Polytope of Type {4,240}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,240}*1920a
Also Known As : {4,240|2}. if this polytope has another name.
Group : SmallGroup(1920,41728)
Rank : 3
Schlafli Type : {4,240}
Number of vertices, edges, etc : 4, 480, 240
Order of s0s1s2 : 240
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 : {4,120}*960a, {2,240}*960
   3-fold quotients : {4,80}*640a
   4-fold quotients : {4,60}*480a, {2,120}*480
   5-fold quotients : {4,48}*384a
   6-fold quotients : {4,40}*320a, {2,80}*320
   8-fold quotients : {2,60}*240, {4,30}*240a
   10-fold quotients : {4,24}*192a, {2,48}*192
   12-fold quotients : {4,20}*160, {2,40}*160
   15-fold quotients : {4,16}*128a
   16-fold quotients : {2,30}*120
   20-fold quotients : {4,12}*96a, {2,24}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {4,8}*64a, {2,16}*64
   32-fold quotients : {2,15}*60
   40-fold quotients : {2,12}*48, {4,6}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32, {2,8}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   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 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
s1 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)
( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)
( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)
(104,113)(105,112)(121,151)(122,155)(123,154)(124,153)(125,152)(126,161)
(127,165)(128,164)(129,163)(130,162)(131,156)(132,160)(133,159)(134,158)
(135,157)(136,166)(137,170)(138,169)(139,168)(140,167)(141,176)(142,180)
(143,179)(144,178)(145,177)(146,171)(147,175)(148,174)(149,173)(150,172)
(181,211)(182,215)(183,214)(184,213)(185,212)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)(196,226)
(197,230)(198,229)(199,228)(200,227)(201,236)(202,240)(203,239)(204,238)
(205,237)(206,231)(207,235)(208,234)(209,233)(210,232)(241,301)(242,305)
(243,304)(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)(250,312)
(251,306)(252,310)(253,309)(254,308)(255,307)(256,316)(257,320)(258,319)
(259,318)(260,317)(261,326)(262,330)(263,329)(264,328)(265,327)(266,321)
(267,325)(268,324)(269,323)(270,322)(271,346)(272,350)(273,349)(274,348)
(275,347)(276,356)(277,360)(278,359)(279,358)(280,357)(281,351)(282,355)
(283,354)(284,353)(285,352)(286,331)(287,335)(288,334)(289,333)(290,332)
(291,341)(292,345)(293,344)(294,343)(295,342)(296,336)(297,340)(298,339)
(299,338)(300,337)(361,451)(362,455)(363,454)(364,453)(365,452)(366,461)
(367,465)(368,464)(369,463)(370,462)(371,456)(372,460)(373,459)(374,458)
(375,457)(376,466)(377,470)(378,469)(379,468)(380,467)(381,476)(382,480)
(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)(390,472)
(391,421)(392,425)(393,424)(394,423)(395,422)(396,431)(397,435)(398,434)
(399,433)(400,432)(401,426)(402,430)(403,429)(404,428)(405,427)(406,436)
(407,440)(408,439)(409,438)(410,437)(411,446)(412,450)(413,449)(414,448)
(415,447)(416,441)(417,445)(418,444)(419,443)(420,442)(481,601)(482,605)
(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)(490,612)
(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)(498,619)
(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)(506,621)
(507,625)(508,624)(509,623)(510,622)(511,646)(512,650)(513,649)(514,648)
(515,647)(516,656)(517,660)(518,659)(519,658)(520,657)(521,651)(522,655)
(523,654)(524,653)(525,652)(526,631)(527,635)(528,634)(529,633)(530,632)
(531,641)(532,645)(533,644)(534,643)(535,642)(536,636)(537,640)(538,639)
(539,638)(540,637)(541,661)(542,665)(543,664)(544,663)(545,662)(546,671)
(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)(553,669)(554,668)
(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)(561,686)(562,690)
