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Polytope of Type {24,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,40}*1920d
if this polytope has a name.
Group : SmallGroup(1920,16595)
Rank : 3
Schlafli Type : {24,40}
Number of vertices, edges, etc : 24, 480, 40
Order of s0s1s2 : 120
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 : {24,20}*960b, {12,40}*960b
   3-fold quotients : {8,40}*640c
   4-fold quotients : {12,20}*480
   5-fold quotients : {24,8}*384c
   6-fold quotients : {4,40}*320b, {8,20}*320b
   8-fold quotients : {12,10}*240, {6,20}*240a
   10-fold quotients : {24,4}*192b, {12,8}*192b
   12-fold quotients : {4,20}*160
   15-fold quotients : {8,8}*128d
   16-fold quotients : {6,10}*120
   20-fold quotients : {12,4}*96a
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {4,8}*64b, {8,4}*64b
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*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 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,251)(  7,252)(  8,253)
(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,346)( 62,347)( 63,348)( 64,349)
( 65,350)( 66,356)( 67,357)( 68,358)( 69,359)( 70,360)( 71,351)( 72,352)
( 73,353)( 74,354)( 75,355)( 76,331)( 77,332)( 78,333)( 79,334)( 80,335)
( 81,341)( 82,342)( 83,343)( 84,344)( 85,345)( 86,336)( 87,337)( 88,338)
( 89,339)( 90,340)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)( 96,326)
( 97,327)( 98,328)( 99,329)(100,330)(101,321)(102,322)(103,323)(104,324)
(105,325)(106,301)(107,302)(108,303)(109,304)(110,305)(111,311)(112,312)
(113,313)(114,314)(115,315)(116,306)(117,307)(118,308)(119,309)(120,310)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,386)(127,387)(128,388)
(129,389)(130,390)(131,381)(132,382)(133,383)(134,384)(135,385)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,371)(142,372)(143,373)(144,374)
(145,375)(146,366)(147,367)(148,368)(149,369)(150,370)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,416)(157,417)(158,418)(159,419)(160,420)
(161,411)(162,412)(163,413)(164,414)(165,415)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,401)(172,402)(173,403)(174,404)(175,405)(176,396)
(177,397)(178,398)(179,399)(180,400)(181,451)(182,452)(183,453)(184,454)
(185,455)(186,461)(187,462)(188,463)(189,464)(190,465)(191,456)(192,457)
(193,458)(194,459)(195,460)(196,466)(197,467)(198,468)(199,469)(200,470)
(201,476)(202,477)(203,478)(204,479)(205,480)(206,471)(207,472)(208,473)
(209,474)(210,475)(211,421)(212,422)(213,423)(214,424)(215,425)(216,431)
(217,432)(218,433)(219,434)(220,435)(221,426)(222,427)(223,428)(224,429)
(225,430)(226,436)(227,437)(228,438)(229,439)(230,440)(231,446)(232,447)
(233,448)(234,449)(235,450)(236,441)(237,442)(238,443)(239,444)(240,445)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,826)(542,827)(543,828)(544,829)
(545,830)(546,836)(547,837)(548,838)(549,839)(550,840)(551,831)(552,832)
(553,833)(554,834)(555,835)(556,811)(557,812)(558,813)(559,814)(560,815)
(561,821)(562,822)(563,823)(564,824)(565,825)(566,816)(567,817)(568,818)
(569,819)(570,820)(571,796)(572,797)(573,798)(574,799)(575,800)(576,806)
(577,807)(578,808)(579,809)(580,810)(581,801)(582,802)(583,803)(584,804)
