Polytope of Type {16,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,60}*1920a
Also Known As : {16,60|2}. if this polytope has another name.
Group : SmallGroup(1920,41725)
Rank : 3
Schlafli Type : {16,60}
Number of vertices, edges, etc : 16, 480, 60
Order of s0s1s2 : 240
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 : {8,60}*960a, {16,30}*960
3-fold quotients : {16,20}*640a
4-fold quotients : {4,60}*480a, {8,30}*480
5-fold quotients : {16,12}*384a
6-fold quotients : {8,20}*320a, {16,10}*320
8-fold quotients : {2,60}*240, {4,30}*240a
10-fold quotients : {8,12}*192a, {16,6}*192
12-fold quotients : {4,20}*160, {8,10}*160
15-fold quotients : {16,4}*128a
16-fold quotients : {2,30}*120
20-fold quotients : {4,12}*96a, {8,6}*96
24-fold quotients : {2,20}*80, {4,10}*80
30-fold quotients : {8,4}*64a, {16,2}*64
32-fold quotients : {2,15}*60
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {2,10}*40
60-fold quotients : {4,4}*32, {8,2}*32
80-fold quotients : {2,6}*24
96-fold quotients : {2,5}*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 := ( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)
( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)( 32,527)
( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)( 40,535)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)( 48,513)
( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 61,541)( 62,542)( 63,543)( 64,544)
( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)( 72,552)
( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)( 80,560)
( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)( 88,568)
( 89,569)( 90,570)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)(184,694)
(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)(192,702)
(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)(200,710)
(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)(208,718)
(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)(216,666)
(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)(224,674)
(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)(232,682)
(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)(240,690)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)(272,767)
(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)(280,775)
(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)(288,753)
(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)(296,761)
(297,762)(298,763)(299,764)(300,765)(301,781)(302,782)(303,783)(304,784)
(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)(312,792)
(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)(320,800)
(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)(328,808)
(329,809)(330,810)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)(424,934)
(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)(432,942)
(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)(440,950)
(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)(448,958)
(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)(456,906)
(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)(464,914)
(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)(472,922)
(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)(480,930);;
s1 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)
( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)
( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)
(104,113)(105,112)(121,151)(122,155)(123,154)(124,153)(125,152)(126,161)
(127,165)(128,164)(129,163)(130,162)(131,156)(132,160)(133,159)(134,158)
(135,157)(136,166)(137,170)(138,169)(139,168)(140,167)(141,176)(142,180)
(143,179)(144,178)(145,177)(146,171)(147,175)(148,174)(149,173)(150,172)
(181,211)(182,215)(183,214)(184,213)(185,212)(186,221)(187,225)(188,224)
(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)(196,226)
(197,230)(198,229)(199,228)(200,227)(201,236)(202,240)(203,239)(204,238)
(205,237)(206,231)(207,235)(208,234)(209,233)(210,232)(241,301)(242,305)
(243,304)(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)(250,312)
(251,306)(252,310)(253,309)(254,308)(255,307)(256,316)(257,320)(258,319)
(259,318)(260,317)(261,326)(262,330)(263,329)(264,328)(265,327)(266,321)
(267,325)(268,324)(269,323)(270,322)(271,346)(272,350)(273,349)(274,348)
(275,347)(276,356)(277,360)(278,359)(279,358)(280,357)(281,351)(282,355)
(283,354)(284,353)(285,352)(286,331)(287,335)(288,334)(289,333)(290,332)