(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)(569,683)(570,682)
(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)
(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)
(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)
(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,901)(722,905)
(723,904)(724,903)(725,902)(726,911)(727,915)(728,914)(729,913)(730,912)
(731,906)(732,910)(733,909)(734,908)(735,907)(736,916)(737,920)(738,919)
(739,918)(740,917)(741,926)(742,930)(743,929)(744,928)(745,927)(746,921)
(747,925)(748,924)(749,923)(750,922)(751,946)(752,950)(753,949)(754,948)
(755,947)(756,956)(757,960)(758,959)(759,958)(760,957)(761,951)(762,955)
(763,954)(764,953)(765,952)(766,931)(767,935)(768,934)(769,933)(770,932)
(771,941)(772,945)(773,944)(774,943)(775,942)(776,936)(777,940)(778,939)
(779,938)(780,937)(781,841)(782,845)(783,844)(784,843)(785,842)(786,851)
(787,855)(788,854)(789,853)(790,852)(791,846)(792,850)(793,849)(794,848)
(795,847)(796,856)(797,860)(798,859)(799,858)(800,857)(801,866)(802,870)
(803,869)(804,868)(805,867)(806,861)(807,865)(808,864)(809,863)(810,862)
(811,886)(812,890)(813,889)(814,888)(815,887)(816,896)(817,900)(818,899)
(819,898)(820,897)(821,891)(822,895)(823,894)(824,893)(825,892)(826,871)
(827,875)(828,874)(829,873)(830,872)(831,881)(832,885)(833,884)(834,883)
(835,882)(836,876)(837,880)(838,879)(839,878)(840,877);;
s2 := (  1,487)(  2,486)(  3,490)(  4,489)(  5,488)(  6,482)(  7,481)(  8,485)
(  9,484)( 10,483)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)( 16,502)
( 17,501)( 18,505)( 19,504)( 20,503)( 21,497)( 22,496)( 23,500)( 24,499)
( 25,498)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,532)( 32,531)
( 33,535)( 34,534)( 35,533)( 36,527)( 37,526)( 38,530)( 39,529)( 40,528)
( 41,537)( 42,536)( 43,540)( 44,539)( 45,538)( 46,517)( 47,516)( 48,520)
( 49,519)( 50,518)( 51,512)( 52,511)( 53,515)( 54,514)( 55,513)( 56,522)
( 57,521)( 58,525)( 59,524)( 60,523)( 61,547)( 62,546)( 63,550)( 64,549)
( 65,548)( 66,542)( 67,541)( 68,545)( 69,544)( 70,543)( 71,552)( 72,551)
( 73,555)( 74,554)( 75,553)( 76,562)( 77,561)( 78,565)( 79,564)( 80,563)
( 81,557)( 82,556)( 83,560)( 84,559)( 85,558)( 86,567)( 87,566)( 88,570)
( 89,569)( 90,568)( 91,592)( 92,591)( 93,595)( 94,594)( 95,593)( 96,587)
( 97,586)( 98,590)( 99,589)(100,588)(101,597)(102,596)(103,600)(104,599)
(105,598)(106,577)(107,576)(108,580)(109,579)(110,578)(111,572)(112,571)
(113,575)(114,574)(115,573)(116,582)(117,581)(118,585)(119,584)(120,583)
(121,637)(122,636)(123,640)(124,639)(125,638)(126,632)(127,631)(128,635)
(129,634)(130,633)(131,642)(132,641)(133,645)(134,644)(135,643)(136,652)
(137,651)(138,655)(139,654)(140,653)(141,647)(142,646)(143,650)(144,649)
(145,648)(146,657)(147,656)(148,660)(149,659)(150,658)(151,607)(152,606)
(153,610)(154,609)(155,608)(156,602)(157,601)(158,605)(159,604)(160,603)
(161,612)(162,611)(163,615)(164,614)(165,613)(166,622)(167,621)(168,625)
(169,624)(170,623)(171,617)(172,616)(173,620)(174,619)(175,618)(176,627)
(177,626)(178,630)(179,629)(180,628)(181,697)(182,696)(183,700)(184,699)
(185,698)(186,692)(187,691)(188,695)(189,694)(190,693)(191,702)(192,701)
(193,705)(194,704)(195,703)(196,712)(197,711)(198,715)(199,714)(200,713)
(201,707)(202,706)(203,710)(204,709)(205,708)(206,717)(207,716)(208,720)
(209,719)(210,718)(211,667)(212,666)(213,670)(214,669)(215,668)(216,662)
(217,661)(218,665)(219,664)(220,663)(221,672)(222,671)(223,675)(224,674)
(225,673)(226,682)(227,681)(228,685)(229,684)(230,683)(231,677)(232,676)
(233,680)(234,679)(235,678)(236,687)(237,686)(238,690)(239,689)(240,688)
(241,727)(242,726)(243,730)(244,729)(245,728)(246,722)(247,721)(248,725)
(249,724)(250,723)(251,732)(252,731)(253,735)(254,734)(255,733)(256,742)
