Polytope of Type {240,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {240,4}*1920a
Also Known As : {240,4|2}. if this polytope has another name.
Group : SmallGroup(1920,41728)
Rank : 3
Schlafli Type : {240,4}
Number of vertices, edges, etc : 240, 480, 4
Order of s0s1s2 : 240
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {120,4}*960a, {240,2}*960
3-fold quotients : {80,4}*640a
4-fold quotients : {60,4}*480a, {120,2}*480
5-fold quotients : {48,4}*384a
6-fold quotients : {40,4}*320a, {80,2}*320
8-fold quotients : {60,2}*240, {30,4}*240a
10-fold quotients : {24,4}*192a, {48,2}*192
12-fold quotients : {20,4}*160, {40,2}*160
15-fold quotients : {16,4}*128a
16-fold quotients : {30,2}*120
20-fold quotients : {12,4}*96a, {24,2}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {8,4}*64a, {16,2}*64
32-fold quotients : {15,2}*60
40-fold quotients : {12,2}*48, {6,4}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {8,2}*32
80-fold quotients : {6,2}*24
96-fold quotients : {5,2}*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 := ( 1,481)( 2,485)( 3,484)( 4,483)( 5,482)( 6,491)( 7,495)( 8,494)
( 9,493)( 10,492)( 11,486)( 12,490)( 13,489)( 14,488)( 15,487)( 16,496)
( 17,500)( 18,499)( 19,498)( 20,497)( 21,506)( 22,510)( 23,509)( 24,508)
( 25,507)( 26,501)( 27,505)( 28,504)( 29,503)( 30,502)( 31,526)( 32,530)
( 33,529)( 34,528)( 35,527)( 36,536)( 37,540)( 38,539)( 39,538)( 40,537)
( 41,531)( 42,535)( 43,534)( 44,533)( 45,532)( 46,511)( 47,515)( 48,514)
( 49,513)( 50,512)( 51,521)( 52,525)( 53,524)( 54,523)( 55,522)( 56,516)
( 57,520)( 58,519)( 59,518)( 60,517)( 61,541)( 62,545)( 63,544)( 64,543)
( 65,542)( 66,551)( 67,555)( 68,554)( 69,553)( 70,552)( 71,546)( 72,550)
( 73,549)( 74,548)( 75,547)( 76,556)( 77,560)( 78,559)( 79,558)( 80,557)
( 81,566)( 82,570)( 83,569)( 84,568)( 85,567)( 86,561)( 87,565)( 88,564)
( 89,563)( 90,562)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)( 96,596)
( 97,600)( 98,599)( 99,598)(100,597)(101,591)(102,595)(103,594)(104,593)
(105,592)(106,571)(107,575)(108,574)(109,573)(110,572)(111,581)(112,585)
(113,584)(114,583)(115,582)(116,576)(117,580)(118,579)(119,578)(120,577)
(121,631)(122,635)(123,634)(124,633)(125,632)(126,641)(127,645)(128,644)
(129,643)(130,642)(131,636)(132,640)(133,639)(134,638)(135,637)(136,646)
(137,650)(138,649)(139,648)(140,647)(141,656)(142,660)(143,659)(144,658)
(145,657)(146,651)(147,655)(148,654)(149,653)(150,652)(151,601)(152,605)
(153,604)(154,603)(155,602)(156,611)(157,615)(158,614)(159,613)(160,612)
(161,606)(162,610)(163,609)(164,608)(165,607)(166,616)(167,620)(168,619)
(169,618)(170,617)(171,626)(172,630)(173,629)(174,628)(175,627)(176,621)
(177,625)(178,624)(179,623)(180,622)(181,691)(182,695)(183,694)(184,693)
(185,692)(186,701)(187,705)(188,704)(189,703)(190,702)(191,696)(192,700)
(193,699)(194,698)(195,697)(196,706)(197,710)(198,709)(199,708)(200,707)
(201,716)(202,720)(203,719)(204,718)(205,717)(206,711)(207,715)(208,714)
(209,713)(210,712)(211,661)(212,665)(213,664)(214,663)(215,662)(216,671)
(217,675)(218,674)(219,673)(220,672)(221,666)(222,670)(223,669)(224,668)
(225,667)(226,676)(227,680)(228,679)(229,678)(230,677)(231,686)(232,690)
(233,689)(234,688)(235,687)(236,681)(237,685)(238,684)(239,683)(240,682)
(241,721)(242,725)(243,724)(244,723)(245,722)(246,731)(247,735)(248,734)
(249,733)(250,732)(251,726)(252,730)(253,729)(254,728)(255,727)(256,736)
(257,740)(258,739)(259,738)(260,737)(261,746)(262,750)(263,749)(264,748)
(265,747)(266,741)(267,745)(268,744)(269,743)(270,742)(271,766)(272,770)
(273,769)(274,768)(275,767)(276,776)(277,780)(278,779)(279,778)(280,777)
(281,771)(282,775)(283,774)(284,773)(285,772)(286,751)(287,755)(288,754)
(289,753)(290,752)(291,761)(292,765)(293,764)(294,763)(295,762)(296,756)
(297,760)(298,759)(299,758)(300,757)(301,781)(302,785)(303,784)(304,783)
(305,782)(306,791)(307,795)(308,794)(309,793)(310,792)(311,786)(312,790)
(313,789)(314,788)(315,787)(316,796)(317,800)(318,799)(319,798)(320,797)
(321,806)(322,810)(323,809)(324,808)(325,807)(326,801)(327,805)(328,804)
(329,803)(330,802)(331,826)(332,830)(333,829)(334,828)(335,827)(336,836)
(337,840)(338,839)(339,838)(340,837)(341,831)(342,835)(343,834)(344,833)
(345,832)(346,811)(347,815)(348,814)(349,813)(350,812)(351,821)(352,825)
(353,824)(354,823)(355,822)(356,816)(357,820)(358,819)(359,818)(360,817)
