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Polytope of Type {240,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {240,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42010)
Rank : 3
Schlafli Type : {240,4}
Number of vertices, edges, etc : 240, 480, 4
Order of s0s1s2 : 240
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {120,4}*960a
   3-fold quotients : {80,4}*640b
   4-fold quotients : {60,4}*480a, {120,2}*480
   5-fold quotients : {48,4}*384b
   6-fold quotients : {40,4}*320a
   8-fold quotients : {60,2}*240, {30,4}*240a
   10-fold quotients : {24,4}*192a
   12-fold quotients : {20,4}*160, {40,2}*160
   15-fold quotients : {16,4}*128b
   16-fold quotients : {30,2}*120
   20-fold quotients : {12,4}*96a, {24,2}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {8,4}*64a
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32, {8,2}*32
   80-fold quotients : {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {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 := (  1,481)(  2,485)(  3,484)(  4,483)(  5,482)(  6,491)(  7,495)(  8,494)
(  9,493)( 10,492)( 11,486)( 12,490)( 13,489)( 14,488)( 15,487)( 16,496)
( 17,500)( 18,499)( 19,498)( 20,497)( 21,506)( 22,510)( 23,509)( 24,508)
( 25,507)( 26,501)( 27,505)( 28,504)( 29,503)( 30,502)( 31,526)( 32,530)
( 33,529)( 34,528)( 35,527)( 36,536)( 37,540)( 38,539)( 39,538)( 40,537)
( 41,531)( 42,535)( 43,534)( 44,533)( 45,532)( 46,511)( 47,515)( 48,514)
( 49,513)( 50,512)( 51,521)( 52,525)( 53,524)( 54,523)( 55,522)( 56,516)
( 57,520)( 58,519)( 59,518)( 60,517)( 61,556)( 62,560)( 63,559)( 64,558)
( 65,557)( 66,566)( 67,570)( 68,569)( 69,568)( 70,567)( 71,561)( 72,565)
( 73,564)( 74,563)( 75,562)( 76,541)( 77,545)( 78,544)( 79,543)( 80,542)
( 81,551)( 82,555)( 83,554)( 84,553)( 85,552)( 86,546)( 87,550)( 88,549)
( 89,548)( 90,547)( 91,571)( 92,575)( 93,574)( 94,573)( 95,572)( 96,581)
( 97,585)( 98,584)( 99,583)(100,582)(101,576)(102,580)(103,579)(104,578)
(105,577)(106,586)(107,590)(108,589)(109,588)(110,587)(111,596)(112,600)
(113,599)(114,598)(115,597)(116,591)(117,595)(118,594)(119,593)(120,592)
(121,631)(122,635)(123,634)(124,633)(125,632)(126,641)(127,645)(128,644)
(129,643)(130,642)(131,636)(132,640)(133,639)(134,638)(135,637)(136,646)
(137,650)(138,649)(139,648)(140,647)(141,656)(142,660)(143,659)(144,658)
(145,657)(146,651)(147,655)(148,654)(149,653)(150,652)(151,601)(152,605)
(153,604)(154,603)(155,602)(156,611)(157,615)(158,614)(159,613)(160,612)
(161,606)(162,610)(163,609)(164,608)(165,607)(166,616)(167,620)(168,619)
(169,618)(170,617)(171,626)(172,630)(173,629)(174,628)(175,627)(176,621)
(177,625)(178,624)(179,623)(180,622)(181,706)(182,710)(183,709)(184,708)
(185,707)(186,716)(187,720)(188,719)(189,718)(190,717)(191,711)(192,715)
(193,714)(194,713)(195,712)(196,691)(197,695)(198,694)(199,693)(200,692)
(201,701)(202,705)(203,704)(204,703)(205,702)(206,696)(207,700)(208,699)
(209,698)(210,697)(211,676)(212,680)(213,679)(214,678)(215,677)(216,686)
(217,690)(218,689)(219,688)(220,687)(221,681)(222,685)(223,684)(224,683)
(225,682)(226,661)(227,665)(228,664)(229,663)(230,662)(231,671)(232,675)
(233,674)(234,673)(235,672)(236,666)(237,670)(238,669)(239,668)(240,667)
(241,721)(242,725)(243,724)(244,723)(245,722)(246,731)(247,735)(248,734)
(249,733)(250,732)(251,726)(252,730)(253,729)(254,728)(255,727)(256,736)
(257,740)(258,739)(259,738)(260,737)(261,746)(262,750)(263,749)(264,748)
(265,747)(266,741)(267,745)(268,744)(269,743)(270,742)(271,766)(272,770)
(273,769)(274,768)(275,767)(276,776)(277,780)(278,779)(279,778)(280,777)
(281,771)(282,775)(283,774)(284,773)(285,772)(286,751)(287,755)(288,754)
(289,753)(290,752)(291,761)(292,765)(293,764)(294,763)(295,762)(296,756)
(297,760)(298,759)(299,758)(300,757)(301,796)(302,800)(303,799)(304,798)
(305,797)(306,806)(307,810)(308,809)(309,808)(310,807)(311,801)(312,805)
(313,804)(314,803)(315,802)(316,781)(317,785)(318,784)(319,783)(320,782)
(321,791)(322,795)(323,794)(324,793)(325,792)(326,786)(327,790)(328,789)
(329,788)(330,787)(331,811)(332,815)(333,814)(334,813)(335,812)(336,821)
(337,825)(338,824)(339,823)(340,822)(341,816)(342,820)(343,819)(344,818)
(345,817)(346,826)(347,830)(348,829)(349,828)(350,827)(351,836)(352,840)
(353,839)(354,838)(355,837)(356,831)(357,835)(358,834)(359,833)(360,832)