(291,341)(292,345)(293,344)(294,343)(295,342)(296,336)(297,340)(298,339)
(299,338)(300,337)(361,451)(362,455)(363,454)(364,453)(365,452)(366,461)
(367,465)(368,464)(369,463)(370,462)(371,456)(372,460)(373,459)(374,458)
(375,457)(376,466)(377,470)(378,469)(379,468)(380,467)(381,476)(382,480)
(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)(390,472)
(391,421)(392,425)(393,424)(394,423)(395,422)(396,431)(397,435)(398,434)
(399,433)(400,432)(401,426)(402,430)(403,429)(404,428)(405,427)(406,436)
(407,440)(408,439)(409,438)(410,437)(411,446)(412,450)(413,449)(414,448)
(415,447)(416,441)(417,445)(418,444)(419,443)(420,442)(481,601)(482,605)
(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)(490,612)
(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)(498,619)
(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)(506,621)
(507,625)(508,624)(509,623)(510,622)(511,646)(512,650)(513,649)(514,648)
(515,647)(516,656)(517,660)(518,659)(519,658)(520,657)(521,651)(522,655)
(523,654)(524,653)(525,652)(526,631)(527,635)(528,634)(529,633)(530,632)
(531,641)(532,645)(533,644)(534,643)(535,642)(536,636)(537,640)(538,639)
(539,638)(540,637)(541,661)(542,665)(543,664)(544,663)(545,662)(546,671)
(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)(553,669)(554,668)
(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)(561,686)(562,690)
(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)(569,683)(570,682)
(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)
(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)
(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)
(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,901)(722,905)
(723,904)(724,903)(725,902)(726,911)(727,915)(728,914)(729,913)(730,912)
(731,906)(732,910)(733,909)(734,908)(735,907)(736,916)(737,920)(738,919)
(739,918)(740,917)(741,926)(742,930)(743,929)(744,928)(745,927)(746,921)
(747,925)(748,924)(749,923)(750,922)(751,946)(752,950)(753,949)(754,948)
(755,947)(756,956)(757,960)(758,959)(759,958)(760,957)(761,951)(762,955)
(763,954)(764,953)(765,952)(766,931)(767,935)(768,934)(769,933)(770,932)
(771,941)(772,945)(773,944)(774,943)(775,942)(776,936)(777,940)(778,939)
(779,938)(780,937)(781,841)(782,845)(783,844)(784,843)(785,842)(786,851)
(787,855)(788,854)(789,853)(790,852)(791,846)(792,850)(793,849)(794,848)
(795,847)(796,856)(797,860)(798,859)(799,858)(800,857)(801,866)(802,870)
(803,869)(804,868)(805,867)(806,861)(807,865)(808,864)(809,863)(810,862)
(811,886)(812,890)(813,889)(814,888)(815,887)(816,896)(817,900)(818,899)
(819,898)(820,897)(821,891)(822,895)(823,894)(824,893)(825,892)(826,871)
(827,875)(828,874)(829,873)(830,872)(831,881)(832,885)(833,884)(834,883)
(835,882)(836,876)(837,880)(838,879)(839,878)(840,877);;
s2 := ( 1,247)( 2,246)( 3,250)( 4,249)( 5,248)( 6,242)( 7,241)( 8,245)
( 9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,262)
( 17,261)( 18,265)( 19,264)( 20,263)( 21,257)( 22,256)( 23,260)( 24,259)
( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,277)( 32,276)
( 33,280)( 34,279)( 35,278)( 36,272)( 37,271)( 38,275)( 39,274)( 40,273)
( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,292)( 47,291)( 48,295)
( 49,294)( 50,293)( 51,287)( 52,286)( 53,290)( 54,289)( 55,288)( 56,297)
( 57,296)( 58,300)( 59,299)( 60,298)( 61,307)( 62,306)( 63,310)( 64,309)
( 65,308)( 66,302)( 67,301)( 68,305)( 69,304)( 70,303)( 71,312)( 72,311)
( 73,315)( 74,314)( 75,313)( 76,322)( 77,321)( 78,325)( 79,324)( 80,323)
( 81,317)( 82,316)( 83,320)( 84,319)( 85,318)( 86,327)( 87,326)( 88,330)
( 89,329)( 90,328)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)( 96,332)
( 97,331)( 98,335)( 99,334)(100,333)(101,342)(102,341)(103,345)(104,344)
(105,343)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)(112,346)
(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)(120,358)
(121,367)(122,366)(123,370)(124,369)(125,368)(126,362)(127,361)(128,365)
(129,364)(130,363)(131,372)(132,371)(133,375)(134,374)(135,373)(136,382)
(137,381)(138,385)(139,384)(140,383)(141,377)(142,376)(143,380)(144,379)
(145,378)(146,387)(147,386)(148,390)(149,389)(150,388)(151,397)(152,396)
(153,400)(154,399)(155,398)(156,392)(157,391)(158,395)(159,394)(160,393)
(161,402)(162,401)(163,405)(164,404)(165,403)(166,412)(167,411)(168,415)
(169,414)(170,413)(171,407)(172,406)(173,410)(174,409)(175,408)(176,417)
(177,416)(178,420)(179,419)(180,418)(181,427)(182,426)(183,430)(184,429)
