Polytope of Type {24,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,13408)
Rank : 3
Schlafli Type : {24,20}
Number of vertices, edges, etc : 48, 480, 40
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {12,20}*960a, {24,20}*960a, {24,20}*960b
3-fold quotients : {8,20}*640a
4-fold quotients : {24,10}*480, {12,20}*480
5-fold quotients : {24,4}*384a
6-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b
8-fold quotients : {12,10}*240, {6,20}*240a
10-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b
12-fold quotients : {4,20}*160, {8,10}*160
15-fold quotients : {8,4}*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, {8,4}*64b, {4,4}*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)( 31,751)( 32,752)
( 33,753)( 34,754)( 35,755)( 36,761)( 37,762)( 38,763)( 39,764)( 40,765)
( 41,756)( 42,757)( 43,758)( 44,759)( 45,760)( 46,766)( 47,767)( 48,768)
( 49,769)( 50,770)( 51,776)( 52,777)( 53,778)( 54,779)( 55,780)( 56,771)
( 57,772)( 58,773)( 59,774)( 60,775)( 61,796)( 62,797)( 63,798)( 64,799)
( 65,800)( 66,806)( 67,807)( 68,808)( 69,809)( 70,810)( 71,801)( 72,802)
( 73,803)( 74,804)( 75,805)( 76,781)( 77,782)( 78,783)( 79,784)( 80,785)
( 81,791)( 82,792)( 83,793)( 84,794)( 85,795)( 86,786)( 87,787)( 88,788)
( 89,789)( 90,790)( 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)
(121,886)(122,887)(123,888)(124,889)(125,890)(126,896)(127,897)(128,898)
(129,899)(130,900)(131,891)(132,892)(133,893)(134,894)(135,895)(136,871)
(137,872)(138,873)(139,874)(140,875)(141,881)(142,882)(143,883)(144,884)
(145,885)(146,876)(147,877)(148,878)(149,879)(150,880)(151,856)(152,857)
(153,858)(154,859)(155,860)(156,866)(157,867)(158,868)(159,869)(160,870)
(161,861)(162,862)(163,863)(164,864)(165,865)(166,841)(167,842)(168,843)
(169,844)(170,845)(171,851)(172,852)(173,853)(174,854)(175,855)(176,846)
(177,847)(178,848)(179,849)(180,850)(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)(271,511)(272,512)
(273,513)(274,514)(275,515)(276,521)(277,522)(278,523)(279,524)(280,525)
(281,516)(282,517)(283,518)(284,519)(285,520)(286,526)(287,527)(288,528)
(289,529)(290,530)(291,536)(292,537)(293,538)(294,539)(295,540)(296,531)
(297,532)(298,533)(299,534)(300,535)(301,556)(302,557)(303,558)(304,559)
(305,560)(306,566)(307,567)(308,568)(309,569)(310,570)(311,561)(312,562)
(313,563)(314,564)(315,565)(316,541)(317,542)(318,543)(319,544)(320,545)
(321,551)(322,552)(323,553)(324,554)(325,555)(326,546)(327,547)(328,548)
(329,549)(330,550)(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)
(361,646)(362,647)(363,648)(364,649)(365,650)(366,656)(367,657)(368,658)
(369,659)(370,660)(371,651)(372,652)(373,653)(374,654)(375,655)(376,631)
(377,632)(378,633)(379,634)(380,635)(381,641)(382,642)(383,643)(384,644)
(385,645)(386,636)(387,637)(388,638)(389,639)(390,640)(391,616)(392,617)
(393,618)(394,619)(395,620)(396,626)(397,627)(398,628)(399,629)(400,630)
(401,621)(402,622)(403,623)(404,624)(405,625)(406,601)(407,602)(408,603)
(409,604)(410,605)(411,611)(412,612)(413,613)(414,614)(415,615)(416,606)
(417,607)(418,608)(419,609)(420,610)(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, 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, 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, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(102,105)
(103,104)(106,111)(107,115)(108,114)(109,113)(110,112)(117,120)(118,119)
(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)(271,336)(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)
(541,666)(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)(571,696)(572,700)
(573,699)(574,698)(575,697)(576,691)(577,695)(578,694)(579,693)(580,692)
(581,701)(582,705)(583,704)(584,703)(585,702)(586,711)(587,715)(588,714)
(589,713)(590,712)(591,706)(592,710)(593,709)(594,708)(595,707)(596,716)
(597,720)(598,719)(599,718)(600,717)(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 := ( 1,242)( 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)