(257,741)(258,745)(259,744)(260,743)(261,737)(262,736)(263,740)(264,739)
(265,738)(266,747)(267,746)(268,750)(269,749)(270,748)(271,772)(272,771)
(273,775)(274,774)(275,773)(276,767)(277,766)(278,770)(279,769)(280,768)
(281,777)(282,776)(283,780)(284,779)(285,778)(286,757)(287,756)(288,760)
(289,759)(290,758)(291,752)(292,751)(293,755)(294,754)(295,753)(296,762)
(297,761)(298,765)(299,764)(300,763)(301,787)(302,786)(303,790)(304,789)
(305,788)(306,782)(307,781)(308,785)(309,784)(310,783)(311,792)(312,791)
(313,795)(314,794)(315,793)(316,802)(317,801)(318,805)(319,804)(320,803)
(321,797)(322,796)(323,800)(324,799)(325,798)(326,807)(327,806)(328,810)
(329,809)(330,808)(331,832)(332,831)(333,835)(334,834)(335,833)(336,827)
(337,826)(338,830)(339,829)(340,828)(341,837)(342,836)(343,840)(344,839)
(345,838)(346,817)(347,816)(348,820)(349,819)(350,818)(351,812)(352,811)
(353,815)(354,814)(355,813)(356,822)(357,821)(358,825)(359,824)(360,823)
(361,877)(362,876)(363,880)(364,879)(365,878)(366,872)(367,871)(368,875)
(369,874)(370,873)(371,882)(372,881)(373,885)(374,884)(375,883)(376,892)
(377,891)(378,895)(379,894)(380,893)(381,887)(382,886)(383,890)(384,889)
(385,888)(386,897)(387,896)(388,900)(389,899)(390,898)(391,847)(392,846)
(393,850)(394,849)(395,848)(396,842)(397,841)(398,845)(399,844)(400,843)
(401,852)(402,851)(403,855)(404,854)(405,853)(406,862)(407,861)(408,865)
(409,864)(410,863)(411,857)(412,856)(413,860)(414,859)(415,858)(416,867)
(417,866)(418,870)(419,869)(420,868)(421,937)(422,936)(423,940)(424,939)
(425,938)(426,932)(427,931)(428,935)(429,934)(430,933)(431,942)(432,941)
(433,945)(434,944)(435,943)(436,952)(437,951)(438,955)(439,954)(440,953)
(441,947)(442,946)(443,950)(444,949)(445,948)(446,957)(447,956)(448,960)
(449,959)(450,958)(451,907)(452,906)(453,910)(454,909)(455,908)(456,902)
(457,901)(458,905)(459,904)(460,903)(461,912)(462,911)(463,915)(464,914)
(465,913)(466,922)(467,921)(468,925)(469,924)(470,923)(471,917)(472,916)
(473,920)(474,919)(475,918)(476,927)(477,926)(478,930)(479,929)(480,928);;
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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*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*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*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)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
s1 := Sym(960)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)
( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)
( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)
( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)
( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)
(103,114)(104,113)(105,112)(121,151)(122,155)(123,154)(124,153)(125,152)
(126,161)(127,165)(128,164)(129,163)(130,162)(131,156)(132,160)(133,159)
(134,158)(135,157)(136,166)(137,170)(138,169)(139,168)(140,167)(141,176)
(142,180)(143,179)(144,178)(145,177)(146,171)(147,175)(148,174)(149,173)
(150,172)(181,211)(182,215)(183,214)(184,213)(185,212)(186,221)(187,225)
(188,224)(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)
(196,226)(197,230)(198,229)(199,228)(200,227)(201,236)(202,240)(203,239)
(204,238)(205,237)(206,231)(207,235)(208,234)(209,233)(210,232)(241,301)
(242,305)(243,304)(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)
(250,312)(251,306)(252,310)(253,309)(254,308)(255,307)(256,316)(257,320)
(258,319)(259,318)(260,317)(261,326)(262,330)(263,329)(264,328)(265,327)
(266,321)(267,325)(268,324)(269,323)(270,322)(271,346)(272,350)(273,349)
(274,348)(275,347)(276,356)(277,360)(278,359)(279,358)(280,357)(281,351)
(282,355)(283,354)(284,353)(285,352)(286,331)(287,335)(288,334)(289,333)
(290,332)(291,341)(292,345)(293,344)(294,343)(295,342)(296,336)(297,340)
(298,339)(299,338)(300,337)(361,451)(362,455)(363,454)(364,453)(365,452)
(366,461)(367,465)(368,464)(369,463)(370,462)(371,456)(372,460)(373,459)
(374,458)(375,457)(376,466)(377,470)(378,469)(379,468)(380,467)(381,476)
(382,480)(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)
(390,472)(391,421)(392,425)(393,424)(394,423)(395,422)(396,431)(397,435)
(398,434)(399,433)(400,432)(401,426)(402,430)(403,429)(404,428)(405,427)
(406,436)(407,440)(408,439)(409,438)(410,437)(411,446)(412,450)(413,449)
(414,448)(415,447)(416,441)(417,445)(418,444)(419,443)(420,442)(481,601)
(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)
(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)
(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)
(506,621)(507,625)(508,624)(509,623)(510,622)(511,646)(512,650)(513,649)
(514,648)(515,647)(516,656)(517,660)(518,659)(519,658)(520,657)(521,651)
(522,655)(523,654)(524,653)(525,652)(526,631)(527,635)(528,634)(529,633)
(530,632)(531,641)(532,645)(533,644)(534,643)(535,642)(536,636)(537,640)
(538,639)(539,638)(540,637)(541,661)(542,665)(543,664)(544,663)(545,662)
(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)(553,669)
(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)(561,686)
(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)(569,683)
(570,682)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)
(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)
(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)
(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,901)
(722,905)(723,904)(724,903)(725,902)(726,911)(727,915)(728,914)(729,913)
(730,912)(731,906)(732,910)(733,909)(734,908)(735,907)(736,916)(737,920)
(738,919)(739,918)(740,917)(741,926)(742,930)(743,929)(744,928)(745,927)
(746,921)(747,925)(748,924)(749,923)(750,922)(751,946)(752,950)(753,949)
(754,948)(755,947)(756,956)(757,960)(758,959)(759,958)(760,957)(761,951)
(762,955)(763,954)(764,953)(765,952)(766,931)(767,935)(768,934)(769,933)
(770,932)(771,941)(772,945)(773,944)(774,943)(775,942)(776,936)(777,940)
(778,939)(779,938)(780,937)(781,841)(782,845)(783,844)(784,843)(785,842)
(786,851)(787,855)(788,854)(789,853)(790,852)(791,846)(792,850)(793,849)
(794,848)(795,847)(796,856)(797,860)(798,859)(799,858)(800,857)(801,866)
(802,870)(803,869)(804,868)(805,867)(806,861)(807,865)(808,864)(809,863)
(810,862)(811,886)(812,890)(813,889)(814,888)(815,887)(816,896)(817,900)
(818,899)(819,898)(820,897)(821,891)(822,895)(823,894)(824,893)(825,892)
(826,871)(827,875)(828,874)(829,873)(830,872)(831,881)(832,885)(833,884)
(834,883)(835,882)(836,876)(837,880)(838,879)(839,878)(840,877);
s2 := Sym(960)!(  1,487)(  2,486)(  3,490)(  4,489)(  5,488)(  6,482)(  7,481)
(  8,485)(  9,484)( 10,483)( 11,492)( 12,491)( 13,495)( 14,494)( 15,493)
( 16,502)( 17,501)( 18,505)( 19,504)( 20,503)( 21,497)( 22,496)( 23,500)
( 24,499)( 25,498)( 26,507)( 27,506)( 28,510)( 29,509)( 30,508)( 31,532)
( 32,531)( 33,535)( 34,534)( 35,533)( 36,527)( 37,526)( 38,530)( 39,529)
( 40,528)( 41,537)( 42,536)( 43,540)( 44,539)( 45,538)( 46,517)( 47,516)
( 48,520)( 49,519)( 50,518)( 51,512)( 52,511)( 53,515)( 54,514)( 55,513)
( 56,522)( 57,521)( 58,525)( 59,524)( 60,523)( 61,547)( 62,546)( 63,550)
( 64,549)( 65,548)( 66,542)( 67,541)( 68,545)( 69,544)( 70,543)( 71,552)
( 72,551)( 73,555)( 74,554)( 75,553)( 76,562)( 77,561)( 78,565)( 79,564)
( 80,563)( 81,557)( 82,556)( 83,560)( 84,559)( 85,558)( 86,567)( 87,566)
( 88,570)( 89,569)( 90,568)( 91,592)( 92,591)( 93,595)( 94,594)( 95,593)
( 96,587)( 97,586)( 98,590)( 99,589)(100,588)(101,597)(102,596)(103,600)
(104,599)(105,598)(106,577)(107,576)(108,580)(109,579)(110,578)(111,572)
(112,571)(113,575)(114,574)(115,573)(116,582)(117,581)(118,585)(119,584)
(120,583)(121,637)(122,636)(123,640)(124,639)(125,638)(126,632)(127,631)
(128,635)(129,634)(130,633)(131,642)(132,641)(133,645)(134,644)(135,643)
(136,652)(137,651)(138,655)(139,654)(140,653)(141,647)(142,646)(143,650)
(144,649)(145,648)(146,657)(147,656)(148,660)(149,659)(150,658)(151,607)
(152,606)(153,610)(154,609)(155,608)(156,602)(157,601)(158,605)(159,604)
(160,603)(161,612)(162,611)(163,615)(164,614)(165,613)(166,622)(167,621)
(168,625)(169,624)(170,623)(171,617)(172,616)(173,620)(174,619)(175,618)
(176,627)(177,626)(178,630)(179,629)(180,628)(181,697)(182,696)(183,700)
(184,699)(185,698)(186,692)(187,691)(188,695)(189,694)(190,693)(191,702)
(192,701)(193,705)(194,704)(195,703)(196,712)(197,711)(198,715)(199,714)
(200,713)(201,707)(202,706)(203,710)(204,709)(205,708)(206,717)(207,716)
(208,720)(209,719)(210,718)(211,667)(212,666)(213,670)(214,669)(215,668)
(216,662)(217,661)(218,665)(219,664)(220,663)(221,672)(222,671)(223,675)
(224,674)(225,673)(226,682)(227,681)(228,685)(229,684)(230,683)(231,677)
(232,676)(233,680)(234,679)(235,678)(236,687)(237,686)(238,690)(239,689)
(240,688)(241,727)(242,726)(243,730)(244,729)(245,728)(246,722)(247,721)
(248,725)(249,724)(250,723)(251,732)(252,731)(253,735)(254,734)(255,733)
(256,742)(257,741)(258,745)(259,744)(260,743)(261,737)(262,736)(263,740)
(264,739)(265,738)(266,747)(267,746)(268,750)(269,749)(270,748)(271,772)
(272,771)(273,775)(274,774)(275,773)(276,767)(277,766)(278,770)(279,769)
(280,768)(281,777)(282,776)(283,780)(284,779)(285,778)(286,757)(287,756)
(288,760)(289,759)(290,758)(291,752)(292,751)(293,755)(294,754)(295,753)
(296,762)(297,761)(298,765)(299,764)(300,763)(301,787)(302,786)(303,790)
(304,789)(305,788)(306,782)(307,781)(308,785)(309,784)(310,783)(311,792)
(312,791)(313,795)(314,794)(315,793)(316,802)(317,801)(318,805)(319,804)
(320,803)(321,797)(322,796)(323,800)(324,799)(325,798)(326,807)(327,806)
(328,810)(329,809)(330,808)(331,832)(332,831)(333,835)(334,834)(335,833)
(336,827)(337,826)(338,830)(339,829)(340,828)(341,837)(342,836)(343,840)
(344,839)(345,838)(346,817)(347,816)(348,820)(349,819)(350,818)(351,812)
(352,811)(353,815)(354,814)(355,813)(356,822)(357,821)(358,825)(359,824)
(360,823)(361,877)(362,876)(363,880)(364,879)(365,878)(366,872)(367,871)
(368,875)(369,874)(370,873)(371,882)(372,881)(373,885)(374,884)(375,883)
(376,892)(377,891)(378,895)(379,894)(380,893)(381,887)(382,886)(383,890)
(384,889)(385,888)(386,897)(387,896)(388,900)(389,899)(390,898)(391,847)
(392,846)(393,850)(394,849)(395,848)(396,842)(397,841)(398,845)(399,844)
(400,843)(401,852)(402,851)(403,855)(404,854)(405,853)(406,862)(407,861)
(408,865)(409,864)(410,863)(411,857)(412,856)(413,860)(414,859)(415,858)
(416,867)(417,866)(418,870)(419,869)(420,868)(421,937)(422,936)(423,940)
(424,939)(425,938)(426,932)(427,931)(428,935)(429,934)(430,933)(431,942)
(432,941)(433,945)(434,944)(435,943)(436,952)(437,951)(438,955)(439,954)
(440,953)(441,947)(442,946)(443,950)(444,949)(445,948)(446,957)(447,956)
(448,960)(449,959)(450,958)(451,907)(452,906)(453,910)(454,909)(455,908)
(456,902)(457,901)(458,905)(459,904)(460,903)(461,912)(462,911)(463,915)
(464,914)(465,913)(466,922)(467,921)(468,925)(469,924)(470,923)(471,917)
(472,916)(473,920)(474,919)(475,918)(476,927)(477,926)(478,930)(479,929)
(480,928);
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*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*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*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*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