(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)(192,431)
(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)(200,443)
(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)(208,450)
(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)(216,452)
(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)(224,464)
(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)(232,466)
(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)(240,478)
(481,727)(482,726)(483,730)(484,729)(485,728)(486,722)(487,721)(488,725)
(489,724)(490,723)(491,732)(492,731)(493,735)(494,734)(495,733)(496,742)
(497,741)(498,745)(499,744)(500,743)(501,737)(502,736)(503,740)(504,739)
(505,738)(506,747)(507,746)(508,750)(509,749)(510,748)(511,757)(512,756)
(513,760)(514,759)(515,758)(516,752)(517,751)(518,755)(519,754)(520,753)
(521,762)(522,761)(523,765)(524,764)(525,763)(526,772)(527,771)(528,775)
(529,774)(530,773)(531,767)(532,766)(533,770)(534,769)(535,768)(536,777)
(537,776)(538,780)(539,779)(540,778)(541,787)(542,786)(543,790)(544,789)
(545,788)(546,782)(547,781)(548,785)(549,784)(550,783)(551,792)(552,791)
(553,795)(554,794)(555,793)(556,802)(557,801)(558,805)(559,804)(560,803)
(561,797)(562,796)(563,800)(564,799)(565,798)(566,807)(567,806)(568,810)
(569,809)(570,808)(571,817)(572,816)(573,820)(574,819)(575,818)(576,812)
(577,811)(578,815)(579,814)(580,813)(581,822)(582,821)(583,825)(584,824)
(585,823)(586,832)(587,831)(588,835)(589,834)(590,833)(591,827)(592,826)
(593,830)(594,829)(595,828)(596,837)(597,836)(598,840)(599,839)(600,838)
(601,847)(602,846)(603,850)(604,849)(605,848)(606,842)(607,841)(608,845)
(609,844)(610,843)(611,852)(612,851)(613,855)(614,854)(615,853)(616,862)
(617,861)(618,865)(619,864)(620,863)(621,857)(622,856)(623,860)(624,859)
(625,858)(626,867)(627,866)(628,870)(629,869)(630,868)(631,877)(632,876)
(633,880)(634,879)(635,878)(636,872)(637,871)(638,875)(639,874)(640,873)
(641,882)(642,881)(643,885)(644,884)(645,883)(646,892)(647,891)(648,895)
(649,894)(650,893)(651,887)(652,886)(653,890)(654,889)(655,888)(656,897)
(657,896)(658,900)(659,899)(660,898)(661,907)(662,906)(663,910)(664,909)
(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)(672,911)
(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)(680,923)
(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)(688,930)
(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)(696,932)
(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)(704,944)
(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)(712,946)
(713,950)(714,949)(715,948)(716,957)(717,956)(718,960)(719,959)(720,958);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)
( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)
( 32,527)( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)
( 40,535)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)
( 48,513)( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 61,541)( 62,542)( 63,543)
( 64,544)( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)
( 72,552)( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)
( 80,560)( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)
( 88,568)( 89,569)( 90,570)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,691)(182,692)(183,693)
(184,694)(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)
(192,702)(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)
(200,710)(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)
(208,718)(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)
(216,666)(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)
(224,674)(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)
(232,682)(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)
(240,690)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)
(272,767)(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)
(280,775)(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)
(288,753)(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)
(296,761)(297,762)(298,763)(299,764)(300,765)(301,781)(302,782)(303,783)
(304,784)(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)
(312,792)(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)
(320,800)(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)
(328,808)(329,809)(330,810)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,931)(422,932)(423,933)
(424,934)(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)
(432,942)(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)
(440,950)(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)
(448,958)(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)
(456,906)(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)
(464,914)(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)
(472,922)(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)
(480,930);
s1 := Sym(960)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)
( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 62, 65)( 63, 64)
( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)
( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,106)( 92,110)( 93,109)( 94,108)
( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)
(103,114)(104,113)(105,112)(121,151)(122,155)(123,154)(124,153)(125,152)
(126,161)(127,165)(128,164)(129,163)(130,162)(131,156)(132,160)(133,159)
(134,158)(135,157)(136,166)(137,170)(138,169)(139,168)(140,167)(141,176)
(142,180)(143,179)(144,178)(145,177)(146,171)(147,175)(148,174)(149,173)
(150,172)(181,211)(182,215)(183,214)(184,213)(185,212)(186,221)(187,225)
(188,224)(189,223)(190,222)(191,216)(192,220)(193,219)(194,218)(195,217)
(196,226)(197,230)(198,229)(199,228)(200,227)(201,236)(202,240)(203,239)
(204,238)(205,237)(206,231)(207,235)(208,234)(209,233)(210,232)(241,301)
(242,305)(243,304)(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)
(250,312)(251,306)(252,310)(253,309)(254,308)(255,307)(256,316)(257,320)
(258,319)(259,318)(260,317)(261,326)(262,330)(263,329)(264,328)(265,327)
(266,321)(267,325)(268,324)(269,323)(270,322)(271,346)(272,350)(273,349)
(274,348)(275,347)(276,356)(277,360)(278,359)(279,358)(280,357)(281,351)
(282,355)(283,354)(284,353)(285,352)(286,331)(287,335)(288,334)(289,333)
(290,332)(291,341)(292,345)(293,344)(294,343)(295,342)(296,336)(297,340)
(298,339)(299,338)(300,337)(361,451)(362,455)(363,454)(364,453)(365,452)
(366,461)(367,465)(368,464)(369,463)(370,462)(371,456)(372,460)(373,459)
(374,458)(375,457)(376,466)(377,470)(378,469)(379,468)(380,467)(381,476)
(382,480)(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)
(390,472)(391,421)(392,425)(393,424)(394,423)(395,422)(396,431)(397,435)
(398,434)(399,433)(400,432)(401,426)(402,430)(403,429)(404,428)(405,427)
(406,436)(407,440)(408,439)(409,438)(410,437)(411,446)(412,450)(413,449)
(414,448)(415,447)(416,441)(417,445)(418,444)(419,443)(420,442)(481,601)
(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)
(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)
(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)
(506,621)(507,625)(508,624)(509,623)(510,622)(511,646)(512,650)(513,649)
(514,648)(515,647)(516,656)(517,660)(518,659)(519,658)(520,657)(521,651)
(522,655)(523,654)(524,653)(525,652)(526,631)(527,635)(528,634)(529,633)
(530,632)(531,641)(532,645)(533,644)(534,643)(535,642)(536,636)(537,640)
(538,639)(539,638)(540,637)(541,661)(542,665)(543,664)(544,663)(545,662)
(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)(553,669)
(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)(561,686)
(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)(569,683)
(570,682)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)
(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)
(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)
(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(721,901)
(722,905)(723,904)(724,903)(725,902)(726,911)(727,915)(728,914)(729,913)
(730,912)(731,906)(732,910)(733,909)(734,908)(735,907)(736,916)(737,920)
(738,919)(739,918)(740,917)(741,926)(742,930)(743,929)(744,928)(745,927)
(746,921)(747,925)(748,924)(749,923)(750,922)(751,946)(752,950)(753,949)
(754,948)(755,947)(756,956)(757,960)(758,959)(759,958)(760,957)(761,951)
(762,955)(763,954)(764,953)(765,952)(766,931)(767,935)(768,934)(769,933)
(770,932)(771,941)(772,945)(773,944)(774,943)(775,942)(776,936)(777,940)
(778,939)(779,938)(780,937)(781,841)(782,845)(783,844)(784,843)(785,842)
(786,851)(787,855)(788,854)(789,853)(790,852)(791,846)(792,850)(793,849)
(794,848)(795,847)(796,856)(797,860)(798,859)(799,858)(800,857)(801,866)
(802,870)(803,869)(804,868)(805,867)(806,861)(807,865)(808,864)(809,863)
(810,862)(811,886)(812,890)(813,889)(814,888)(815,887)(816,896)(817,900)
(818,899)(819,898)(820,897)(821,891)(822,895)(823,894)(824,893)(825,892)
(826,871)(827,875)(828,874)(829,873)(830,872)(831,881)(832,885)(833,884)