(585,805)(586,781)(587,782)(588,783)(589,784)(590,785)(591,791)(592,792)
(593,793)(594,794)(595,795)(596,786)(597,787)(598,788)(599,789)(600,790)
(601,856)(602,857)(603,858)(604,859)(605,860)(606,866)(607,867)(608,868)
(609,869)(610,870)(611,861)(612,862)(613,863)(614,864)(615,865)(616,841)
(617,842)(618,843)(619,844)(620,845)(621,851)(622,852)(623,853)(624,854)
(625,855)(626,846)(627,847)(628,848)(629,849)(630,850)(631,886)(632,887)
(633,888)(634,889)(635,890)(636,896)(637,897)(638,898)(639,899)(640,900)
(641,891)(642,892)(643,893)(644,894)(645,895)(646,871)(647,872)(648,873)
(649,874)(650,875)(651,881)(652,882)(653,883)(654,884)(655,885)(656,876)
(657,877)(658,878)(659,879)(660,880)(661,931)(662,932)(663,933)(664,934)
(665,935)(666,941)(667,942)(668,943)(669,944)(670,945)(671,936)(672,937)
(673,938)(674,939)(675,940)(676,946)(677,947)(678,948)(679,949)(680,950)
(681,956)(682,957)(683,958)(684,959)(685,960)(686,951)(687,952)(688,953)
(689,954)(690,955)(691,901)(692,902)(693,903)(694,904)(695,905)(696,911)
(697,912)(698,913)(699,914)(700,915)(701,906)(702,907)(703,908)(704,909)
(705,910)(706,916)(707,917)(708,918)(709,919)(710,920)(711,926)(712,927)
(713,928)(714,929)(715,930)(716,921)(717,922)(718,923)(719,924)(720,925);;
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, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61,111)( 62,115)( 63,114)( 64,113)
( 65,112)( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,116)( 72,120)
( 73,119)( 74,118)( 75,117)( 76, 96)( 77,100)( 78, 99)( 79, 98)( 80, 97)
( 81, 91)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86,101)( 87,105)( 88,104)
( 89,103)( 90,102)(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)
(181,201)(182,205)(183,204)(184,203)(185,202)(186,196)(187,200)(188,199)
(189,198)(190,197)(191,206)(192,210)(193,209)(194,208)(195,207)(211,231)
(212,235)(213,234)(214,233)(215,232)(216,226)(217,230)(218,229)(219,228)
(220,227)(221,236)(222,240)(223,239)(224,238)(225,237)(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)(271,336)(272,340)(273,339)(274,338)
(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)(281,341)(282,345)
(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)(289,353)(290,352)
(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)(297,360)(298,359)
(299,358)(300,357)(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)(511,636)(512,640)(513,639)(514,638)
(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)(521,641)(522,645)
(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)(529,653)(530,652)
(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)(537,660)(538,659)
(539,658)(540,657)(541,711)(542,715)(543,714)(544,713)(545,712)(546,706)
(547,710)(548,709)(549,708)(550,707)(551,716)(552,720)(553,719)(554,718)
(555,717)(556,696)(557,700)(558,699)(559,698)(560,697)(561,691)(562,695)
(563,694)(564,693)(565,692)(566,701)(567,705)(568,704)(569,703)(570,702)
(571,681)(572,685)(573,684)(574,683)(575,682)(576,676)(577,680)(578,679)
(579,678)(580,677)(581,686)(582,690)(583,689)(584,688)(585,687)(586,666)
(587,670)(588,669)(589,668)(590,667)(591,661)(592,665)(593,664)(594,663)
(595,662)(596,671)(597,675)(598,674)(599,673)(600,672)(721,921)(722,925)
(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)(730,917)
(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)(738,909)
(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)(746,911)
(747,915)(748,914)(749,913)(750,912)(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)(781,861)(782,865)(783,864)(784,863)(785,862)(786,856)
(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)(794,868)
(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)(802,845)
(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)(810,852)
(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 := (  1,722)(  2,721)(  3,725)(  4,724)(  5,723)(  6,727)(  7,726)(  8,730)
(  9,729)( 10,728)( 11,732)( 12,731)( 13,735)( 14,734)( 15,733)( 16,737)
( 17,736)( 18,740)( 19,739)( 20,738)( 21,742)( 22,741)( 23,745)( 24,744)
( 25,743)( 26,747)( 27,746)( 28,750)( 29,749)( 30,748)( 31,752)( 32,751)
( 33,755)( 34,754)( 35,753)( 36,757)( 37,756)( 38,760)( 39,759)( 40,758)
( 41,762)( 42,761)( 43,765)( 44,764)( 45,763)( 46,767)( 47,766)( 48,770)
( 49,769)( 50,768)( 51,772)( 52,771)( 53,775)( 54,774)( 55,773)( 56,777)
( 57,776)( 58,780)( 59,779)( 60,778)( 61,812)( 62,811)( 63,815)( 64,814)
( 65,813)( 66,817)( 67,816)( 68,820)( 69,819)( 70,818)( 71,822)( 72,821)
( 73,825)( 74,824)( 75,823)( 76,827)( 77,826)( 78,830)( 79,829)( 80,828)
( 81,832)( 82,831)( 83,835)( 84,834)( 85,833)( 86,837)( 87,836)( 88,840)
( 89,839)( 90,838)( 91,782)( 92,781)( 93,785)( 94,784)( 95,783)( 96,787)
( 97,786)( 98,790)( 99,789)(100,788)(101,792)(102,791)(103,795)(104,794)
(105,793)(106,797)(107,796)(108,800)(109,799)(110,798)(111,802)(112,801)
(113,805)(114,804)(115,803)(116,807)(117,806)(118,810)(119,809)(120,808)
(121,887)(122,886)(123,890)(124,889)(125,888)(126,892)(127,891)(128,895)
(129,894)(130,893)(131,897)(132,896)(133,900)(134,899)(135,898)(136,872)
(137,871)(138,875)(139,874)(140,873)(141,877)(142,876)(143,880)(144,879)
(145,878)(146,882)(147,881)(148,885)(149,884)(150,883)(151,857)(152,856)
(153,860)(154,859)(155,858)(156,862)(157,861)(158,865)(159,864)(160,863)
(161,867)(162,866)(163,870)(164,869)(165,868)(166,842)(167,841)(168,845)
(169,844)(170,843)(171,847)(172,846)(173,850)(174,849)(175,848)(176,852)
(177,851)(178,855)(179,854)(180,853)(181,917)(182,916)(183,920)(184,919)
(185,918)(186,922)(187,921)(188,925)(189,924)(190,923)(191,927)(192,926)
(193,930)(194,929)(195,928)(196,902)(197,901)(198,905)(199,904)(200,903)
(201,907)(202,906)(203,910)(204,909)(205,908)(206,912)(207,911)(208,915)
(209,914)(210,913)(211,947)(212,946)(213,950)(214,949)(215,948)(216,952)
(217,951)(218,955)(219,954)(220,953)(221,957)(222,956)(223,960)(224,959)
(225,958)(226,932)(227,931)(228,935)(229,934)(230,933)(231,937)(232,936)
(233,940)(234,939)(235,938)(236,942)(237,941)(238,945)(239,944)(240,943)
(241,482)(242,481)(243,485)(244,484)(245,483)(246,487)(247,486)(248,490)
(249,489)(250,488)(251,492)(252,491)(253,495)(254,494)(255,493)(256,497)
(257,496)(258,500)(259,499)(260,498)(261,502)(262,501)(263,505)(264,504)
(265,503)(266,507)(267,506)(268,510)(269,509)(270,508)(271,512)(272,511)
