,919)(830,920)(831,926)(832,927)(833,928)(834,929)
(835,930)(836,921)(837,922)(838,923)(839,924)(840,925);;
s1 := ( 1,726)( 2,730)( 3,729)( 4,728)( 5,727)( 6,721)( 7,725)( 8,724)
( 9,723)( 10,722)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)( 16,741)
( 17,745)( 18,744)( 19,743)( 20,742)( 21,736)( 22,740)( 23,739)( 24,738)
( 25,737)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,771)( 32,775)
( 33,774)( 34,773)( 35,772)( 36,766)( 37,770)( 38,769)( 39,768)( 40,767)
( 41,776)( 42,780)( 43,779)( 44,778)( 45,777)( 46,756)( 47,760)( 48,759)
( 49,758)( 50,757)( 51,751)( 52,755)( 53,754)( 54,753)( 55,752)( 56,761)
( 57,765)( 58,764)( 59,763)( 60,762)( 61,816)( 62,820)( 63,819)( 64,818)
( 65,817)( 66,811)( 67,815)( 68,814)( 69,813)( 70,812)( 71,821)( 72,825)
( 73,824)( 74,823)( 75,822)( 76,831)( 77,835)( 78,834)( 79,833)( 80,832)
( 81,826)( 82,830)( 83,829)( 84,828)( 85,827)( 86,836)( 87,840)( 88,839)
( 89,838)( 90,837)( 91,786)( 92,790)( 93,789)( 94,788)( 95,787)( 96,781)
( 97,785)( 98,784)( 99,783)(100,782)(101,791)(102,795)(103,794)(104,793)
(105,792)(106,801)(107,805)(108,804)(109,803)(110,802)(111,796)(112,800)
(113,799)(114,798)(115,797)(116,806)(117,810)(118,809)(119,808)(120,807)
(121,906)(122,910)(123,909)(124,908)(125,907)(126,901)(127,905)(128,904)
(129,903)(130,902)(131,911)(132,915)(133,914)(134,913)(135,912)(136,921)
(137,925)(138,924)(139,923)(140,922)(141,916)(142,920)(143,919)(144,918)
(145,917)(146,926)(147,930)(148,929)(149,928)(150,927)(151,951)(152,955)
(153,954)(154,953)(155,952)(156,946)(157,950)(158,949)(159,948)(160,947)
(161,956)(162,960)(163,959)(164,958)(165,957)(166,936)(167,940)(168,939)
(169,938)(170,937)(171,931)(172,935)(173,934)(174,933)(175,932)(176,941)
(177,945)(178,944)(179,943)(180,942)(181,846)(182,850)(183,849)(184,848)
(185,847)(186,841)(187,845)(188,844)(189,843)(190,842)(191,851)(192,855)
(193,854)(194,853)(195,852)(196,861)(197,865)(198,864)(199,863)(200,862)
(201,856)(202,860)(203,859)(204,858)(205,857)(206,866)(207,870)(208,869)
(209,868)(210,867)(211,891)(212,895)(213,894)(214,893)(215,892)(216,886)
(217,890)(218,889)(219,888)(220,887)(221,896)(222,900)(223,899)(224,898)
(225,897)(226,876)(227,880)(228,879)(229,878)(230,877)(231,871)(232,875)
(233,874)(234,873)(235,872)(236,881)(237,885)(238,884)(239,883)(240,882)
(241,486)(242,490)(243,489)(244,488)(245,487)(246,481)(247,485)(248,484)
(249,483)(250,482)(251,491)(252,495)(253,494)(254,493)(255,492)(256,501)
(257,505)(258,504)(259,503)(260,502)(261,496)(262,500)(263,499)(264,498)
(265,497)(266,506)(267,510)(268,509)(269,508)(270,507)(271,531)(272,535)
(273,534)(274,533)(275,532)(276,526)(277,530)(278,529)(279,528)(280,527)
(281,536)(282,540)(283,539)(284,538)(285,537)(286,516)(287,520)(288,519)
(289,518)(290,517)(291,511)(292,515)(293,514)(294,513)(295,512)(296,521)
(297,525)(298,524)(299,523)(300,522)(301,576)(302,580)(303,579)(304,578)
(305,577)(306,571)(307,575)(308,574)(309,573)(310,572)(311,581)(312,585)
(313,584)(314,583)(315,582)(316,591)(317,595)(318,594)(319,593)(320,592)
(321,586)(322,590)(323,589)(324,588)(325,587)(326,596)(327,600)(328,599)
(329,598)(330,597)(331,546)(332,550)(333,549)(334,548)(335,547)(336,541)
