Polytope of Type {40,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,24}*1920a
Also Known As : {40,24|2}. if this polytope has another name.
Group : SmallGroup(1920,14533)
Rank : 3
Schlafli Type : {40,24}
Number of vertices, edges, etc : 40, 480, 24
Order of s0s1s2 : 120
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 : {20,24}*960a, {40,12}*960a
3-fold quotients : {40,8}*640b
4-fold quotients : {10,24}*480, {40,6}*480, {20,12}*480
5-fold quotients : {8,24}*384b
6-fold quotients : {40,4}*320a, {20,8}*320a
8-fold quotients : {10,12}*240, {20,6}*240a
10-fold quotients : {4,24}*192a, {8,12}*192a
12-fold quotients : {20,4}*160, {40,2}*160, {10,8}*160
15-fold quotients : {8,8}*128b
16-fold quotients : {10,6}*120
20-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {4,8}*64a, {8,4}*64a
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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)( 61,781)( 62,785)( 63,784)( 64,783)
( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)( 72,795)
( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)( 80,797)
( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)( 88,809)
( 89,808)( 90,807)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)( 96,816)
( 97,820)( 98,819)( 99,818)(100,817)(101,821)(102,825)(103,824)(104,823)
(105,822)(106,826)(107,830)(108,829)(109,828)(110,827)(111,831)(112,835)
(113,834)(114,833)(115,832)(116,836)(117,840)(118,839)(119,838)(120,837)
(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)(181,946)(182,950)(183,949)(184,948)
(185,947)(186,951)(187,955)(188,954)(189,953)(190,952)(191,956)(192,960)
(193,959)(194,958)(195,957)(196,931)(197,935)(198,934)(199,933)(200,932)
(201,936)(202,940)(203,939)(204,938)(205,937)(206,941)(207,945)(208,944)
(209,943)(210,942)(211,916)(212,920)(213,919)(214,918)(215,917)(216,921)
(217,925)(218,924)(219,923)(220,922)(221,926)(222,930)(223,929)(224,928)
(225,927)(226,901)(227,905)(228,904)(229,903)(230,902)(231,906)(232,910)
(233,909)(234,908)(235,907)(236,911)(237,915)(238,914)(239,913)(240,912)
(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)(301,541)(302,545)(303,544)(304,543)
(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)(312,555)
(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)(320,557)
(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)(328,569)
(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)(336,576)
(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)(344,583)
(345,582)(346,586)(347,590)(348,589)(349,588)(350,587)(351,591)(352,595)
(353,594)(354,593)(355,592)(356,596)(357,600)(358,599)(359,598)(360,597)
(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)(421,706)(422,710)(423,709)(424,708)
(425,707)(426,711)(427,715)(428,714)(429,713)(430,712)(431,716)(432,720)
(433,719)(434,718)(435,717)(436,691)(437,695)(438,694)(439,693)(440,692)
(441,696)(442,700)(443,699)(444,698)(445,697)(446,701)(447,705)(448,704)
(449,703)(450,702)(451,676)(452,680)(453,679)(454,678)(455,677)(456,681)
(457,685)(458,684)(459,683)(460,682)(461,686)(462,690)(463,689)(464,688)
(465,687)(466,661)(467,665)(468,664)(469,663)(470,662)(471,666)(472,670)
(473,669)(474,668)(475,667)(476,671)(477,675)(478,674)(479,673)(480,672);;
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, 77)( 62, 76)( 63, 80)( 64, 79)
( 65, 78)( 66, 87)( 67, 86)( 68, 90)( 69, 89)( 70, 88)( 71, 82)( 72, 81)
( 73, 85)( 74, 84)( 75, 83)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)
( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)
(104,114)(105,113)(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)
(181,227)(182,226)(183,230)(184,229)(185,228)(186,237)(187,236)(188,240)
(189,239)(190,238)(191,232)(192,231)(193,235)(194,234)(195,233)(196,212)
(197,211)(198,215)(199,214)(200,213)(201,222)(202,221)(203,225)(204,224)
(205,223)(206,217)(207,216)(208,220)(209,219)(210,218)(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)(541,677)(542,676)(543,680)(544,679)(545,678)(546,687)
(547,686)(548,690)(549,689)(550,688)(551,682)(552,681)(553,685)(554,684)
(555,683)(556,662)(557,661)(558,665)(559,664)(560,663)(561,672)(562,671)
(563,675)(564,674)(565,673)(566,667)(567,666)(568,670)(569,669)(570,668)
(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)(578,720)
(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)(586,692)
(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)(594,704)
(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(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)( 61,321)( 62,322)( 63,323)( 64,324)
( 65,325)( 66,316)( 67,317)( 68,318)( 69,319)( 70,320)( 71,326)( 72,327)
( 73,328)( 74,329)( 75,330)( 76,306)( 77,307)( 78,308)( 79,309)( 80,310)
( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,351)( 92,352)( 93,353)( 94,354)( 95,355)( 96,346)
( 97,347)( 98,348)( 99,349)(100,350)(101,356)(102,357)(103,358)(104,359)
(105,360)(106,336)(107,337)(108,338)(109,339)(110,340)(111,331)(112,332)
(113,333)(114,334)(115,335)(116,341)(117,342)(118,343)(119,344)(120,345)
(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)(181,426)(182,427)(183,428)(184,429)
(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)(200,445)
(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)(216,451)
(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)(232,467)
(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)(240,480)
(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)(541,801)(542,802)(543,803)(544,804)
(545,805)(546,796)(547,797)(548,798)(549,799)(550,800)(551,806)(552,807)
(553,808)(554,809)(555,810)(556,786)(557,787)(558,788)(559,789)(560,790)
(561,781)(562,782)(563,783)(564,784)(565,785)(566,791)(567,792)(568,793)
(569,794)(570,795)(571,831)(572,832)(573,833)(574,834)(575,835)(576,826)
(577,827)(578,828)(579,829)(580,830)(581,836)(582,837)(583,838)(584,839)
(585,840)(586,816)(587,817)(588,818)(589,819)(590,820)(591,811)(592,812)
(593,813)(594,814)(595,815)(596,821)(597,822)(598,823)(599,824)(600,825)
(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)(661,906)(662,907)(663,908)(664,909)
(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)(680,925)
(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)(696,931)
(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)(712,947)
(713,948)(714,949)(715,950)(716,956)(717,957)(718,958)(719,959)(720,960);;
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*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 ];;
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)( 61,781)( 62,785)( 63,784)
( 64,783)( 65,782)( 66,786)( 67,790)( 68,789)( 69,788)( 70,787)( 71,791)
( 72,795)( 73,794)( 74,793)( 75,792)( 76,796)( 77,800)( 78,799)( 79,798)
( 80,797)( 81,801)( 82,805)( 83,804)( 84,803)( 85,802)( 86,806)( 87,810)
( 88,809)( 89,808)( 90,807)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)
( 96,816)( 97,820)( 98,819)( 99,818)(100,817)(101,821)(102,825)(103,824)
(104,823)(105,822)(106,826)(107,830)(108,829)(109,828)(110,827)(111,831)
(112,835)(113,834)(114,833)(115,832)(116,836)(117,840)(118,839)(119,838)
(120,837)(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)(181,946)(182,950)(183,949)
(184,948)(185,947)(186,951)(187,955)(188,954)(189,953)(190,952)(191,956)
(192,960)(193,959)(194,958)(195,957)(196,931)(197,935)(198,934)(199,933)
(200,932)(201,936)(202,940)(203,939)(204,938)(205,937)(206,941)(207,945)
(208,944)(209,943)(210,942)(211,916)(212,920)(213,919)(214,918)(215,917)
(216,921)(217,925)(218,924)(219,923)(220,922)(221,926)(222,930)(223,929)
(224,928)(225,927)(226,901)(227,905)(228,904)(229,903)(230,902)(231,906)
(232,910)(233,909)(234,908)(235,907)(236,911)(237,915)(238,914)(239,913)
(240,912)(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)(301,541)(302,545)(303,544)
(304,543)(305,542)(306,546)(307,550)(308,549)(309,548)(310,547)(311,551)
(312,555)(313,554)(314,553)(315,552)(316,556)(317,560)(318,559)(319,558)
(320,557)(321,561)(322,565)(323,564)(324,563)(325,562)(326,566)(327,570)
(328,569)(329,568)(330,567)(331,571)(332,575)(333,574)(334,573)(335,572)
(336,576)(337,580)(338,579)(339,578)(340,577)(341,581)(342,585)(343,584)
(344,583)(345,582)(346,586)(347,590)(348,589)(349,588)(350,587)(351,591)
(352,595)(353,594)(354,593)(355,592)(356,596)(357,600)(358,599)(359,598)
(360,597)(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)(421,706)(422,710)(423,709)
(424,708)(425,707)(426,711)(427,715)(428,714)(429,713)(430,712)(431,716)
(432,720)(433,719)(434,718)(435,717)(436,691)(437,695)(438,694)(439,693)
(440,692)(441,696)(442,700)(443,699)(444,698)(445,697)(446,701)(447,705)
(448,704)(449,703)(450,702)(451,676)(452,680)(453,679)(454,678)(455,677)
(456,681)(457,685)(458,684)(459,683)(460,682)(461,686)(462,690)(463,689)
(464,688)(465,687)(466,661)(467,665)(468,664)(469,663)(470,662)(471,666)
(472,670)(473,669)(474,668)(475,667)(476,671)(477,675)(478,674)(479,673)
(480,672);
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, 77)( 62, 76)( 63, 80)
( 64, 79)( 65, 78)( 66, 87)( 67, 86)( 68, 90)( 69, 89)( 70, 88)( 71, 82)
( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 91,107)( 92,106)( 93,110)( 94,109)
( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)
(103,115)(104,114)(105,113)(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)(181,227)(182,226)(183,230)(184,229)(185,228)(186,237)(187,236)
(188,240)(189,239)(190,238)(191,232)(192,231)(193,235)(194,234)(195,233)
(196,212)(197,211)(198,215)(199,214)(200,213)(201,222)(202,221)(203,225)
(204,224)(205,223)(206,217)(207,216)(208,220)(209,219)(210,218)(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)(541,677)(542,676)(543,680)(544,679)(545,678)
(546,687)(547,686)(548,690)(549,689)(550,688)(551,682)(552,681)(553,685)
(554,684)(555,683)(556,662)(557,661)(558,665)(559,664)(560,663)(561,672)
(562,671)(563,675)(564,674)(565,673)(566,667)(567,666)(568,670)(569,669)
(570,668)(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)
(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)
(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)
(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(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)( 61,321)( 62,322)( 63,323)
( 64,324)( 65,325)( 66,316)( 67,317)( 68,318)( 69,319)( 70,320)( 71,326)
( 72,327)( 73,328)( 74,329)( 75,330)( 76,306)( 77,307)( 78,308)( 79,309)
( 80,310)( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,351)( 92,352)( 93,353)( 94,354)( 95,355)
( 96,346)( 97,347)( 98,348)( 99,349)(100,350)(101,356)(102,357)(103,358)
(104,359)(105,360)(106,336)(107,337)(108,338)(109,339)(110,340)(111,331)
(112,332)(113,333)(114,334)(115,335)(116,341)(117,342)(118,343)(119,344)
(120,345)(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)(181,426)(182,427)(183,428)
(184,429)(185,430)(186,421)(187,422)(188,423)(189,424)(190,425)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,441)(197,442)(198,443)(199,444)
(200,445)(201,436)(202,437)(203,438)(204,439)(205,440)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,456)(212,457)(213,458)(214,459)(215,460)
(216,451)(217,452)(218,453)(219,454)(220,455)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,471)(227,472)(228,473)(229,474)(230,475)(231,466)
(232,467)(233,468)(234,469)(235,470)(236,476)(237,477)(238,478)(239,479)
(240,480)(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)(541,801)(542,802)(543,803)
(544,804)(545,805)(546,796)(547,797)(548,798)(549,799)(550,800)(551,806)
(552,807)(553,808)(554,809)(555,810)(556,786)(557,787)(558,788)(559,789)
(560,790)(561,781)(562,782)(563,783)(564,784)(565,785)(566,791)(567,792)
(568,793)(569,794)(570,795)(571,831)(572,832)(573,833)(574,834)(575,835)
(576,826)(577,827)(578,828)(579,829)(580,830)(581,836)(582,837)(583,838)
(584,839)(585,840)(586,816)(587,817)(588,818)(589,819)(590,820)(591,811)
(592,812)(593,813)(594,814)(595,815)(596,821)(597,822)(598,823)(599,824)
(600,825)(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)(661,906)(662,907)(663,908)
(664,909)(665,910)(666,901)(667,902)(668,903)(669,904)(670,905)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,921)(677,922)(678,923)(679,924)
(680,925)(681,916)(682,917)(683,918)(684,919)(685,920)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,936)(692,937)(693,938)(694,939)(695,940)
(696,931)(697,932)(698,933)(699,934)(700,935)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,951)(707,952)(708,953)(709,954)(710,955)(711,946)
(712,947)(713,948)(714,949)(715,950)(716,956)(717,957)(718,958)(719,959)
(720,960);
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*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 >;
References : None.
to this polytope