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Polytope of Type {48,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,20}*1920a
Also Known As : {48,20|2}. if this polytope has another name.
Group : SmallGroup(1920,41749)
Rank : 3
Schlafli Type : {48,20}
Number of vertices, edges, etc : 48, 480, 20
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 : {48,10}*960, {24,20}*960a
   3-fold quotients : {16,20}*640a
   4-fold quotients : {24,10}*480, {12,20}*480
   5-fold quotients : {48,4}*384a
   6-fold quotients : {8,20}*320a, {16,10}*320
   8-fold quotients : {12,10}*240, {6,20}*240a
   10-fold quotients : {24,4}*192a, {48,2}*192
   12-fold quotients : {4,20}*160, {8,10}*160
   15-fold quotients : {16,4}*128a
   16-fold quotients : {6,10}*120
   20-fold quotients : {12,4}*96a, {24,2}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {8,4}*64a, {16,2}*64
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32, {8,2}*32
   80-fold quotients : {6,2}*24
   96-fold quotients : {2,5}*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 := (  1,721)(  2,722)(  3,723)(  4,724)(  5,725)(  6,731)(  7,732)(  8,733)
(  9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)( 16,736)
( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)( 24,749)
( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,766)( 32,767)
( 33,768)( 34,769)( 35,770)( 36,776)( 37,777)( 38,778)( 39,779)( 40,780)
( 41,771)( 42,772)( 43,773)( 44,774)( 45,775)( 46,751)( 47,752)( 48,753)
( 49,754)( 50,755)( 51,761)( 52,762)( 53,763)( 54,764)( 55,765)( 56,756)
( 57,757)( 58,758)( 59,759)( 60,760)( 61,781)( 62,782)( 63,783)( 64,784)
( 65,785)( 66,791)( 67,792)( 68,793)( 69,794)( 70,795)( 71,786)( 72,787)
( 73,788)( 74,789)( 75,790)( 76,796)( 77,797)( 78,798)( 79,799)( 80,800)
( 81,806)( 82,807)( 83,808)( 84,809)( 85,810)( 86,801)( 87,802)( 88,803)
( 89,804)( 90,805)( 91,826)( 92,827)( 93,828)( 94,829)( 95,830)( 96,836)
( 97,837)( 98,838)( 99,839)(100,840)(101,831)(102,832)(103,833)(104,834)
(105,835)(106,811)(107,812)(108,813)(109,814)(110,815)(111,821)(112,822)
(113,823)(114,824)(115,825)(116,816)(117,817)(118,818)(119,819)(120,820)
(121,871)(122,872)(123,873)(124,874)(125,875)(126,881)(127,882)(128,883)
(129,884)(130,885)(131,876)(132,877)(133,878)(134,879)(135,880)(136,886)
(137,887)(138,888)(139,889)(140,890)(141,896)(142,897)(143,898)(144,899)
(145,900)(146,891)(147,892)(148,893)(149,894)(150,895)(151,841)(152,842)
(153,843)(154,844)(155,845)(156,851)(157,852)(158,853)(159,854)(160,855)
(161,846)(162,847)(163,848)(164,849)(165,850)(166,856)(167,857)(168,858)
(169,859)(170,860)(171,866)(172,867)(173,868)(174,869)(175,870)(176,861)
(177,862)(178,863)(179,864)(180,865)(181,931)(182,932)(183,933)(184,934)
(185,935)(186,941)(187,942)(188,943)(189,944)(190,945)(191,936)(192,937)
(193,938)(194,939)(195,940)(196,946)(197,947)(198,948)(199,949)(200,950)
(201,956)(202,957)(203,958)(204,959)(205,960)(206,951)(207,952)(208,953)
(209,954)(210,955)(211,901)(212,902)(213,903)(214,904)(215,905)(216,911)
(217,912)(218,913)(219,914)(220,915)(221,906)(222,907)(223,908)(224,909)
(225,910)(226,916)(227,917)(228,918)(229,919)(230,920)(231,926)(232,927)
(233,928)(234,929)(235,930)(236,921)(237,922)(238,923)(239,924)(240,925)
(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)(248,493)
(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)(256,496)
(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)(264,509)
(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,526)(272,527)
(273,528)(274,529)(275,530)(276,536)(277,537)(278,538)(279,539)(280,540)