(361,871)(362,875)(363,874)(364,873)(365,872)(366,881)(367,885)(368,884)
(369,883)(370,882)(371,876)(372,880)(373,879)(374,878)(375,877)(376,886)
(377,890)(378,889)(379,888)(380,887)(381,896)(382,900)(383,899)(384,898)
(385,897)(386,891)(387,895)(388,894)(389,893)(390,892)(391,841)(392,845)
(393,844)(394,843)(395,842)(396,851)(397,855)(398,854)(399,853)(400,852)
(401,846)(402,850)(403,849)(404,848)(405,847)(406,856)(407,860)(408,859)
(409,858)(410,857)(411,866)(412,870)(413,869)(414,868)(415,867)(416,861)
(417,865)(418,864)(419,863)(420,862)(421,946)(422,950)(423,949)(424,948)
(425,947)(426,956)(427,960)(428,959)(429,958)(430,957)(431,951)(432,955)
(433,954)(434,953)(435,952)(436,931)(437,935)(438,934)(439,933)(440,932)
(441,941)(442,945)(443,944)(444,943)(445,942)(446,936)(447,940)(448,939)
(449,938)(450,937)(451,916)(452,920)(453,919)(454,918)(455,917)(456,926)
(457,930)(458,929)(459,928)(460,927)(461,921)(462,925)(463,924)(464,923)
(465,922)(466,901)(467,905)(468,904)(469,903)(470,902)(471,911)(472,915)
(473,914)(474,913)(475,912)(476,906)(477,910)(478,909)(479,908)(480,907);;
s1 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)
( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)
(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)
(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)
(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)(142,166)
(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)(150,178)
(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)(188,215)
(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)(196,232)
(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)(204,229)
(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)(242,306)
(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)
(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)(258,325)
(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)(266,327)
(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)(274,354)
(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)(282,356)
(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)(290,338)
(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)(298,345)
(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)(366,452)
(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)(374,464)
(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)(382,466)
(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)(390,478)
(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)(398,425)
(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)(406,442)
(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)(414,439)
(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)(482,606)
(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)
(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)
(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)
(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)(514,654)
(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)(522,656)
(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)(530,638)
(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)(538,645)
(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)
(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)
(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)
(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)
(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)(578,710)
(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)(586,697)
(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)(594,694)
(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,922)(722,921)
(723,925)(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)
(731,927)(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)
(739,909)(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)
(747,911)(748,915)(749,914)(750,913)(751,937)(752,936)(753,940)(754,939)
(755,938)(756,932)(757,931)(758,935)(759,934)(760,933)(761,942)(762,941)
(763,945)(764,944)(765,943)(766,952)(767,951)(768,955)(769,954)(770,953)
(771,947)(772,946)(773,950)(774,949)(775,948)(776,957)(777,956)(778,960)
(779,959)(780,958)(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)
(787,856)(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)
(795,868)(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)
(803,845)(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)