(121,377)(122,376)(123,380)(124,379)(125,378)(126,382)(127,381)(128,385)
(129,384)(130,383)(131,387)(132,386)(133,390)(134,389)(135,388)(136,362)
(137,361)(138,365)(139,364)(140,363)(141,367)(142,366)(143,370)(144,369)
(145,368)(146,372)(147,371)(148,375)(149,374)(150,373)(151,407)(152,406)
(153,410)(154,409)(155,408)(156,412)(157,411)(158,415)(159,414)(160,413)
(161,417)(162,416)(163,420)(164,419)(165,418)(166,392)(167,391)(168,395)
(169,394)(170,393)(171,397)(172,396)(173,400)(174,399)(175,398)(176,402)
(177,401)(178,405)(179,404)(180,403)(181,437)(182,436)(183,440)(184,439)
(185,438)(186,442)(187,441)(188,445)(189,444)(190,443)(191,447)(192,446)
(193,450)(194,449)(195,448)(196,422)(197,421)(198,425)(199,424)(200,423)
(201,427)(202,426)(203,430)(204,429)(205,428)(206,432)(207,431)(208,435)
(209,434)(210,433)(211,467)(212,466)(213,470)(214,469)(215,468)(216,472)
(217,471)(218,475)(219,474)(220,473)(221,477)(222,476)(223,480)(224,479)
(225,478)(226,452)(227,451)(228,455)(229,454)(230,453)(231,457)(232,456)
(233,460)(234,459)(235,458)(236,462)(237,461)(238,465)(239,464)(240,463)
(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)
(601,857)(602,856)(603,860)(604,859)(605,858)(606,862)(607,861)(608,865)
(609,864)(610,863)(611,867)(612,866)(613,870)(614,869)(615,868)(616,842)
(617,841)(618,845)(619,844)(620,843)(621,847)(622,846)(623,850)(624,849)
(625,848)(626,852)(627,851)(628,855)(629,854)(630,853)(631,887)(632,886)
(633,890)(634,889)(635,888)(636,892)(637,891)(638,895)(639,894)(640,893)
(641,897)(642,896)(643,900)(644,899)(645,898)(646,872)(647,871)(648,875)
(649,874)(650,873)(651,877)(652,876)(653,880)(654,879)(655,878)(656,882)
(657,881)(658,885)(659,884)(660,883)(661,917)(662,916)(663,920)(664,919)
(665,918)(666,922)(667,921)(668,925)(669,924)(670,923)(671,927)(672,926)
(673,930)(674,929)(675,928)(676,902)(677,901)(678,905)(679,904)(680,903)
(681,907)(682,906)(683,910)(684,909)(685,908)(686,912)(687,911)(688,915)
(689,914)(690,913)(691,947)(692,946)(693,950)(694,949)(695,948)(696,952)
(697,951)(698,955)(699,954)(700,953)(701,957)(702,956)(703,960)(704,959)
(705,958)(706,932)(707,931)(708,935)(709,934)(710,933)(711,937)(712,936)
(713,940)(714,939)(715,938)(716,942)(717,941)(718,945)(719,944)(720,943);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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)( 31,751)
( 32,752)( 33,753)( 34,754)( 35,755)( 36,761)( 37,762)( 38,763)( 39,764)
( 40,765)( 41,756)( 42,757)( 43,758)( 44,759)( 45,760)( 46,766)( 47,767)
( 48,768)( 49,769)( 50,770)( 51,776)( 52,777)( 53,778)( 54,779)( 55,780)
( 56,771)( 57,772)( 58,773)( 59,774)( 60,775)( 61,796)( 62,797)( 63,798)
( 64,799)( 65,800)( 66,806)( 67,807)( 68,808)( 69,809)( 70,810)( 71,801)
( 72,802)( 73,803)( 74,804)( 75,805)( 76,781)( 77,782)( 78,783)( 79,784)
( 80,785)( 81,791)( 82,792)( 83,793)( 84,794)( 85,795)( 86,786)( 87,787)
( 88,788)( 89,789)( 90,790)( 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)(121,886)(122,887)(123,888)(124,889)(125,890)(126,896)(127,897)
(128,898)(129,899)(130,900)(131,891)(132,892)(133,893)(134,894)(135,895)
(136,871)(137,872)(138,873)(139,874)(140,875)(141,881)(142,882)(143,883)
(144,884)(145,885)(146,876)(147,877)(148,878)(149,879)(150,880)(151,856)
(152,857)(153,858)(154,859)(155,860)(156,866)(157,867)(158,868)(159,869)
(160,870)(161,861)(162,862)(163,863)(164,864)(165,865)(166,841)(167,842)
(168,843)(169,844)(170,845)(171,851)(172,852)(173,853)(174,854)(175,855)
(176,846)(177,847)(178,848)(179,849)(180,850)(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)(271,511)
(272,512)(273,513)(274,514)(275,515)(276,521)(277,522)(278,523)(279,524)
(280,525)(281,516)(282,517)(283,518)(284,519)(285,520)(286,526)(287,527)
(288,528)(289,529)(290,530)(291,536)(292,537)(293,538)(294,539)(295,540)
(296,531)(297,532)(298,533)(299,534)(300,535)(301,556)(302,557)(303,558)
(304,559)(305,560)(306,566)(307,567)(308,568)(309,569)(310,570)(311,561)