(281,531)(282,532)(283,533)(284,534)(285,535)(286,511)(287,512)(288,513)
(289,514)(290,515)(291,521)(292,522)(293,523)(294,524)(295,525)(296,516)
(297,517)(298,518)(299,519)(300,520)(301,541)(302,542)(303,543)(304,544)
(305,545)(306,551)(307,552)(308,553)(309,554)(310,555)(311,546)(312,547)
(313,548)(314,549)(315,550)(316,556)(317,557)(318,558)(319,559)(320,560)
(321,566)(322,567)(323,568)(324,569)(325,570)(326,561)(327,562)(328,563)
(329,564)(330,565)(331,586)(332,587)(333,588)(334,589)(335,590)(336,596)
(337,597)(338,598)(339,599)(340,600)(341,591)(342,592)(343,593)(344,594)
(345,595)(346,571)(347,572)(348,573)(349,574)(350,575)(351,581)(352,582)
(353,583)(354,584)(355,585)(356,576)(357,577)(358,578)(359,579)(360,580)
(361,631)(362,632)(363,633)(364,634)(365,635)(366,641)(367,642)(368,643)
(369,644)(370,645)(371,636)(372,637)(373,638)(374,639)(375,640)(376,646)
(377,647)(378,648)(379,649)(380,650)(381,656)(382,657)(383,658)(384,659)
(385,660)(386,651)(387,652)(388,653)(389,654)(390,655)(391,601)(392,602)
(393,603)(394,604)(395,605)(396,611)(397,612)(398,613)(399,614)(400,615)
(401,606)(402,607)(403,608)(404,609)(405,610)(406,616)(407,617)(408,618)
(409,619)(410,620)(411,626)(412,627)(413,628)(414,629)(415,630)(416,621)
(417,622)(418,623)(419,624)(420,625)(421,691)(422,692)(423,693)(424,694)
(425,695)(426,701)(427,702)(428,703)(429,704)(430,705)(431,696)(432,697)
(433,698)(434,699)(435,700)(436,706)(437,707)(438,708)(439,709)(440,710)
(441,716)(442,717)(443,718)(444,719)(445,720)(446,711)(447,712)(448,713)
(449,714)(450,715)(451,661)(452,662)(453,663)(454,664)(455,665)(456,671)
(457,672)(458,673)(459,674)(460,675)(461,666)(462,667)(463,668)(464,669)
(465,670)(466,676)(467,677)(468,678)(469,679)(470,680)(471,686)(472,687)
(473,688)(474,689)(475,690)(476,681)(477,682)(478,683)(479,684)(480,685);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)( 32, 55)
( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)
( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)( 63, 69)
( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)
( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)
(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)(134,163)
(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)
(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)(150,177)
(181,216)(182,220)(183,219)(184,218)(185,217)(186,211)(187,215)(188,214)
(189,213)(190,212)(191,221)(192,225)(193,224)(194,223)(195,222)(196,231)
(197,235)(198,234)(199,233)(200,232)(201,226)(202,230)(203,229)(204,228)
(205,227)(206,236)(207,240)(208,239)(209,238)(210,237)(241,306)(242,310)
(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)
(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)(258,324)
(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)(266,326)
(267,330)(268,329)(269,328)(270,327)(271,351)(272,355)(273,354)(274,353)
(275,352)(276,346)(277,350)(278,349)(279,348)(280,347)(281,356)(282,360)
(283,359)(284,358)(285,357)(286,336)(287,340)(288,339)(289,338)(290,337)
(291,331)(292,335)(293,334)(294,333)(295,332)(296,341)(297,345)(298,344)
(299,343)(300,342)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)
(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)(374,463)
(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)(382,470)
(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)(390,477)
(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)(398,424)
(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)(406,441)
(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)(414,438)
(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)(482,610)