(337,545)(338,544)(339,543)(340,542)(341,551)(342,555)(343,554)(344,553)
(345,552)(346,561)(347,565)(348,564)(349,563)(350,562)(351,556)(352,560)
(353,559)(354,558)(355,557)(356,566)(357,570)(358,569)(359,568)(360,567)
(361,666)(362,670)(363,669)(364,668)(365,667)(366,661)(367,665)(368,664)
(369,663)(370,662)(371,671)(372,675)(373,674)(374,673)(375,672)(376,681)
(377,685)(378,684)(379,683)(380,682)(381,676)(382,680)(383,679)(384,678)
(385,677)(386,686)(387,690)(388,689)(389,688)(390,687)(391,711)(392,715)
(393,714)(394,713)(395,712)(396,706)(397,710)(398,709)(399,708)(400,707)
(401,716)(402,720)(403,719)(404,718)(405,717)(406,696)(407,700)(408,699)
(409,698)(410,697)(411,691)(412,695)(413,694)(414,693)(415,692)(416,701)
(417,705)(418,704)(419,703)(420,702)(421,606)(422,610)(423,609)(424,608)
(425,607)(426,601)(427,605)(428,604)(429,603)(430,602)(431,611)(432,615)
(433,614)(434,613)(435,612)(436,621)(437,625)(438,624)(439,623)(440,622)
(441,616)(442,620)(443,619)(444,618)(445,617)(446,626)(447,630)(448,629)
(449,628)(450,627)(451,651)(452,655)(453,654)(454,653)(455,652)(456,646)
(457,650)(458,649)(459,648)(460,647)(461,656)(462,660)(463,659)(464,658)
(465,657)(466,636)(467,640)(468,639)(469,638)(470,637)(471,631)(472,635)
(473,634)(474,633)(475,632)(476,641)(477,645)(478,644)(479,643)(480,642);;
s2 := ( 1,242)( 2,241)( 3,245)( 4,244)( 5,243)( 6,247)( 7,246)( 8,250)
( 9,249)( 10,248)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,257)
( 17,256)( 18,260)( 19,259)( 20,258)( 21,262)( 22,261)( 23,265)( 24,264)
( 25,263)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,272)( 32,271)
( 33,275)( 34,274)( 35,273)( 36,277)( 37,276)( 38,280)( 39,279)( 40,278)
( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,287)( 47,286)( 48,290)
( 49,289)( 50,288)( 51,292)( 52,291)( 53,295)( 54,294)( 55,293)( 56,297)
( 57,296)( 58,300)( 59,299)( 60,298)( 61,302)( 62,301)( 63,305)( 64,304)
( 65,303)( 66,307)( 67,306)( 68,310)( 69,309)( 70,308)( 71,312)( 72,311)
( 73,315)( 74,314)( 75,313)( 76,317)( 77,316)( 78,320)( 79,319)( 80,318)
( 81,322)( 82,321)( 83,325)( 84,324)( 85,323)( 86,327)( 87,326)( 88,330)
( 89,329)( 90,328)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)( 96,337)
( 97,336)( 98,340)( 99,339)(100,338)(101,342)(102,341)(103,345)(104,344)
(105,343)(106,347)(107,346)(108,350)(109,349)(110,348)(111,352)(112,351)
(113,355)(114,354)(115,353)(116,357)(117,356)(118,360)(119,359)(120,358)
(121,362)(122,361)(123,365)(124,364)(125,363)(126,367)(127,366)(128,370)
(129,369)(130,368)(131,372)(132,371)(133,375)(134,374)(135,373)(136,377)
(137,376)(138,380)(139,379)(140,378)(141,382)(142,381)(143,385)(144,384)
(145,383)(146,387)(147,386)(148,390)(149,389)(150,388)(151,392)(152,391)
(153,395)(154,394)(155,393)(156,397)(157,396)(158,400)(159,399)(160,398)
(161,402)(162,401)(163,405)(164,404)(165,403)(166,407)(167,406)(168,410)
(169,409)(170,408)(171,412)(172,411)(173,415)(174,414)(175,413)(176,417)
(177,416)(178,420)(179,419)(180,418)(181,422)(182,421)(183,425)(184,424)
(185,423)(186,427)(187,426)(188,430)(189,429)(190,428)(191,432)(192,431)
(193,435)(194,434)(195,433)(196,437)(197,436)(198,440)(199,439)(200,438)