(312,562)(313,563)(314,564)(315,565)(316,541)(317,542)(318,543)(319,544)
(320,545)(321,551)(322,552)(323,553)(324,554)(325,555)(326,546)(327,547)
(328,548)(329,549)(330,550)(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)(361,646)(362,647)(363,648)(364,649)(365,650)(366,656)(367,657)
(368,658)(369,659)(370,660)(371,651)(372,652)(373,653)(374,654)(375,655)
(376,631)(377,632)(378,633)(379,634)(380,635)(381,641)(382,642)(383,643)
(384,644)(385,645)(386,636)(387,637)(388,638)(389,639)(390,640)(391,616)
(392,617)(393,618)(394,619)(395,620)(396,626)(397,627)(398,628)(399,629)
(400,630)(401,621)(402,622)(403,623)(404,624)(405,625)(406,601)(407,602)
(408,603)(409,604)(410,605)(411,611)(412,612)(413,613)(414,614)(415,615)
(416,606)(417,607)(418,608)(419,609)(420,610)(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, 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, 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, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)
(102,105)(103,104)(106,111)(107,115)(108,114)(109,113)(110,112)(117,120)
(118,119)(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)(271,336)(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)(541,666)(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)(571,696)
(572,700)(573,699)(574,698)(575,697)(576,691)(577,695)(578,694)(579,693)
(580,692)(581,701)(582,705)(583,704)(584,703)(585,702)(586,711)(587,715)
(588,714)(589,713)(590,712)(591,706)(592,710)(593,709)(594,708)(595,707)
(596,716)(597,720)(598,719)(599,718)(600,717)(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)!( 1,242)( 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)(121,377)(122,376)(123,380)(124,379)(125,378)(126,382)(127,381)
(128,385)(129,384)(130,383)(131,387)(132,386)(133,390)(134,389)(135,388)
(136,362)(137,361)(138,365)(139,364)(140,363)(141,367)(142,366)(143,370)
(144,369)(145,368)(146,372)(147,371)(148,375)(149,374)(150,373)(151,407)
(152,406)(153,410)(154,409)(155,408)(156,412)(157,411)(158,415)(159,414)
(160,413)(161,417)(162,416)(163,420)(164,419)(165,418)(166,392)(167,391)
(168,395)(169,394)(170,393)(171,397)(172,396)(173,400)(174,399)(175,398)
(176,402)(177,401)(178,405)(179,404)(180,403)(181,437)(182,436)(183,440)
(184,439)(185,438)(186,442)(187,441)(188,445)(189,444)(190,443)(191,447)
(192,446)(193,450)(194,449)(195,448)(196,422)(197,421)(198,425)(199,424)
(200,423)(201,427)(202,426)(203,430)(204,429)(205,428)(206,432)(207,431)
(208,435)(209,434)(210,433)(211,467)(212,466)(213,470)(214,469)(215,468)
(216,472)(217,471)(218,475)(219,474)(220,473)(221,477)(222,476)(223,480)
(224,479)(225,478)(226,452)(227,451)(228,455)(229,454)(230,453)(231,457)
(232,456)(233,460)(234,459)(235,458)(236,462)(237,461)(238,465)(239,464)
(240,463)(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)(601,857)(602,856)(603,860)(604,859)(605,858)(606,862)(607,861)
(608,865)(609,864)(610,863)(611,867)(612,866)(613,870)(614,869)(615,868)
(616,842)(617,841)(618,845)(619,844)(620,843)(621,847)(622,846)(623,850)
(624,849)(625,848)(626,852)(627,851)(628,855)(629,854)(630,853)(631,887)
(632,886)(633,890)(634,889)(635,888)(636,892)(637,891)(638,895)(639,894)
(640,893)(641,897)(642,896)(643,900)(644,899)(645,898)(646,872)(647,871)
(648,875)(649,874)(650,873)(651,877)(652,876)(653,880)(654,879)(655,878)
(656,882)(657,881)(658,885)(659,884)(660,883)(661,917)(662,916)(663,920)
(664,919)(665,918)(666,922)(667,921)(668,925)(669,924)(670,923)(671,927)
(672,926)(673,930)(674,929)(675,928)(676,902)(677,901)(678,905)(679,904)
(680,903)(681,907)(682,906)(683,910)(684,909)(685,908)(686,912)(687,911)
(688,915)(689,914)(690,913)(691,947)(692,946)(693,950)(694,949)(695,948)
(696,952)(697,951)(698,955)(699,954)(700,953)(701,957)(702,956)(703,960)
(704,959)(705,958)(706,932)(707,931)(708,935)(709,934)(710,933)(711,937)
(712,936)(713,940)(714,939)(715,938)(716,942)(717,941)(718,945)(719,944)
(720,943);
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope