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Polytope of Type {4,240}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,240}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42010)
Rank : 3
Schlafli Type : {4,240}
Number of vertices, edges, etc : 4, 480, 240
Order of s0s1s2 : 240
Order of s0s1s2s1 : 4
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
   3-fold quotients : {4,80}*640b
   4-fold quotients : {4,60}*480a, {2,120}*480
   5-fold quotients : {4,48}*384b
   6-fold quotients : {4,40}*320a
   8-fold quotients : {2,60}*240, {4,30}*240a
   10-fold quotients : {4,24}*192a
   12-fold quotients : {4,20}*160, {2,40}*160
   15-fold quotients : {4,16}*128b
   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
   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)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)
(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)(144,369)
(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)(160,415)
(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)(192,447)
(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)(216,471)
(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(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)
(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)(608,863)
(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)(616,841)
(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)(624,849)
(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)(632,887)
(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)(640,895)
(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)(648,873)
(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)(656,881)
(657,882)(658,883)(659,884)(660,885)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)(672,927)
(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)(688,913)
(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)(696,951)
(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)(704,959)
(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)(712,937)
(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)(720,945);;
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)(721,916)(722,920)
(723,919)(724,918)(725,917)(726,926)(727,930)(728,929)(729,928)(730,927)
(731,921)(732,925)(733,924)(734,923)(735,922)(736,901)(737,905)(738,904)
(739,903)(740,902)(741,911)(742,915)(743,914)(744,913)(745,912)(746,906)
(747,910)(748,909)(749,908)(750,907)(751,931)(752,935)(753,934)(754,933)
(755,932)(756,941)(757,945)(758,944)(759,943)(760,942)(761,936)(762,940)
(763,939)(764,938)(765,937)(766,946)(767,950)(768,949)(769,948)(770,947)
(771,956)(772,960)(773,959)(774,958)(775,957)(776,951)(777,955)(778,954)
(779,953)(780,952)(781,856)(782,860)(783,859)(784,858)(785,857)(786,866)
(787,870)(788,869)(789,868)(790,867)(791,861)(792,865)(793,864)(794,863)
(795,862)(796,841)(797,845)(798,844)(799,843)(800,842)(801,851)(802,855)
(803,854)(804,853)(805,852)(806,846)(807,850)(808,849)(809,848)(810,847)
(811,871)(812,875)(813,874)(814,873)(815,872)(816,881)(817,885)(818,884)
(819,883)(820,882)(821,876)(822,880)(823,879)(824,878)(825,877)(826,886)
(827,890)(828,889)(829,888)(830,887)(831,896)(832,900)(833,899)(834,898)
(835,897)(836,891)(837,895)(838,894)(839,893)(840,892);;
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)( 61,562)( 62,561)( 63,565)( 64,564)
( 65,563)( 66,557)( 67,556)( 68,560)( 69,559)( 70,558)( 71,567)( 72,566)
( 73,570)( 74,569)( 75,568)( 76,547)( 77,546)( 78,550)( 79,549)( 80,548)
( 81,542)( 82,541)( 83,545)( 84,544)( 85,543)( 86,552)( 87,551)( 88,555)
( 89,554)( 90,553)( 91,577)( 92,576)( 93,580)( 94,579)( 95,578)( 96,572)
( 97,571)( 98,575)( 99,574)(100,573)(101,582)(102,581)(103,585)(104,584)
(105,583)(106,592)(107,591)(108,595)(109,594)(110,593)(111,587)(112,586)
(113,590)(114,589)(115,588)(116,597)(117,596)(118,600)(119,599)(120,598)
(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)(181,712)(182,711)(183,715)(184,714)
(185,713)(186,707)(187,706)(188,710)(189,709)(190,708)(191,717)(192,716)
(193,720)(194,719)(195,718)(196,697)(197,696)(198,700)(199,699)(200,698)
(201,692)(202,691)(203,695)(204,694)(205,693)(206,702)(207,701)(208,705)
(209,704)(210,703)(211,682)(212,681)(213,685)(214,684)(215,683)(216,677)
(217,676)(218,680)(219,679)(220,678)(221,687)(222,686)(223,690)(224,689)
(225,688)(226,667)(227,666)(228,670)(229,669)(230,668)(231,662)(232,661)
(233,665)(234,664)(235,663)(236,672)(237,671)(238,675)(239,674)(240,673)
(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)(301,802)(302,801)(303,805)(304,804)
(305,803)(306,797)(307,796)(308,800)(309,799)(310,798)(311,807)(312,806)
(313,810)(314,809)(315,808)(316,787)(317,786)(318,790)(319,789)(320,788)
(321,782)(322,781)(323,785)(324,784)(325,783)(326,792)(327,791)(328,795)
(329,794)(330,793)(331,817)(332,816)(333,820)(334,819)(335,818)(336,812)
(337,811)(338,815)(339,814)(340,813)(341,822)(342,821)(343,825)(344,824)
(345,823)(346,832)(347,831)(348,835)(349,834)(350,833)(351,827)(352,826)
(353,830)(354,829)(355,828)(356,837)(357,836)(358,840)(359,839)(360,838)
(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)(421,952)(422,951)(423,955)(424,954)
(425,953)(426,947)(427,946)(428,950)(429,949)(430,948)(431,957)(432,956)
(433,960)(434,959)(435,958)(436,937)(437,936)(438,940)(439,939)(440,938)
(441,932)(442,931)(443,935)(444,934)(445,933)(446,942)(447,941)(448,945)
(449,944)(450,943)(451,922)(452,921)(453,925)(454,924)(455,923)(456,917)