(201,442)(202,441)(203,445)(204,444)(205,443)(206,447)(207,446)(208,450)
(209,449)(210,448)(211,452)(212,451)(213,455)(214,454)(215,453)(216,457)
(217,456)(218,460)(219,459)(220,458)(221,462)(222,461)(223,465)(224,464)
(225,463)(226,467)(227,466)(228,470)(229,469)(230,468)(231,472)(232,471)
(233,475)(234,474)(235,473)(236,477)(237,476)(238,480)(239,479)(240,478)
(481,722)(482,721)(483,725)(484,724)(485,723)(486,727)(487,726)(488,730)
(489,729)(490,728)(491,732)(492,731)(493,735)(494,734)(495,733)(496,737)
(497,736)(498,740)(499,739)(500,738)(501,742)(502,741)(503,745)(504,744)
(505,743)(506,747)(507,746)(508,750)(509,749)(510,748)(511,752)(512,751)
(513,755)(514,754)(515,753)(516,757)(517,756)(518,760)(519,759)(520,758)
(521,762)(522,761)(523,765)(524,764)(525,763)(526,767)(527,766)(528,770)
(529,769)(530,768)(531,772)(532,771)(533,775)(534,774)(535,773)(536,777)
(537,776)(538,780)(539,779)(540,778)(541,782)(542,781)(543,785)(544,784)
(545,783)(546,787)(547,786)(548,790)(549,789)(550,788)(551,792)(552,791)
(553,795)(554,794)(555,793)(556,797)(557,796)(558,800)(559,799)(560,798)
(561,802)(562,801)(563,805)(564,804)(565,803)(566,807)(567,806)(568,810)
(569,809)(570,808)(571,812)(572,811)(573,815)(574,814)(575,813)(576,817)
(577,816)(578,820)(579,819)(580,818)(581,822)(582,821)(583,825)(584,824)
(585,823)(586,827)(587,826)(588,830)(589,829)(590,828)(591,832)(592,831)
(593,835)(594,834)(595,833)(596,837)(597,836)(598,840)(599,839)(600,838)
(601,842)(602,841)(603,845)(604,844)(605,843)(606,847)(607,846)(608,850)
(609,849)(610,848)(611,852)(612,851)(613,855)(614,854)(615,853)(616,857)
(617,856)(618,860)(619,859)(620,858)(621,862)(622,861)(623,865)(624,864)
(625,863)(626,867)(627,866)(628,870)(629,869)(630,868)(631,872)(632,871)
(633,875)(634,874)(635,873)(636,877)(637,876)(638,880)(639,879)(640,878)
(641,882)(642,881)(643,885)(644,884)(645,883)(646,887)(647,886)(648,890)
(649,889)(650,888)(651,892)(652,891)(653,895)(654,894)(655,893)(656,897)
(657,896)(658,900)(659,899)(660,898)(661,902)(662,901)(663,905)(664,904)
(665,903)(666,907)(667,906)(668,910)(669,909)(670,908)(671,912)(672,911)
(673,915)(674,914)(675,913)(676,917)(677,916)(678,920)(679,919)(680,918)
(681,922)(682,921)(683,925)(684,924)(685,923)(686,927)(687,926)(688,930)
(689,929)(690,928)(691,932)(692,931)(693,935)(694,934)(695,933)(696,937)
(697,936)(698,940)(699,939)(700,938)(701,942)(702,941)(703,945)(704,944)
(705,943)(706,947)(707,946)(708,950)(709,949)(710,948)(711,952)(712,951)
(713,955)(714,954)(715,953)(716,957)(717,956)(718,960)(719,959)(720,958);;
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*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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*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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 56)( 37, 57)( 38, 58)( 39, 59)( 40, 60)( 41, 51)( 42, 52)( 43, 53)
( 44, 54)( 45, 55)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)
( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)
( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)
( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)
(121,181)(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)
(129,194)(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)
(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)
(153,228)(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)
(161,231)(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)
(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)
(177,217)(178,218)(179,219)(180,220)(246,251)(247,252)(248,253)(249,254)
(250,255)(261,266)(262,267)(263,268)(264,269)(265,270)(271,286)(272,287)
(273,288)(274,289)(275,290)(276,296)(277,297)(278,298)(279,299)(280,300)
(281,291)(282,292)(283,293)(284,294)(285,295)(301,331)(302,332)(303,333)
(304,334)(305,335)(306,341)(307,342)(308,343)(309,344)(310,345)(311,336)
(312,337)(313,338)(314,339)(315,340)(316,346)(317,347)(318,348)(319,349)
(320,350)(321,356)(322,357)(323,358)(324,359)(325,360)(326,351)(327,352)
(328,353)(329,354)(330,355)(361,421)(362,422)(363,423)(364,424)(365,425)
(366,431)(367,432)(368,433)(369,434)(370,435)(371,426)(372,427)(373,428)
(374,429)(375,430)(376,436)(377,437)(378,438)(379,439)(380,440)(381,446)
(382,447)(383,448)(384,449)(385,450)(386,441)(387,442)(388,443)(389,444)
(390,445)(391,466)(392,467)(393,468)(394,469)(395,470)(396,476)(397,477)
(398,478)(399,479)(400,480)(401,471)(402,472)(403,473)(404,474)(405,475)
(406,451)(407,452)(408,453)(409,454)(410,455)(411,461)(412,462)(413,463)
(414,464)(415,465)(416,456)(417,457)(418,458)(419,459)(420,460)(481,601)
(482,602)(483,603)(484,604)(485,605)(486,611)(487,612)(488,613)(489,614)
(490,615)(491,606)(492,607)(493,608)(494,609)(495,610)(496,616)(497,617)
(498,618)(499,619)(500,620)(501,626)(502,627)(503,628)(504,629)(505,630)
(506,621)(507,622)(508,623)(509,624)(510,625)(511,646)(512,647)(513,648)
(514,649)(515,650)(516,656)(517,657)(518,658)(519,659)(520,660)(521,651)
(522,652)(523,653)(524,654)(525,655)(526,631)(527,632)(528,633)(529,634)
(530,635)(531,641)(532,642)(533,643)(534,644)(535,645)(536,636)(537,637)
(538,638)(539,639)(540,640)(541,691)(542,692)(543,693)(544,694)(545,695)
(546,701)(547,702)(548,703)(549,704)(550,705)(551,696)(552,697)(553,698)
(554,699)(555,700)(556,706)(557,707)(558,708)(559,709)(560,710)(561,716)
(562,717)(563,718)(564,719)(565,720)(566,711)(567,712)(568,713)(569,714)
(570,715)(571,661)(572,662)(573,663)(574,664)(575,665)(576,671)(577,672)
(578,673)(579,674)(580,675)(581,666)(582,667)(583,668)(584,669)(585,670)
(586,676)(587,677)(588,678)(589,679)(590,680)(591,686)(592,687)(593,688)
(594,689)(595,690)(596,681)(597,682)(598,683)(599,684)(600,685)(721,841)
(722,842)(723,843)(724,844)(725,845)(726,851)(727,852)(728,853)(729,854)
(730,855)(731,846)(732,847)(733,848)(734,849)(735,850)(736,856)(737,857)
(738,858)(739,859)(740,860)(741,866)(742,867)(743,868)(744,869)(745,870)
(746,861)(747,862)(748,863)(749,864)(750,865)(751,886)(752,887)(753,888)
(754,889)(755,890)(756,896)(757,897)(758,898)(759,899)(760,900)(761,891)
(762,892)(763,893)(764,894)(765,895)(766,871)(767,872)(768,873)(769,874)
(770,875)(771,881)(772,882)(773,883)(774,884)(775,885)(776,876)(777,877)
(778,878)(779,879)(780,880)(781,931)(782,932)(783,933)(784,934)(785,935)
(786,941)(787,942)(788,943)(789,944)(790,945)(791,936)(792,937)(793,938)
(794,939)(795,940)(796,946)(797,947)(798,948)(799,949)(800,950)(801,956)