(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)(490,602)
(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)(498,624)
(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)(506,626)
(507,630)(508,629)(509,628)(510,627)(511,651)(512,655)(513,654)(514,653)
(515,652)(516,646)(517,650)(518,649)(519,648)(520,647)(521,656)(522,660)
(523,659)(524,658)(525,657)(526,636)(527,640)(528,639)(529,638)(530,637)
(531,631)(532,635)(533,634)(534,633)(535,632)(536,641)(537,645)(538,644)
(539,643)(540,642)(541,666)(542,670)(543,669)(544,668)(545,667)(546,661)
(547,665)(548,664)(549,663)(550,662)(551,671)(552,675)(553,674)(554,673)
(555,672)(556,681)(557,685)(558,684)(559,683)(560,682)(561,676)(562,680)
(563,679)(564,678)(565,677)(566,686)(567,690)(568,689)(569,688)(570,687)
(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)(578,709)
(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)(586,696)
(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)(594,693)
(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,906)(722,910)
(723,909)(724,908)(725,907)(726,901)(727,905)(728,904)(729,903)(730,902)
(731,911)(732,915)(733,914)(734,913)(735,912)(736,921)(737,925)(738,924)
(739,923)(740,922)(741,916)(742,920)(743,919)(744,918)(745,917)(746,926)
(747,930)(748,929)(749,928)(750,927)(751,951)(752,955)(753,954)(754,953)
(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)(762,960)
(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)(770,937)
(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)(778,944)
(779,943)(780,942)(781,846)(782,850)(783,849)(784,848)(785,847)(786,841)
(787,845)(788,844)(789,843)(790,842)(791,851)(792,855)(793,854)(794,853)
(795,852)(796,861)(797,865)(798,864)(799,863)(800,862)(801,856)(802,860)
(803,859)(804,858)(805,857)(806,866)(807,870)(808,869)(809,868)(810,867)
(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)(818,889)
(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)(826,876)
(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)(834,873)
(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,721)(  2,722)(  3,723)(  4,724)(  5,725)(  6,731)(  7,732)
(  8,733)(  9,734)( 10,735)( 11,726)( 12,727)( 13,728)( 14,729)( 15,730)
( 16,736)( 17,737)( 18,738)( 19,739)( 20,740)( 21,746)( 22,747)( 23,748)
( 24,749)( 25,750)( 26,741)( 27,742)( 28,743)( 29,744)( 30,745)( 31,766)
( 32,767)( 33,768)( 34,769)( 35,770)( 36,776)( 37,777)( 38,778)( 39,779)
( 40,780)( 41,771)( 42,772)( 43,773)( 44,774)( 45,775)( 46,751)( 47,752)
( 48,753)( 49,754)( 50,755)( 51,761)( 52,762)( 53,763)( 54,764)( 55,765)
( 56,756)( 57,757)( 58,758)( 59,759)( 60,760)( 61,781)( 62,782)( 63,783)
( 64,784)( 65,785)( 66,791)( 67,792)( 68,793)( 69,794)( 70,795)( 71,786)
( 72,787)( 73,788)( 74,789)( 75,790)( 76,796)( 77,797)( 78,798)( 79,799)
( 80,800)( 81,806)( 82,807)( 83,808)( 84,809)( 85,810)( 86,801)( 87,802)
( 88,803)( 89,804)( 90,805)( 91,826)( 92,827)( 93,828)( 94,829)( 95,830)
( 96,836)( 97,837)( 98,838)( 99,839)(100,840)(101,831)(102,832)(103,833)
(104,834)(105,835)(106,811)(107,812)(108,813)(109,814)(110,815)(111,821)
(112,822)(113,823)(114,824)(115,825)(116,816)(117,817)(118,818)(119,819)
(120,820)(121,871)(122,872)(123,873)(124,874)(125,875)(126,881)(127,882)
(128,883)(129,884)(130,885)(131,876)(132,877)(133,878)(134,879)(135,880)
(136,886)(137,887)(138,888)(139,889)(140,890)(141,896)(142,897)(143,898)
(144,899)(145,900)(146,891)(147,892)(148,893)(149,894)(150,895)(151,841)
(152,842)(153,843)(154,844)(155,845)(156,851)(157,852)(158,853)(159,854)