(811,877)(812,876)(813,880)(814,879)(815,878)(816,872)(817,871)(818,875)
(819,874)(820,873)(821,882)(822,881)(823,885)(824,884)(825,883)(826,892)
(827,891)(828,895)(829,894)(830,893)(831,887)(832,886)(833,890)(834,889)
(835,888)(836,897)(837,896)(838,900)(839,899)(840,898);;
s2 := (  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);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s2*s1*s0*s1*s0*s2*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)!(  1,481)(  2,485)(  3,484)(  4,483)(  5,482)(  6,491)(  7,495)
(  8,494)(  9,493)( 10,492)( 11,486)( 12,490)( 13,489)( 14,488)( 15,487)
( 16,496)( 17,500)( 18,499)( 19,498)( 20,497)( 21,506)( 22,510)( 23,509)
( 24,508)( 25,507)( 26,501)( 27,505)( 28,504)( 29,503)( 30,502)( 31,526)
( 32,530)( 33,529)( 34,528)( 35,527)( 36,536)( 37,540)( 38,539)( 39,538)
( 40,537)( 41,531)( 42,535)( 43,534)( 44,533)( 45,532)( 46,511)( 47,515)
( 48,514)( 49,513)( 50,512)( 51,521)( 52,525)( 53,524)( 54,523)( 55,522)
( 56,516)( 57,520)( 58,519)( 59,518)( 60,517)( 61,556)( 62,560)( 63,559)
( 64,558)( 65,557)( 66,566)( 67,570)( 68,569)( 69,568)( 70,567)( 71,561)
( 72,565)( 73,564)( 74,563)( 75,562)( 76,541)( 77,545)( 78,544)( 79,543)
( 80,542)( 81,551)( 82,555)( 83,554)( 84,553)( 85,552)( 86,546)( 87,550)
( 88,549)( 89,548)( 90,547)( 91,571)( 92,575)( 93,574)( 94,573)( 95,572)
( 96,581)( 97,585)( 98,584)( 99,583)(100,582)(101,576)(102,580)(103,579)
(104,578)(105,577)(106,586)(107,590)(108,589)(109,588)(110,587)(111,596)
(112,600)(113,599)(114,598)(115,597)(116,591)(117,595)(118,594)(119,593)
(120,592)(121,631)(122,635)(123,634)(124,633)(125,632)(126,641)(127,645)
(128,644)(129,643)(130,642)(131,636)(132,640)(133,639)(134,638)(135,637)
(136,646)(137,650)(138,649)(139,648)(140,647)(141,656)(142,660)(143,659)
(144,658)(145,657)(146,651)(147,655)(148,654)(149,653)(150,652)(151,601)
(152,605)(153,604)(154,603)(155,602)(156,611)(157,615)(158,614)(159,613)
(160,612)(161,606)(162,610)(163,609)(164,608)(165,607)(166,616)(167,620)
(168,619)(169,618)(170,617)(171,626)(172,630)(173,629)(174,628)(175,627)
(176,621)(177,625)(178,624)(179,623)(180,622)(181,706)(182,710)(183,709)
(184,708)(185,707)(186,716)(187,720)(188,719)(189,718)(190,717)(191,711)
(192,715)(193,714)(194,713)(195,712)(196,691)(197,695)(198,694)(199,693)
(200,692)(201,701)(202,705)(203,704)(204,703)(205,702)(206,696)(207,700)
(208,699)(209,698)(210,697)(211,676)(212,680)(213,679)(214,678)(215,677)
(216,686)(217,690)(218,689)(219,688)(220,687)(221,681)(222,685)(223,684)
(224,683)(225,682)(226,661)(227,665)(228,664)(229,663)(230,662)(231,671)
(232,675)(233,674)(234,673)(235,672)(236,666)(237,670)(238,669)(239,668)
(240,667)(241,721)(242,725)(243,724)(244,723)(245,722)(246,731)(247,735)
(248,734)(249,733)(250,732)(251,726)(252,730)(253,729)(254,728)(255,727)
(256,736)(257,740)(258,739)(259,738)(260,737)(261,746)(262,750)(263,749)
(264,748)(265,747)(266,741)(267,745)(268,744)(269,743)(270,742)(271,766)
(272,770)(273,769)(274,768)(275,767)(276,776)(277,780)(278,779)(279,778)
(280,777)(281,771)(282,775)(283,774)(284,773)(285,772)(286,751)(287,755)
(288,754)(289,753)(290,752)(291,761)(292,765)(293,764)(294,763)(295,762)
(296,756)(297,760)(298,759)(299,758)(300,757)(301,796)(302,800)(303,799)
(304,798)(305,797)(306,806)(307,810)(308,809)(309,808)(310,807)(311,801)
(312,805)(313,804)(314,803)(315,802)(316,781)(317,785)(318,784)(319,783)
(320,782)(321,791)(322,795)(323,794)(324,793)(325,792)(326,786)(327,790)
(328,789)(329,788)(330,787)(331,811)(332,815)(333,814)(334,813)(335,812)
(336,821)(337,825)(338,824)(339,823)(340,822)(341,816)(342,820)(343,819)
(344,818)(345,817)(346,826)(347,830)(348,829)(349,828)(350,827)(351,836)
(352,840)(353,839)(354,838)(355,837)(356,831)(357,835)(358,834)(359,833)
(360,832)(361,871)(362,875)(363,874)(364,873)(365,872)(366,881)(367,885)
(368,884)(369,883)(370,882)(371,876)(372,880)(373,879)(374,878)(375,877)
(376,886)(377,890)(378,889)(379,888)(380,887)(381,896)(382,900)(383,899)
(384,898)(385,897)(386,891)(387,895)(388,894)(389,893)(390,892)(391,841)
(392,845)(393,844)(394,843)(395,842)(396,851)(397,855)(398,854)(399,853)
(400,852)(401,846)(402,850)(403,849)(404,848)(405,847)(406,856)(407,860)
(408,859)(409,858)(410,857)(411,866)(412,870)(413,869)(414,868)(415,867)
(416,861)(417,865)(418,864)(419,863)(420,862)(421,946)(422,950)(423,949)
(424,948)(425,947)(426,956)(427,960)(428,959)(429,958)(430,957)(431,951)
(432,955)(433,954)(434,953)(435,952)(436,931)(437,935)(438,934)(439,933)
(440,932)(441,941)(442,945)(443,944)(444,943)(445,942)(446,936)(447,940)
(448,939)(449,938)(450,937)(451,916)(452,920)(453,919)(454,918)(455,917)
(456,926)(457,930)(458,929)(459,928)(460,927)(461,921)(462,925)(463,924)
(464,923)(465,922)(466,901)(467,905)(468,904)(469,903)(470,902)(471,911)
(472,915)(473,914)(474,913)(475,912)(476,906)(477,910)(478,909)(479,908)
(480,907);
s1 := Sym(960)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)
( 63, 70)( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)
( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)
(103,120)(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)
(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)
(134,164)(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)
(142,166)(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)
(150,178)(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)
(188,215)(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)
(196,232)(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)
(204,229)(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)
(242,306)(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)
(250,303)(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)
(258,325)(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)
(266,327)(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)
(274,354)(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)
(282,356)(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)
(290,338)(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)
(298,345)(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)
(366,452)(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)
(374,464)(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)
(382,466)(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)
(390,478)(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)
(398,425)(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)
(406,442)(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)
(414,439)(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)
(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)
(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)
(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)
(506,627)(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)
(514,654)(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)
(522,656)(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)
(530,638)(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)
(538,645)(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)
(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)
(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)
(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)
(570,688)(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)
(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)
(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)
(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,922)
(722,921)(723,925)(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)
(730,918)(731,927)(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)
(738,910)(739,909)(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)
(746,912)(747,911)(748,915)(749,914)(750,913)(751,937)(752,936)(753,940)
(754,939)(755,938)(756,932)(757,931)(758,935)(759,934)(760,933)(761,942)
(762,941)(763,945)(764,944)(765,943)(766,952)(767,951)(768,955)(769,954)
(770,953)(771,947)(772,946)(773,950)(774,949)(775,948)(776,957)(777,956)
(778,960)(779,959)(780,958)(781,862)(782,861)(783,865)(784,864)(785,863)
(786,857)(787,856)(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)
(794,869)(795,868)(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)
(802,841)(803,845)(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)
(810,853)(811,877)(812,876)(813,880)(814,879)(815,878)(816,872)(817,871)
(818,875)(819,874)(820,873)(821,882)(822,881)(823,885)(824,884)(825,883)
(826,892)(827,891)(828,895)(829,894)(830,893)(831,887)(832,886)(833,890)
(834,889)(835,888)(836,897)(837,896)(838,900)(839,899)(840,898);
s2 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*s2*s1*s0*s1*s0*s2*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