(802,957)(803,958)(804,959)(805,960)(806,951)(807,952)(808,953)(809,954)
(810,955)(811,901)(812,902)(813,903)(814,904)(815,905)(816,911)(817,912)
(818,913)(819,914)(820,915)(821,906)(822,907)(823,908)(824,909)(825,910)
(826,916)(827,917)(828,918)(829,919)(830,920)(831,926)(832,927)(833,928)
(834,929)(835,930)(836,921)(837,922)(838,923)(839,924)(840,925);
s1 := Sym(960)!( 1,726)( 2,730)( 3,729)( 4,728)( 5,727)( 6,721)( 7,725)
( 8,724)( 9,723)( 10,722)( 11,731)( 12,735)( 13,734)( 14,733)( 15,732)
( 16,741)( 17,745)( 18,744)( 19,743)( 20,742)( 21,736)( 22,740)( 23,739)
( 24,738)( 25,737)( 26,746)( 27,750)( 28,749)( 29,748)( 30,747)( 31,771)
( 32,775)( 33,774)( 34,773)( 35,772)( 36,766)( 37,770)( 38,769)( 39,768)
( 40,767)( 41,776)( 42,780)( 43,779)( 44,778)( 45,777)( 46,756)( 47,760)
( 48,759)( 49,758)( 50,757)( 51,751)( 52,755)( 53,754)( 54,753)( 55,752)
( 56,761)( 57,765)( 58,764)( 59,763)( 60,762)( 61,816)( 62,820)( 63,819)
( 64,818)( 65,817)( 66,811)( 67,815)( 68,814)( 69,813)( 70,812)( 71,821)
( 72,825)( 73,824)( 74,823)( 75,822)( 76,831)( 77,835)( 78,834)( 79,833)
( 80,832)( 81,826)( 82,830)( 83,829)( 84,828)( 85,827)( 86,836)( 87,840)
( 88,839)( 89,838)( 90,837)( 91,786)( 92,790)( 93,789)( 94,788)( 95,787)
( 96,781)( 97,785)( 98,784)( 99,783)(100,782)(101,791)(102,795)(103,794)
(104,793)(105,792)(106,801)(107,805)(108,804)(109,803)(110,802)(111,796)
(112,800)(113,799)(114,798)(115,797)(116,806)(117,810)(118,809)(119,808)
(120,807)(121,906)(122,910)(123,909)(124,908)(125,907)(126,901)(127,905)
(128,904)(129,903)(130,902)(131,911)(132,915)(133,914)(134,913)(135,912)
(136,921)(137,925)(138,924)(139,923)(140,922)(141,916)(142,920)(143,919)
(144,918)(145,917)(146,926)(147,930)(148,929)(149,928)(150,927)(151,951)
(152,955)(153,954)(154,953)(155,952)(156,946)(157,950)(158,949)(159,948)
(160,947)(161,956)(162,960)(163,959)(164,958)(165,957)(166,936)(167,940)
(168,939)(169,938)(170,937)(171,931)(172,935)(173,934)(174,933)(175,932)
(176,941)(177,945)(178,944)(179,943)(180,942)(181,846)(182,850)(183,849)
(184,848)(185,847)(186,841)(187,845)(188,844)(189,843)(190,842)(191,851)
(192,855)(193,854)(194,853)(195,852)(196,861)(197,865)(198,864)(199,863)
(200,862)(201,856)(202,860)(203,859)(204,858)(205,857)(206,866)(207,870)
(208,869)(209,868)(210,867)(211,891)(212,895)(213,894)(214,893)(215,892)
(216,886)(217,890)(218,889)(219,888)(220,887)(221,896)(222,900)(223,899)
(224,898)(225,897)(226,876)(227,880)(228,879)(229,878)(230,877)(231,871)
(232,875)(233,874)(234,873)(235,872)(236,881)(237,885)(238,884)(239,883)
(240,882)(241,486)(242,490)(243,489)(244,488)(245,487)(246,481)(247,485)
(248,484)(249,483)(250,482)(251,491)(252,495)(253,494)(254,493)(255,492)
(256,501)(257,505)(258,504)(259,503)(260,502)(261,496)(262,500)(263,499)
(264,498)(265,497)(266,506)(267,510)(268,509)(269,508)(270,507)(271,531)
(272,535)(273,534)(274,533)(275,532)(276,526)(277,530)(278,529)(279,528)
(280,527)(281,536)(282,540)(283,539)(284,538)(285,537)(286,516)(287,520)
(288,519)(289,518)(290,517)(291,511)(292,515)(293,514)(294,513)(295,512)
(296,521)(297,525)(298,524)(299,523)(300,522)(301,576)(302,580)(303,579)