(273,515)(274,514)(275,513)(276,517)(277,516)(278,520)(279,519)(280,518)
(281,522)(282,521)(283,525)(284,524)(285,523)(286,527)(287,526)(288,530)
(289,529)(290,528)(291,532)(292,531)(293,535)(294,534)(295,533)(296,537)
(297,536)(298,540)(299,539)(300,538)(301,572)(302,571)(303,575)(304,574)
(305,573)(306,577)(307,576)(308,580)(309,579)(310,578)(311,582)(312,581)
(313,585)(314,584)(315,583)(316,587)(317,586)(318,590)(319,589)(320,588)
(321,592)(322,591)(323,595)(324,594)(325,593)(326,597)(327,596)(328,600)
(329,599)(330,598)(331,542)(332,541)(333,545)(334,544)(335,543)(336,547)
(337,546)(338,550)(339,549)(340,548)(341,552)(342,551)(343,555)(344,554)
(345,553)(346,557)(347,556)(348,560)(349,559)(350,558)(351,562)(352,561)
(353,565)(354,564)(355,563)(356,567)(357,566)(358,570)(359,569)(360,568)
(361,647)(362,646)(363,650)(364,649)(365,648)(366,652)(367,651)(368,655)
(369,654)(370,653)(371,657)(372,656)(373,660)(374,659)(375,658)(376,632)
(377,631)(378,635)(379,634)(380,633)(381,637)(382,636)(383,640)(384,639)
(385,638)(386,642)(387,641)(388,645)(389,644)(390,643)(391,617)(392,616)
(393,620)(394,619)(395,618)(396,622)(397,621)(398,625)(399,624)(400,623)
(401,627)(402,626)(403,630)(404,629)(405,628)(406,602)(407,601)(408,605)
(409,604)(410,603)(411,607)(412,606)(413,610)(414,609)(415,608)(416,612)
(417,611)(418,615)(419,614)(420,613)(421,677)(422,676)(423,680)(424,679)
(425,678)(426,682)(427,681)(428,685)(429,684)(430,683)(431,687)(432,686)
(433,690)(434,689)(435,688)(436,662)(437,661)(438,665)(439,664)(440,663)
(441,667)(442,666)(443,670)(444,669)(445,668)(446,672)(447,671)(448,675)
(449,674)(450,673)(451,707)(452,706)(453,710)(454,709)(455,708)(456,712)
(457,711)(458,715)(459,714)(460,713)(461,717)(462,716)(463,720)(464,719)
(465,718)(466,692)(467,691)(468,695)(469,694)(470,693)(471,697)(472,696)
(473,700)(474,699)(475,698)(476,702)(477,701)(478,705)(479,704)(480,703);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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, 
s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,251)(  7,252)
(  8,253)(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,346)( 62,347)( 63,348)
( 64,349)( 65,350)( 66,356)( 67,357)( 68,358)( 69,359)( 70,360)( 71,351)
( 72,352)( 73,353)( 74,354)( 75,355)( 76,331)( 77,332)( 78,333)( 79,334)
( 80,335)( 81,341)( 82,342)( 83,343)( 84,344)( 85,345)( 86,336)( 87,337)
( 88,338)( 89,339)( 90,340)( 91,316)( 92,317)( 93,318)( 94,319)( 95,320)
( 96,326)( 97,327)( 98,328)( 99,329)(100,330)(101,321)(102,322)(103,323)
(104,324)(105,325)(106,301)(107,302)(108,303)(109,304)(110,305)(111,311)
(112,312)(113,313)(114,314)(115,315)(116,306)(117,307)(118,308)(119,309)
(120,310)(121,376)(122,377)(123,378)(124,379)(125,380)(126,386)(127,387)
(128,388)(129,389)(130,390)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,371)(142,372)(143,373)
(144,374)(145,375)(146,366)(147,367)(148,368)(149,369)(150,370)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,416)(157,417)(158,418)(159,419)
(160,420)(161,411)(162,412)(163,413)(164,414)(165,415)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,401)(172,402)(173,403)(174,404)(175,405)