(834,883)(835,882)(836,876)(837,880)(838,879)(839,878)(840,877);
s2 := Sym(960)!( 1,247)( 2,246)( 3,250)( 4,249)( 5,248)( 6,242)( 7,241)
( 8,245)( 9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)
( 16,262)( 17,261)( 18,265)( 19,264)( 20,263)( 21,257)( 22,256)( 23,260)
( 24,259)( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,277)
( 32,276)( 33,280)( 34,279)( 35,278)( 36,272)( 37,271)( 38,275)( 39,274)
( 40,273)( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,292)( 47,291)
( 48,295)( 49,294)( 50,293)( 51,287)( 52,286)( 53,290)( 54,289)( 55,288)
( 56,297)( 57,296)( 58,300)( 59,299)( 60,298)( 61,307)( 62,306)( 63,310)
( 64,309)( 65,308)( 66,302)( 67,301)( 68,305)( 69,304)( 70,303)( 71,312)
( 72,311)( 73,315)( 74,314)( 75,313)( 76,322)( 77,321)( 78,325)( 79,324)
( 80,323)( 81,317)( 82,316)( 83,320)( 84,319)( 85,318)( 86,327)( 87,326)
( 88,330)( 89,329)( 90,328)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)
( 96,332)( 97,331)( 98,335)( 99,334)(100,333)(101,342)(102,341)(103,345)
(104,344)(105,343)(106,352)(107,351)(108,355)(109,354)(110,353)(111,347)
(112,346)(113,350)(114,349)(115,348)(116,357)(117,356)(118,360)(119,359)
(120,358)(121,367)(122,366)(123,370)(124,369)(125,368)(126,362)(127,361)
(128,365)(129,364)(130,363)(131,372)(132,371)(133,375)(134,374)(135,373)
(136,382)(137,381)(138,385)(139,384)(140,383)(141,377)(142,376)(143,380)
(144,379)(145,378)(146,387)(147,386)(148,390)(149,389)(150,388)(151,397)
(152,396)(153,400)(154,399)(155,398)(156,392)(157,391)(158,395)(159,394)
(160,393)(161,402)(162,401)(163,405)(164,404)(165,403)(166,412)(167,411)
(168,415)(169,414)(170,413)(171,407)(172,406)(173,410)(174,409)(175,408)
(176,417)(177,416)(178,420)(179,419)(180,418)(181,427)(182,426)(183,430)
(184,429)(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)
(192,431)(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)
(200,443)(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)
(208,450)(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)
(216,452)(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)
(224,464)(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)
(232,466)(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)
(240,478)(481,727)(482,726)(483,730)(484,729)(485,728)(486,722)(487,721)
(488,725)(489,724)(490,723)(491,732)(492,731)(493,735)(494,734)(495,733)
(496,742)(497,741)(498,745)(499,744)(500,743)(501,737)(502,736)(503,740)
(504,739)(505,738)(506,747)(507,746)(508,750)(509,749)(510,748)(511,757)
(512,756)(513,760)(514,759)(515,758)(516,752)(517,751)(518,755)(519,754)
(520,753)(521,762)(522,761)(523,765)(524,764)(525,763)(526,772)(527,771)
(528,775)(529,774)(530,773)(531,767)(532,766)(533,770)(534,769)(535,768)
(536,777)(537,776)(538,780)(539,779)(540,778)(541,787)(542,786)(543,790)
(544,789)(545,788)(546,782)(547,781)(548,785)(549,784)(550,783)(551,792)
(552,791)(553,795)(554,794)(555,793)(556,802)(557,801)(558,805)(559,804)
(560,803)(561,797)(562,796)(563,800)(564,799)(565,798)(566,807)(567,806)
(568,810)(569,809)(570,808)(571,817)(572,816)(573,820)(574,819)(575,818)
(576,812)(577,811)(578,815)(579,814)(580,813)(581,822)(582,821)(583,825)
(584,824)(585,823)(586,832)(587,831)(588,835)(589,834)(590,833)(591,827)
(592,826)(593,830)(594,829)(595,828)(596,837)(597,836)(598,840)(599,839)
(600,838)(601,847)(602,846)(603,850)(604,849)(605,848)(606,842)(607,841)
(608,845)(609,844)(610,843)(611,852)(612,851)(613,855)(614,854)(615,853)
(616,862)(617,861)(618,865)(619,864)(620,863)(621,857)(622,856)(623,860)
(624,859)(625,858)(626,867)(627,866)(628,870)(629,869)(630,868)(631,877)
(632,876)(633,880)(634,879)(635,878)(636,872)(637,871)(638,875)(639,874)
(640,873)(641,882)(642,881)(643,885)(644,884)(645,883)(646,892)(647,891)
(648,895)(649,894)(650,893)(651,887)(652,886)(653,890)(654,889)(655,888)
(656,897)(657,896)(658,900)(659,899)(660,898)(661,907)(662,906)(663,910)
(664,909)(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)
(672,911)(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)
(680,923)(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)
(688,930)(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)
(696,932)(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)
(704,944)(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)
(712,946)(713,950)(714,949)(715,948)(716,957)(717,956)(718,960)(719,959)
(720,958);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope