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