(176,396)(177,397)(178,398)(179,399)(180,400)(181,451)(182,452)(183,453)
(184,454)(185,455)(186,461)(187,462)(188,463)(189,464)(190,465)(191,456)
(192,457)(193,458)(194,459)(195,460)(196,466)(197,467)(198,468)(199,469)
(200,470)(201,476)(202,477)(203,478)(204,479)(205,480)(206,471)(207,472)
(208,473)(209,474)(210,475)(211,421)(212,422)(213,423)(214,424)(215,425)
(216,431)(217,432)(218,433)(219,434)(220,435)(221,426)(222,427)(223,428)
(224,429)(225,430)(226,436)(227,437)(228,438)(229,439)(230,440)(231,446)
(232,447)(233,448)(234,449)(235,450)(236,441)(237,442)(238,443)(239,444)
(240,445)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,826)(542,827)(543,828)
(544,829)(545,830)(546,836)(547,837)(548,838)(549,839)(550,840)(551,831)
(552,832)(553,833)(554,834)(555,835)(556,811)(557,812)(558,813)(559,814)
(560,815)(561,821)(562,822)(563,823)(564,824)(565,825)(566,816)(567,817)
(568,818)(569,819)(570,820)(571,796)(572,797)(573,798)(574,799)(575,800)
(576,806)(577,807)(578,808)(579,809)(580,810)(581,801)(582,802)(583,803)
(584,804)(585,805)(586,781)(587,782)(588,783)(589,784)(590,785)(591,791)
(592,792)(593,793)(594,794)(595,795)(596,786)(597,787)(598,788)(599,789)
(600,790)(601,856)(602,857)(603,858)(604,859)(605,860)(606,866)(607,867)
(608,868)(609,869)(610,870)(611,861)(612,862)(613,863)(614,864)(615,865)
(616,841)(617,842)(618,843)(619,844)(620,845)(621,851)(622,852)(623,853)
(624,854)(625,855)(626,846)(627,847)(628,848)(629,849)(630,850)(631,886)
(632,887)(633,888)(634,889)(635,890)(636,896)(637,897)(638,898)(639,899)
(640,900)(641,891)(642,892)(643,893)(644,894)(645,895)(646,871)(647,872)
(648,873)(649,874)(650,875)(651,881)(652,882)(653,883)(654,884)(655,885)
(656,876)(657,877)(658,878)(659,879)(660,880)(661,931)(662,932)(663,933)
(664,934)(665,935)(666,941)(667,942)(668,943)(669,944)(670,945)(671,936)
(672,937)(673,938)(674,939)(675,940)(676,946)(677,947)(678,948)(679,949)
(680,950)(681,956)(682,957)(683,958)(684,959)(685,960)(686,951)(687,952)
(688,953)(689,954)(690,955)(691,901)(692,902)(693,903)(694,904)(695,905)
(696,911)(697,912)(698,913)(699,914)(700,915)(701,906)(702,907)(703,908)
(704,909)(705,910)(706,916)(707,917)(708,918)(709,919)(710,920)(711,926)
(712,927)(713,928)(714,929)(715,930)(716,921)(717,922)(718,923)(719,924)
(720,925);
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, 36)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)
( 48, 54)( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61,111)( 62,115)( 63,114)
( 64,113)( 65,112)( 66,106)( 67,110)( 68,109)( 69,108)( 70,107)( 71,116)
( 72,120)( 73,119)( 74,118)( 75,117)( 76, 96)( 77,100)( 78, 99)( 79, 98)
( 80, 97)( 81, 91)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86,101)( 87,105)
( 88,104)( 89,103)( 90,102)(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)(181,201)(182,205)(183,204)(184,203)(185,202)(186,196)(187,200)
(188,199)(189,198)(190,197)(191,206)(192,210)(193,209)(194,208)(195,207)
(211,231)(212,235)(213,234)(214,233)(215,232)(216,226)(217,230)(218,229)
(219,228)(220,227)(221,236)(222,240)(223,239)(224,238)(225,237)(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)(271,336)(272,340)(273,339)
(274,338)(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)(281,341)
(282,345)(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)(289,353)
(290,352)(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)(297,360)
(298,359)(299,358)(300,357)(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)(511,636)(512,640)(513,639)
(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)(521,641)
(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)(529,653)
(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)(537,660)
(538,659)(539,658)(540,657)(541,711)(542,715)(543,714)(544,713)(545,712)
(546,706)(547,710)(548,709)(549,708)(550,707)(551,716)(552,720)(553,719)
(554,718)(555,717)(556,696)(557,700)(558,699)(559,698)(560,697)(561,691)
(562,695)(563,694)(564,693)(565,692)(566,701)(567,705)(568,704)(569,703)
(570,702)(571,681)(572,685)(573,684)(574,683)(575,682)(576,676)(577,680)
(578,679)(579,678)(580,677)(581,686)(582,690)(583,689)(584,688)(585,687)
(586,666)(587,670)(588,669)(589,668)(590,667)(591,661)(592,665)(593,664)
(594,663)(595,662)(596,671)(597,675)(598,674)(599,673)(600,672)(721,921)
(722,925)(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)
(730,917)(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)
(738,909)(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)
(746,911)(747,915)(748,914)(749,913)(750,912)(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)(781,861)(782,865)(783,864)(784,863)(785,862)
(786,856)(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)
(794,868)(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)
(802,845)(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)
(810,852)(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)!(  1,722)(  2,721)(  3,725)(  4,724)(  5,723)(  6,727)(  7,726)
(  8,730)(  9,729)( 10,728)( 11,732)( 12,731)( 13,735)( 14,734)( 15,733)
( 16,737)( 17,736)( 18,740)( 19,739)( 20,738)( 21,742)( 22,741)( 23,745)
( 24,744)( 25,743)( 26,747)( 27,746)( 28,750)( 29,749)( 30,748)( 31,752)
( 32,751)( 33,755)( 34,754)( 35,753)( 36,757)( 37,756)( 38,760)( 39,759)
( 40,758)( 41,762)( 42,761)( 43,765)( 44,764)( 45,763)( 46,767)( 47,766)
( 48,770)( 49,769)( 50,768)( 51,772)( 52,771)( 53,775)( 54,774)( 55,773)
( 56,777)( 57,776)( 58,780)( 59,779)( 60,778)( 61,812)( 62,811)( 63,815)
( 64,814)( 65,813)( 66,817)( 67,816)( 68,820)( 69,819)( 70,818)( 71,822)
( 72,821)( 73,825)( 74,824)( 75,823)( 76,827)( 77,826)( 78,830)( 79,829)
( 80,828)( 81,832)( 82,831)( 83,835)( 84,834)( 85,833)( 86,837)( 87,836)
( 88,840)( 89,839)( 90,838)( 91,782)( 92,781)( 93,785)( 94,784)( 95,783)
( 96,787)( 97,786)( 98,790)( 99,789)(100,788)(101,792)(102,791)(103,795)
(104,794)(105,793)(106,797)(107,796)(108,800)(109,799)(110,798)(111,802)
(112,801)(113,805)(114,804)(115,803)(116,807)(117,806)(118,810)(119,809)
(120,808)(121,887)(122,886)(123,890)(124,889)(125,888)(126,892)(127,891)
(128,895)(129,894)(130,893)(131,897)(132,896)(133,900)(134,899)(135,898)
(136,872)(137,871)(138,875)(139,874)(140,873)(141,877)(142,876)(143,880)
(144,879)(145,878)(146,882)(147,881)(148,885)(149,884)(150,883)(151,857)
(152,856)(153,860)(154,859)(155,858)(156,862)(157,861)(158,865)(159,864)
(160,863)(161,867)(162,866)(163,870)(164,869)(165,868)(166,842)(167,841)
(168,845)(169,844)(170,843)(171,847)(172,846)(173,850)(174,849)(175,848)
(176,852)(177,851)(178,855)(179,854)(180,853)(181,917)(182,916)(183,920)
(184,919)(185,918)(186,922)(187,921)(188,925)(189,924)(190,923)(191,927)
(192,926)(193,930)(194,929)(195,928)(196,902)(197,901)(198,905)(199,904)
(200,903)(201,907)(202,906)(203,910)(204,909)(205,908)(206,912)(207,911)
(208,915)(209,914)(210,913)(211,947)(212,946)(213,950)(214,949)(215,948)
(216,952)(217,951)(218,955)(219,954)(220,953)(221,957)(222,956)(223,960)
(224,959)(225,958)(226,932)(227,931)(228,935)(229,934)(230,933)(231,937)
(232,936)(233,940)(234,939)(235,938)(236,942)(237,941)(238,945)(239,944)
(240,943)(241,482)(242,481)(243,485)(244,484)(245,483)(246,487)(247,486)
(248,490)(249,489)(250,488)(251,492)(252,491)(253,495)(254,494)(255,493)
(256,497)(257,496)(258,500)(259,499)(260,498)(261,502)(262,501)(263,505)
(264,504)(265,503)(266,507)(267,506)(268,510)(269,509)(270,508)(271,512)
(272,511)(273,515)(274,514)(275,513)(276,517)(277,516)(278,520)(279,519)
(280,518)(281,522)(282,521)(283,525)(284,524)(285,523)(286,527)(287,526)
(288,530)(289,529)(290,528)(291,532)(292,531)(293,535)(294,534)(295,533)
(296,537)(297,536)(298,540)(299,539)(300,538)(301,572)(302,571)(303,575)
(304,574)(305,573)(306,577)(307,576)(308,580)(309,579)(310,578)(311,582)
(312,581)(313,585)(314,584)(315,583)(316,587)(317,586)(318,590)(319,589)
(320,588)(321,592)(322,591)(323,595)(324,594)(325,593)(326,597)(327,596)
(328,600)(329,599)(330,598)(331,542)(332,541)(333,545)(334,544)(335,543)
(336,547)(337,546)(338,550)(339,549)(340,548)(341,552)(342,551)(343,555)
(344,554)(345,553)(346,557)(347,556)(348,560)(349,559)(350,558)(351,562)
(352,561)(353,565)(354,564)(355,563)(356,567)(357,566)(358,570)(359,569)
(360,568)(361,647)(362,646)(363,650)(364,649)(365,648)(366,652)(367,651)
(368,655)(369,654)(370,653)(371,657)(372,656)(373,660)(374,659)(375,658)
(376,632)(377,631)(378,635)(379,634)(380,633)(381,637)(382,636)(383,640)
(384,639)(385,638)(386,642)(387,641)(388,645)(389,644)(390,643)(391,617)
(392,616)(393,620)(394,619)(395,618)(396,622)(397,621)(398,625)(399,624)
(400,623)(401,627)(402,626)(403,630)(404,629)(405,628)(406,602)(407,601)
(408,605)(409,604)(410,603)(411,607)(412,606)(413,610)(414,609)(415,608)
(416,612)(417,611)(418,615)(419,614)(420,613)(421,677)(422,676)(423,680)
(424,679)(425,678)(426,682)(427,681)(428,685)(429,684)(430,683)(431,687)
(432,686)(433,690)(434,689)(435,688)(436,662)(437,661)(438,665)(439,664)
(440,663)(441,667)(442,666)(443,670)(444,669)(445,668)(446,672)(447,671)
(448,675)(449,674)(450,673)(451,707)(452,706)(453,710)(454,709)(455,708)
(456,712)(457,711)(458,715)(459,714)(460,713)(461,717)(462,716)(463,720)
(464,719)(465,718)(466,692)(467,691)(468,695)(469,694)(470,693)(471,697)
(472,696)(473,700)(474,699)(475,698)(476,702)(477,701)(478,705)(479,704)
(480,703);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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, 
s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
to this polytope