(160,855)(161,846)(162,847)(163,848)(164,849)(165,850)(166,856)(167,857)
(168,858)(169,859)(170,860)(171,866)(172,867)(173,868)(174,869)(175,870)
(176,861)(177,862)(178,863)(179,864)(180,865)(181,931)(182,932)(183,933)
(184,934)(185,935)(186,941)(187,942)(188,943)(189,944)(190,945)(191,936)
(192,937)(193,938)(194,939)(195,940)(196,946)(197,947)(198,948)(199,949)
(200,950)(201,956)(202,957)(203,958)(204,959)(205,960)(206,951)(207,952)
(208,953)(209,954)(210,955)(211,901)(212,902)(213,903)(214,904)(215,905)
(216,911)(217,912)(218,913)(219,914)(220,915)(221,906)(222,907)(223,908)
(224,909)(225,910)(226,916)(227,917)(228,918)(229,919)(230,920)(231,926)
(232,927)(233,928)(234,929)(235,930)(236,921)(237,922)(238,923)(239,924)
(240,925)(241,481)(242,482)(243,483)(244,484)(245,485)(246,491)(247,492)
(248,493)(249,494)(250,495)(251,486)(252,487)(253,488)(254,489)(255,490)
(256,496)(257,497)(258,498)(259,499)(260,500)(261,506)(262,507)(263,508)
(264,509)(265,510)(266,501)(267,502)(268,503)(269,504)(270,505)(271,526)
(272,527)(273,528)(274,529)(275,530)(276,536)(277,537)(278,538)(279,539)
(280,540)(281,531)(282,532)(283,533)(284,534)(285,535)(286,511)(287,512)
(288,513)(289,514)(290,515)(291,521)(292,522)(293,523)(294,524)(295,525)
(296,516)(297,517)(298,518)(299,519)(300,520)(301,541)(302,542)(303,543)
(304,544)(305,545)(306,551)(307,552)(308,553)(309,554)(310,555)(311,546)
(312,547)(313,548)(314,549)(315,550)(316,556)(317,557)(318,558)(319,559)
(320,560)(321,566)(322,567)(323,568)(324,569)(325,570)(326,561)(327,562)
(328,563)(329,564)(330,565)(331,586)(332,587)(333,588)(334,589)(335,590)
(336,596)(337,597)(338,598)(339,599)(340,600)(341,591)(342,592)(343,593)
(344,594)(345,595)(346,571)(347,572)(348,573)(349,574)(350,575)(351,581)
(352,582)(353,583)(354,584)(355,585)(356,576)(357,577)(358,578)(359,579)
(360,580)(361,631)(362,632)(363,633)(364,634)(365,635)(366,641)(367,642)
(368,643)(369,644)(370,645)(371,636)(372,637)(373,638)(374,639)(375,640)
(376,646)(377,647)(378,648)(379,649)(380,650)(381,656)(382,657)(383,658)
(384,659)(385,660)(386,651)(387,652)(388,653)(389,654)(390,655)(391,601)
(392,602)(393,603)(394,604)(395,605)(396,611)(397,612)(398,613)(399,614)
(400,615)(401,606)(402,607)(403,608)(404,609)(405,610)(406,616)(407,617)
(408,618)(409,619)(410,620)(411,626)(412,627)(413,628)(414,629)(415,630)
(416,621)(417,622)(418,623)(419,624)(420,625)(421,691)(422,692)(423,693)
(424,694)(425,695)(426,701)(427,702)(428,703)(429,704)(430,705)(431,696)
(432,697)(433,698)(434,699)(435,700)(436,706)(437,707)(438,708)(439,709)
(440,710)(441,716)(442,717)(443,718)(444,719)(445,720)(446,711)(447,712)
(448,713)(449,714)(450,715)(451,661)(452,662)(453,663)(454,664)(455,665)
(456,671)(457,672)(458,673)(459,674)(460,675)(461,666)(462,667)(463,668)
(464,669)(465,670)(466,676)(467,677)(468,678)(469,679)(470,680)(471,686)
(472,687)(473,688)(474,689)(475,690)(476,681)(477,682)(478,683)(479,684)
(480,685);
s1 := Sym(960)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 12, 15)( 13, 14)
( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)
( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)
( 40, 47)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 66)( 62, 70)
( 63, 69)( 64, 68)( 65, 67)( 72, 75)( 73, 74)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 87, 90)( 88, 89)( 91,111)( 92,115)( 93,114)( 94,113)
( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)
(103,119)(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)
(126,151)(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)
(134,163)(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)
(142,170)(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)
(150,177)(181,216)(182,220)(183,219)(184,218)(185,217)(186,211)(187,215)
(188,214)(189,213)(190,212)(191,221)(192,225)(193,224)(194,223)(195,222)
(196,231)(197,235)(198,234)(199,233)(200,232)(201,226)(202,230)(203,229)
(204,228)(205,227)(206,236)(207,240)(208,239)(209,238)(210,237)(241,306)
(242,310)(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)
(250,302)(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)
(258,324)(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)
(266,326)(267,330)(268,329)(269,328)(270,327)(271,351)(272,355)(273,354)
(274,353)(275,352)(276,346)(277,350)(278,349)(279,348)(280,347)(281,356)
(282,360)(283,359)(284,358)(285,357)(286,336)(287,340)(288,339)(289,338)
(290,337)(291,331)(292,335)(293,334)(294,333)(295,332)(296,341)(297,345)
(298,344)(299,343)(300,342)(361,456)(362,460)(363,459)(364,458)(365,457)
(366,451)(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)
(374,463)(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)
(382,470)(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)
(390,477)(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)
(398,424)(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)
(406,441)(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)
(414,438)(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)
(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)
(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)
(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)
(506,626)(507,630)(508,629)(509,628)(510,627)(511,651)(512,655)(513,654)
(514,653)(515,652)(516,646)(517,650)(518,649)(519,648)(520,647)(521,656)
(522,660)(523,659)(524,658)(525,657)(526,636)(527,640)(528,639)(529,638)
(530,637)(531,631)(532,635)(533,634)(534,633)(535,632)(536,641)(537,645)
(538,644)(539,643)(540,642)(541,666)(542,670)(543,669)(544,668)(545,667)
(546,661)(547,665)(548,664)(549,663)(550,662)(551,671)(552,675)(553,674)
(554,673)(555,672)(556,681)(557,685)(558,684)(559,683)(560,682)(561,676)
(562,680)(563,679)(564,678)(565,677)(566,686)(567,690)(568,689)(569,688)
(570,687)(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)
(578,709)(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)
(586,696)(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)
(594,693)(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,906)
(722,910)(723,909)(724,908)(725,907)(726,901)(727,905)(728,904)(729,903)
(730,902)(731,911)(732,915)(733,914)(734,913)(735,912)(736,921)(737,925)
(738,924)(739,923)(740,922)(741,916)(742,920)(743,919)(744,918)(745,917)
(746,926)(747,930)(748,929)(749,928)(750,927)(751,951)(752,955)(753,954)
(754,953)(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)
(762,960)(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)
(770,937)(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)
(778,944)(779,943)(780,942)(781,846)(782,850)(783,849)(784,848)(785,847)
(786,841)(787,845)(788,844)(789,843)(790,842)(791,851)(792,855)(793,854)
(794,853)(795,852)(796,861)(797,865)(798,864)(799,863)(800,862)(801,856)
(802,860)(803,859)(804,858)(805,857)(806,866)(807,870)(808,869)(809,868)
(810,867)(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)
(818,889)(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)
(826,876)(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)
(834,873)(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);
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*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 >; 
 
References : None.
to this polytope