(304,578)(305,577)(306,571)(307,575)(308,574)(309,573)(310,572)(311,581)
(312,585)(313,584)(314,583)(315,582)(316,591)(317,595)(318,594)(319,593)
(320,592)(321,586)(322,590)(323,589)(324,588)(325,587)(326,596)(327,600)
(328,599)(329,598)(330,597)(331,546)(332,550)(333,549)(334,548)(335,547)
(336,541)(337,545)(338,544)(339,543)(340,542)(341,551)(342,555)(343,554)
(344,553)(345,552)(346,561)(347,565)(348,564)(349,563)(350,562)(351,556)
(352,560)(353,559)(354,558)(355,557)(356,566)(357,570)(358,569)(359,568)
(360,567)(361,666)(362,670)(363,669)(364,668)(365,667)(366,661)(367,665)
(368,664)(369,663)(370,662)(371,671)(372,675)(373,674)(374,673)(375,672)
(376,681)(377,685)(378,684)(379,683)(380,682)(381,676)(382,680)(383,679)
(384,678)(385,677)(386,686)(387,690)(388,689)(389,688)(390,687)(391,711)
(392,715)(393,714)(394,713)(395,712)(396,706)(397,710)(398,709)(399,708)
(400,707)(401,716)(402,720)(403,719)(404,718)(405,717)(406,696)(407,700)
(408,699)(409,698)(410,697)(411,691)(412,695)(413,694)(414,693)(415,692)
(416,701)(417,705)(418,704)(419,703)(420,702)(421,606)(422,610)(423,609)
(424,608)(425,607)(426,601)(427,605)(428,604)(429,603)(430,602)(431,611)
(432,615)(433,614)(434,613)(435,612)(436,621)(437,625)(438,624)(439,623)
(440,622)(441,616)(442,620)(443,619)(444,618)(445,617)(446,626)(447,630)
(448,629)(449,628)(450,627)(451,651)(452,655)(453,654)(454,653)(455,652)
(456,646)(457,650)(458,649)(459,648)(460,647)(461,656)(462,660)(463,659)
(464,658)(465,657)(466,636)(467,640)(468,639)(469,638)(470,637)(471,631)
(472,635)(473,634)(474,633)(475,632)(476,641)(477,645)(478,644)(479,643)
(480,642);
s2 := Sym(960)!( 1,242)( 2,241)( 3,245)( 4,244)( 5,243)( 6,247)( 7,246)
( 8,250)( 9,249)( 10,248)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)
( 16,257)( 17,256)( 18,260)( 19,259)( 20,258)( 21,262)( 22,261)( 23,265)
( 24,264)( 25,263)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,272)
( 32,271)( 33,275)( 34,274)( 35,273)( 36,277)( 37,276)( 38,280)( 39,279)
( 40,278)( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,287)( 47,286)
( 48,290)( 49,289)( 50,288)( 51,292)( 52,291)( 53,295)( 54,294)( 55,293)
( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,302)( 62,301)( 63,305)
( 64,304)( 65,303)( 66,307)( 67,306)( 68,310)( 69,309)( 70,308)( 71,312)
( 72,311)( 73,315)( 74,314)( 75,313)( 76,317)( 77,316)( 78,320)( 79,319)
( 80,318)( 81,322)( 82,321)( 83,325)( 84,324)( 85,323)( 86,327)( 87,326)
( 88,330)( 89,329)( 90,328)( 91,332)( 92,331)( 93,335)( 94,334)( 95,333)
( 96,337)( 97,336)( 98,340)( 99,339)(100,338)(101,342)(102,341)(103,345)
(104,344)(105,343)(106,347)(107,346)(108,350)(109,349)(110,348)(111,352)
(112,351)(113,355)(114,354)(115,353)(116,357)(117,356)(118,360)(119,359)
(120,358)(121,362)(122,361)(123,365)(124,364)(125,363)(126,367)(127,366)
(128,370)(129,369)(130,368)(131,372)(132,371)(133,375)(134,374)(135,373)
(136,377)(137,376)(138,380)(139,379)(140,378)(141,382)(142,381)(143,385)
(144,384)(145,383)(146,387)(147,386)(148,390)(149,389)(150,388)(151,392)
(152,391)(153,395)(154,394)(155,393)(156,397)(157,396)(158,400)(159,399)
(160,398)(161,402)(162,401)(163,405)(164,404)(165,403)(166,407)(167,406)
(168,410)(169,409)(170,408)(171,412)(172,411)(173,415)(174,414)(175,413)
(176,417)(177,416)(178,420)(179,419)(180,418)(181,422)(182,421)(183,425)
(184,424)(185,423)(186,427)(187,426)(188,430)(189,429)(190,428)(191,432)
(192,431)(193,435)(194,434)(195,433)(196,437)(197,436)(198,440)(199,439)
(200,438)(201,442)(202,441)(203,445)(204,444)(205,443)(206,447)(207,446)
(208,450)(209,449)(210,448)(211,452)(212,451)(213,455)(214,454)(215,453)
(216,457)(217,456)(218,460)(219,459)(220,458)(221,462)(222,461)(223,465)
(224,464)(225,463)(226,467)(227,466)(228,470)(229,469)(230,468)(231,472)
(232,471)(233,475)(234,474)(235,473)(236,477)(237,476)(238,480)(239,479)
(240,478)(481,722)(482,721)(483,725)(484,724)(485,723)(486,727)(487,726)
(488,730)(489,729)(490,728)(491,732)(492,731)(493,735)(494,734)(495,733)
(496,737)(497,736)(498,740)(499,739)(500,738)(501,742)(502,741)(503,745)
(504,744)(505,743)(506,747)(507,746)(508,750)(509,749)(510,748)(511,752)
(512,751)(513,755)(514,754)(515,753)(516,757)(517,756)(518,760)(519,759)
(520,758)(521,762)(522,761)(523,765)(524,764)(525,763)(526,767)(527,766)
(528,770)(529,769)(530,768)(531,772)(532,771)(533,775)(534,774)(535,773)
(536,777)(537,776)(538,780)(539,779)(540,778)(541,782)(542,781)(543,785)
(544,784)(545,783)(546,787)(547,786)(548,790)(549,789)(550,788)(551,792)
(552,791)(553,795)(554,794)(555,793)(556,797)(557,796)(558,800)(559,799)
(560,798)(561,802)(562,801)(563,805)(564,804)(565,803)(566,807)(567,806)
(568,810)(569,809)(570,808)(571,812)(572,811)(573,815)(574,814)(575,813)
(576,817)(577,816)(578,820)(579,819)(580,818)(581,822)(582,821)(583,825)
(584,824)(585,823)(586,827)(587,826)(588,830)(589,829)(590,828)(591,832)
(592,831)(593,835)(594,834)(595,833)(596,837)(597,836)(598,840)(599,839)
(600,838)(601,842)(602,841)(603,845)(604,844)(605,843)(606,847)(607,846)
(608,850)(609,849)(610,848)(611,852)(612,851)(613,855)(614,854)(615,853)
(616,857)(617,856)(618,860)(619,859)(620,858)(621,862)(622,861)(623,865)
(624,864)(625,863)(626,867)(627,866)(628,870)(629,869)(630,868)(631,872)
(632,871)(633,875)(634,874)(635,873)(636,877)(637,876)(638,880)(639,879)
(640,878)(641,882)(642,881)(643,885)(644,884)(645,883)(646,887)(647,886)
(648,890)(649,889)(650,888)(651,892)(652,891)(653,895)(654,894)(655,893)
(656,897)(657,896)(658,900)(659,899)(660,898)(661,902)(662,901)(663,905)
(664,904)(665,903)(666,907)(667,906)(668,910)(669,909)(670,908)(671,912)
(672,911)(673,915)(674,914)(675,913)(676,917)(677,916)(678,920)(679,919)
(680,918)(681,922)(682,921)(683,925)(684,924)(685,923)(686,927)(687,926)
(688,930)(689,929)(690,928)(691,932)(692,931)(693,935)(694,934)(695,933)
(696,937)(697,936)(698,940)(699,939)(700,938)(701,942)(702,941)(703,945)
(704,944)(705,943)(706,947)(707,946)(708,950)(709,949)(710,948)(711,952)
(712,951)(713,955)(714,954)(715,953)(716,957)(717,956)(718,960)(719,959)
(720,958);
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*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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*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*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*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 >;
References : None.
to this polytope