(361,871)(362,875)(363,874)(364,873)(365,872)(366,881)(367,885)(368,884)
(369,883)(370,882)(371,876)(372,880)(373,879)(374,878)(375,877)(376,886)
(377,890)(378,889)(379,888)(380,887)(381,896)(382,900)(383,899)(384,898)
(385,897)(386,891)(387,895)(388,894)(389,893)(390,892)(391,841)(392,845)
(393,844)(394,843)(395,842)(396,851)(397,855)(398,854)(399,853)(400,852)
(401,846)(402,850)(403,849)(404,848)(405,847)(406,856)(407,860)(408,859)
(409,858)(410,857)(411,866)(412,870)(413,869)(414,868)(415,867)(416,861)
(417,865)(418,864)(419,863)(420,862)(421,931)(422,935)(423,934)(424,933)
(425,932)(426,941)(427,945)(428,944)(429,943)(430,942)(431,936)(432,940)
(433,939)(434,938)(435,937)(436,946)(437,950)(438,949)(439,948)(440,947)
(441,956)(442,960)(443,959)(444,958)(445,957)(446,951)(447,955)(448,954)
(449,953)(450,952)(451,901)(452,905)(453,904)(454,903)(455,902)(456,911)
(457,915)(458,914)(459,913)(460,912)(461,906)(462,910)(463,909)(464,908)
(465,907)(466,916)(467,920)(468,919)(469,918)(470,917)(471,926)(472,930)
(473,929)(474,928)(475,927)(476,921)(477,925)(478,924)(479,923)(480,922);;
s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)
( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)
(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)
(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)
(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)(142,166)
(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)(150,178)
(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)(188,215)
(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)(196,232)
(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)(204,229)
(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)(242,306)
(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)
(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)(258,325)
(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)(266,327)
(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)(274,354)
(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)(282,356)
(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)(290,338)
(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)(298,345)
(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)(366,452)
(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)(374,464)
(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)(382,466)
(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)(390,478)
(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)(398,425)
(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)(406,442)
(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)(414,439)
(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)(482,606)
(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)
(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)
(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)
(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)(514,654)
(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)(522,656)
(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)(530,638)
(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)(538,645)
(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)
(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)
(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)
(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)
(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)(578,710)
(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)(586,697)
(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)(594,694)
(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,907)(722,906)
(723,910)(724,909)(725,908)(726,902)(727,901)(728,905)(729,904)(730,903)
(731,912)(732,911)(733,915)(734,914)(735,913)(736,922)(737,921)(738,925)
(739,924)(740,923)(741,917)(742,916)(743,920)(744,919)(745,918)(746,927)
(747,926)(748,930)(749,929)(750,928)(751,952)(752,951)(753,955)(754,954)
(755,953)(756,947)(757,946)(758,950)(759,949)(760,948)(761,957)(762,956)
(763,960)(764,959)(765,958)(766,937)(767,936)(768,940)(769,939)(770,938)
(771,932)(772,931)(773,935)(774,934)(775,933)(776,942)(777,941)(778,945)
(779,944)(780,943)(781,847)(782,846)(783,850)(784,849)(785,848)(786,842)
(787,841)(788,845)(789,844)(790,843)(791,852)(792,851)(793,855)(794,854)
(795,853)(796,862)(797,861)(798,865)(799,864)(800,863)(801,857)(802,856)
(803,860)(804,859)(805,858)(806,867)(807,866)(808,870)(809,869)(810,868)