(457,916)(458,920)(459,919)(460,918)(461,927)(462,926)(463,930)(464,929)
(465,928)(466,907)(467,906)(468,910)(469,909)(470,908)(471,902)(472,901)
(473,905)(474,904)(475,903)(476,912)(477,911)(478,915)(479,914)(480,913);;
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, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
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)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)
(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)
(144,369)(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)
(160,415)(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)
(192,447)(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,471)(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)
(232,457)(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(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)(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)
(608,863)(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)
(616,841)(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)
(624,849)(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)
(632,887)(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)
(640,895)(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)
(648,873)(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)
(656,881)(657,882)(658,883)(659,884)(660,885)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)
(672,927)(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)
(688,913)(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,951)(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)
(704,959)(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)
(712,937)(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)
(720,945);
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)(721,916)
(722,920)(723,919)(724,918)(725,917)(726,926)(727,930)(728,929)(729,928)
(730,927)(731,921)(732,925)(733,924)(734,923)(735,922)(736,901)(737,905)
(738,904)(739,903)(740,902)(741,911)(742,915)(743,914)(744,913)(745,912)
(746,906)(747,910)(748,909)(749,908)(750,907)(751,931)(752,935)(753,934)
(754,933)(755,932)(756,941)(757,945)(758,944)(759,943)(760,942)(761,936)
(762,940)(763,939)(764,938)(765,937)(766,946)(767,950)(768,949)(769,948)
(770,947)(771,956)(772,960)(773,959)(774,958)(775,957)(776,951)(777,955)
(778,954)(779,953)(780,952)(781,856)(782,860)(783,859)(784,858)(785,857)
(786,866)(787,870)(788,869)(789,868)(790,867)(791,861)(792,865)(793,864)
(794,863)(795,862)(796,841)(797,845)(798,844)(799,843)(800,842)(801,851)
(802,855)(803,854)(804,853)(805,852)(806,846)(807,850)(808,849)(809,848)
(810,847)(811,871)(812,875)(813,874)(814,873)(815,872)(816,881)(817,885)
(818,884)(819,883)(820,882)(821,876)(822,880)(823,879)(824,878)(825,877)
(826,886)(827,890)(828,889)(829,888)(830,887)(831,896)(832,900)(833,899)
(834,898)(835,897)(836,891)(837,895)(838,894)(839,893)(840,892);
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)( 61,562)( 62,561)( 63,565)
( 64,564)( 65,563)( 66,557)( 67,556)( 68,560)( 69,559)( 70,558)( 71,567)
( 72,566)( 73,570)( 74,569)( 75,568)( 76,547)( 77,546)( 78,550)( 79,549)
( 80,548)( 81,542)( 82,541)( 83,545)( 84,544)( 85,543)( 86,552)( 87,551)
( 88,555)( 89,554)( 90,553)( 91,577)( 92,576)( 93,580)( 94,579)( 95,578)
( 96,572)( 97,571)( 98,575)( 99,574)(100,573)(101,582)(102,581)(103,585)
(104,584)(105,583)(106,592)(107,591)(108,595)(109,594)(110,593)(111,587)
(112,586)(113,590)(114,589)(115,588)(116,597)(117,596)(118,600)(119,599)
(120,598)(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)(181,712)(182,711)(183,715)
(184,714)(185,713)(186,707)(187,706)(188,710)(189,709)(190,708)(191,717)
(192,716)(193,720)(194,719)(195,718)(196,697)(197,696)(198,700)(199,699)
(200,698)(201,692)(202,691)(203,695)(204,694)(205,693)(206,702)(207,701)
(208,705)(209,704)(210,703)(211,682)(212,681)(213,685)(214,684)(215,683)
(216,677)(217,676)(218,680)(219,679)(220,678)(221,687)(222,686)(223,690)
(224,689)(225,688)(226,667)(227,666)(228,670)(229,669)(230,668)(231,662)
(232,661)(233,665)(234,664)(235,663)(236,672)(237,671)(238,675)(239,674)
(240,673)(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)(301,802)(302,801)(303,805)
(304,804)(305,803)(306,797)(307,796)(308,800)(309,799)(310,798)(311,807)
(312,806)(313,810)(314,809)(315,808)(316,787)(317,786)(318,790)(319,789)
(320,788)(321,782)(322,781)(323,785)(324,784)(325,783)(326,792)(327,791)
(328,795)(329,794)(330,793)(331,817)(332,816)(333,820)(334,819)(335,818)
(336,812)(337,811)(338,815)(339,814)(340,813)(341,822)(342,821)(343,825)
(344,824)(345,823)(346,832)(347,831)(348,835)(349,834)(350,833)(351,827)
(352,826)(353,830)(354,829)(355,828)(356,837)(357,836)(358,840)(359,839)
(360,838)(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)(421,952)(422,951)(423,955)
(424,954)(425,953)(426,947)(427,946)(428,950)(429,949)(430,948)(431,957)
(432,956)(433,960)(434,959)(435,958)(436,937)(437,936)(438,940)(439,939)
(440,938)(441,932)(442,931)(443,935)(444,934)(445,933)(446,942)(447,941)
(448,945)(449,944)(450,943)(451,922)(452,921)(453,925)(454,924)(455,923)
(456,917)(457,916)(458,920)(459,919)(460,918)(461,927)(462,926)(463,930)
(464,929)(465,928)(466,907)(467,906)(468,910)(469,909)(470,908)(471,902)
(472,901)(473,905)(474,904)(475,903)(476,912)(477,911)(478,915)(479,914)
(480,913);
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, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >; 
 
References : None.
to this polytope