(811,892)(812,891)(813,895)(814,894)(815,893)(816,887)(817,886)(818,890)
(819,889)(820,888)(821,897)(822,896)(823,900)(824,899)(825,898)(826,877)
(827,876)(828,880)(829,879)(830,878)(831,872)(832,871)(833,875)(834,874)
(835,873)(836,882)(837,881)(838,885)(839,884)(840,883);;
s2 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,481)( 2,485)( 3,484)( 4,483)( 5,482)( 6,491)( 7,495)
( 8,494)( 9,493)( 10,492)( 11,486)( 12,490)( 13,489)( 14,488)( 15,487)
( 16,496)( 17,500)( 18,499)( 19,498)( 20,497)( 21,506)( 22,510)( 23,509)
( 24,508)( 25,507)( 26,501)( 27,505)( 28,504)( 29,503)( 30,502)( 31,526)
( 32,530)( 33,529)( 34,528)( 35,527)( 36,536)( 37,540)( 38,539)( 39,538)
( 40,537)( 41,531)( 42,535)( 43,534)( 44,533)( 45,532)( 46,511)( 47,515)
( 48,514)( 49,513)( 50,512)( 51,521)( 52,525)( 53,524)( 54,523)( 55,522)
( 56,516)( 57,520)( 58,519)( 59,518)( 60,517)( 61,541)( 62,545)( 63,544)
( 64,543)( 65,542)( 66,551)( 67,555)( 68,554)( 69,553)( 70,552)( 71,546)
( 72,550)( 73,549)( 74,548)( 75,547)( 76,556)( 77,560)( 78,559)( 79,558)
( 80,557)( 81,566)( 82,570)( 83,569)( 84,568)( 85,567)( 86,561)( 87,565)
( 88,564)( 89,563)( 90,562)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)
( 96,596)( 97,600)( 98,599)( 99,598)(100,597)(101,591)(102,595)(103,594)
(104,593)(105,592)(106,571)(107,575)(108,574)(109,573)(110,572)(111,581)
(112,585)(113,584)(114,583)(115,582)(116,576)(117,580)(118,579)(119,578)
(120,577)(121,631)(122,635)(123,634)(124,633)(125,632)(126,641)(127,645)
(128,644)(129,643)(130,642)(131,636)(132,640)(133,639)(134,638)(135,637)
(136,646)(137,650)(138,649)(139,648)(140,647)(141,656)(142,660)(143,659)
(144,658)(145,657)(146,651)(147,655)(148,654)(149,653)(150,652)(151,601)
(152,605)(153,604)(154,603)(155,602)(156,611)(157,615)(158,614)(159,613)
(160,612)(161,606)(162,610)(163,609)(164,608)(165,607)(166,616)(167,620)
(168,619)(169,618)(170,617)(171,626)(172,630)(173,629)(174,628)(175,627)
(176,621)(177,625)(178,624)(179,623)(180,622)(181,691)(182,695)(183,694)
(184,693)(185,692)(186,701)(187,705)(188,704)(189,703)(190,702)(191,696)
(192,700)(193,699)(194,698)(195,697)(196,706)(197,710)(198,709)(199,708)
(200,707)(201,716)(202,720)(203,719)(204,718)(205,717)(206,711)(207,715)
(208,714)(209,713)(210,712)(211,661)(212,665)(213,664)(214,663)(215,662)
(216,671)(217,675)(218,674)(219,673)(220,672)(221,666)(222,670)(223,669)
(224,668)(225,667)(226,676)(227,680)(228,679)(229,678)(230,677)(231,686)
(232,690)(233,689)(234,688)(235,687)(236,681)(237,685)(238,684)(239,683)
(240,682)(241,721)(242,725)(243,724)(244,723)(245,722)(246,731)(247,735)
(248,734)(249,733)(250,732)(251,726)(252,730)(253,729)(254,728)(255,727)
(256,736)(257,740)(258,739)(259,738)(260,737)(261,746)(262,750)(263,749)
(264,748)(265,747)(266,741)(267,745)(268,744)(269,743)(270,742)(271,766)
(272,770)(273,769)(274,768)(275,767)(276,776)(277,780)(278,779)(279,778)
(280,777)(281,771)(282,775)(283,774)(284,773)(285,772)(286,751)(287,755)
(288,754)(289,753)(290,752)(291,761)(292,765)(293,764)(294,763)(295,762)
(296,756)(297,760)(298,759)(299,758)(300,757)(301,781)(302,785)(303,784)
(304,783)(305,782)(306,791)(307,795)(308,794)(309,793)(310,792)(311,786)
(312,790)(313,789)(314,788)(315,787)(316,796)(317,800)(318,799)(319,798)
(320,797)(321,806)(322,810)(323,809)(324,808)(325,807)(326,801)(327,805)
(328,804)(329,803)(330,802)(331,826)(332,830)(333,829)(334,828)(335,827)
(336,836)(337,840)(338,839)(339,838)(340,837)(341,831)(342,835)(343,834)
(344,833)(345,832)(346,811)(347,815)(348,814)(349,813)(350,812)(351,821)
(352,825)(353,824)(354,823)(355,822)(356,816)(357,820)(358,819)(359,818)
(360,817)(361,871)(362,875)(363,874)(364,873)(365,872)(366,881)(367,885)
(368,884)(369,883)(370,882)(371,876)(372,880)(373,879)(374,878)(375,877)
(376,886)(377,890)(378,889)(379,888)(380,887)(381,896)(382,900)(383,899)
(384,898)(385,897)(386,891)(387,895)(388,894)(389,893)(390,892)(391,841)
(392,845)(393,844)(394,843)(395,842)(396,851)(397,855)(398,854)(399,853)
(400,852)(401,846)(402,850)(403,849)(404,848)(405,847)(406,856)(407,860)
(408,859)(409,858)(410,857)(411,866)(412,870)(413,869)(414,868)(415,867)
(416,861)(417,865)(418,864)(419,863)(420,862)(421,931)(422,935)(423,934)
(424,933)(425,932)(426,941)(427,945)(428,944)(429,943)(430,942)(431,936)
(432,940)(433,939)(434,938)(435,937)(436,946)(437,950)(438,949)(439,948)
(440,947)(441,956)(442,960)(443,959)(444,958)(445,957)(446,951)(447,955)
(448,954)(449,953)(450,952)(451,901)(452,905)(453,904)(454,903)(455,902)
(456,911)(457,915)(458,914)(459,913)(460,912)(461,906)(462,910)(463,909)
(464,908)(465,907)(466,916)(467,920)(468,919)(469,918)(470,917)(471,926)
(472,930)(473,929)(474,928)(475,927)(476,921)(477,925)(478,924)(479,923)
(480,922);
s1 := Sym(960)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 67)( 62, 66)
( 63, 70)( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 87)( 88, 90)( 91,112)( 92,111)( 93,115)( 94,114)
( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)
(103,120)(104,119)(105,118)(121,157)(122,156)(123,160)(124,159)(125,158)
(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)
(134,164)(135,163)(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)
(142,166)(143,170)(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)
(150,178)(181,217)(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)
(188,215)(189,214)(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)
(196,232)(197,231)(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)
(204,229)(205,228)(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)
(242,306)(243,310)(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)
(250,303)(251,312)(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)
(258,325)(259,324)(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)
(266,327)(267,326)(268,330)(269,329)(270,328)(271,352)(272,351)(273,355)
(274,354)(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)
(282,356)(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)
(290,338)(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)
(298,345)(299,344)(300,343)(361,457)(362,456)(363,460)(364,459)(365,458)
(366,452)(367,451)(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)
(374,464)(375,463)(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)
(382,466)(383,470)(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)
(390,478)(391,427)(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)
(398,425)(399,424)(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)
(406,442)(407,441)(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)
(414,439)(415,438)(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)
(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)
(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)
(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)
(506,627)(507,626)(508,630)(509,629)(510,628)(511,652)(512,651)(513,655)
(514,654)(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)
(522,656)(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)
(530,638)(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)
(538,645)(539,644)(540,643)(541,667)(542,666)(543,670)(544,669)(545,668)
(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)
(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)
(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)
(570,688)(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)
(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)
(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)
(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,907)
(722,906)(723,910)(724,909)(725,908)(726,902)(727,901)(728,905)(729,904)
(730,903)(731,912)(732,911)(733,915)(734,914)(735,913)(736,922)(737,921)
(738,925)(739,924)(740,923)(741,917)(742,916)(743,920)(744,919)(745,918)
(746,927)(747,926)(748,930)(749,929)(750,928)(751,952)(752,951)(753,955)
(754,954)(755,953)(756,947)(757,946)(758,950)(759,949)(760,948)(761,957)
(762,956)(763,960)(764,959)(765,958)(766,937)(767,936)(768,940)(769,939)
(770,938)(771,932)(772,931)(773,935)(774,934)(775,933)(776,942)(777,941)
(778,945)(779,944)(780,943)(781,847)(782,846)(783,850)(784,849)(785,848)
(786,842)(787,841)(788,845)(789,844)(790,843)(791,852)(792,851)(793,855)
(794,854)(795,853)(796,862)(797,861)(798,865)(799,864)(800,863)(801,857)
(802,856)(803,860)(804,859)(805,858)(806,867)(807,866)(808,870)(809,869)
(810,868)(811,892)(812,891)(813,895)(814,894)(815,893)(816,887)(817,886)
(818,890)(819,889)(820,888)(821,897)(822,896)(823,900)(824,899)(825,898)
(826,877)(827,876)(828,880)(829,879)(830,878)(831,872)(832,871)(833,875)
(834,874)(835,873)(836,882)(837,881)(838,885)(839,884)(840,883);
s2 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope