Polytope of Type {16,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,60}*1920b
if this polytope has a name.
Group : SmallGroup(1920,42007)
Rank : 3
Schlafli Type : {16,60}
Number of vertices, edges, etc : 16, 480, 60
Order of s0s1s2 : 240
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 : {8,60}*960a
3-fold quotients : {16,20}*640b
4-fold quotients : {4,60}*480a, {8,30}*480
5-fold quotients : {16,12}*384b
6-fold quotients : {8,20}*320a
8-fold quotients : {2,60}*240, {4,30}*240a
10-fold quotients : {8,12}*192a
12-fold quotients : {4,20}*160, {8,10}*160
15-fold quotients : {16,4}*128b
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
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)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)( 96,576)
( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)(112,592)
(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)(120,600)
(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)(181,706)(182,707)(183,708)(184,709)
(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)(192,717)
(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)(200,695)
(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)(208,703)
(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)(216,681)
(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)(224,689)
(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)(240,675)
(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)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,811)(332,812)(333,813)(334,814)(335,815)(336,816)
(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)(344,824)
(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)(352,832)
(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)(360,840)
(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)(421,946)(422,947)(423,948)(424,949)
(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)(432,957)
(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)(440,935)
(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)(448,943)
(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)(456,921)
(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)(464,929)
(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)(472,907)
(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)(480,915);;
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)(721,916)(722,920)
(723,919)(724,918)(725,917)(726,926)(727,930)(728,929)(729,928)(730,927)
(731,921)(732,925)(733,924)(734,923)(735,922)(736,901)(737,905)(738,904)
(739,903)(740,902)(741,911)(742,915)(743,914)(744,913)(745,912)(746,906)
(747,910)(748,909)(749,908)(750,907)(751,931)(752,935)(753,934)(754,933)
(755,932)(756,941)(757,945)(758,944)(759,943)(760,942)(761,936)(762,940)
(763,939)(764,938)(765,937)(766,946)(767,950)(768,949)(769,948)(770,947)
(771,956)(772,960)(773,959)(774,958)(775,957)(776,951)(777,955)(778,954)
(779,953)(780,952)(781,856)(782,860)(783,859)(784,858)(785,857)(786,866)
(787,870)(788,869)(789,868)(790,867)(791,861)(792,865)(793,864)(794,863)
(795,862)(796,841)(797,845)(798,844)(799,843)(800,842)(801,851)(802,855)
(803,854)(804,853)(805,852)(806,846)(807,850)(808,849)(809,848)(810,847)
(811,871)(812,875)(813,874)(814,873)(815,872)(816,881)(817,885)(818,884)
(819,883)(820,882)(821,876)(822,880)(823,879)(824,878)(825,877)(826,886)
(827,890)(828,889)(829,888)(830,887)(831,896)(832,900)(833,899)(834,898)
(835,897)(836,891)(837,895)(838,894)(839,893)(840,892);;
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)
(121,382)(122,381)(123,385)(124,384)(125,383)(126,377)(127,376)(128,380)
(129,379)(130,378)(131,387)(132,386)(133,390)(134,389)(135,388)(136,367)
(137,366)(138,370)(139,369)(140,368)(141,362)(142,361)(143,365)(144,364)
(145,363)(146,372)(147,371)(148,375)(149,374)(150,373)(151,412)(152,411)
(153,415)(154,414)(155,413)(156,407)(157,406)(158,410)(159,409)(160,408)
(161,417)(162,416)(163,420)(164,419)(165,418)(166,397)(167,396)(168,400)
(169,399)(170,398)(171,392)(172,391)(173,395)(174,394)(175,393)(176,402)
(177,401)(178,405)(179,404)(180,403)(181,442)(182,441)(183,445)(184,444)
(185,443)(186,437)(187,436)(188,440)(189,439)(190,438)(191,447)(192,446)
(193,450)(194,449)(195,448)(196,427)(197,426)(198,430)(199,429)(200,428)
(201,422)(202,421)(203,425)(204,424)(205,423)(206,432)(207,431)(208,435)
(209,434)(210,433)(211,472)(212,471)(213,475)(214,474)(215,473)(216,467)
(217,466)(218,470)(219,469)(220,468)(221,477)(222,476)(223,480)(224,479)
(225,478)(226,457)(227,456)(228,460)(229,459)(230,458)(231,452)(232,451)
(233,455)(234,454)(235,453)(236,462)(237,461)(238,465)(239,464)(240,463)
(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)
(601,862)(602,861)(603,865)(604,864)(605,863)(606,857)(607,856)(608,860)
(609,859)(610,858)(611,867)(612,866)(613,870)(614,869)(615,868)(616,847)
(617,846)(618,850)(619,849)(620,848)(621,842)(622,841)(623,845)(624,844)
(625,843)(626,852)(627,851)(628,855)(629,854)(630,853)(631,892)(632,891)
(633,895)(634,894)(635,893)(636,887)(637,886)(638,890)(639,889)(640,888)
(641,897)(642,896)(643,900)(644,899)(645,898)(646,877)(647,876)(648,880)
(649,879)(650,878)(651,872)(652,871)(653,875)(654,874)(655,873)(656,882)
(657,881)(658,885)(659,884)(660,883)(661,922)(662,921)(663,925)(664,924)
(665,923)(666,917)(667,916)(668,920)(669,919)(670,918)(671,927)(672,926)
(673,930)(674,929)(675,928)(676,907)(677,906)(678,910)(679,909)(680,908)
(681,902)(682,901)(683,905)(684,904)(685,903)(686,912)(687,911)(688,915)
(689,914)(690,913)(691,952)(692,951)(693,955)(694,954)(695,953)(696,947)
(697,946)(698,950)(699,949)(700,948)(701,957)(702,956)(703,960)(704,959)
(705,958)(706,937)(707,936)(708,940)(709,939)(710,938)(711,932)(712,931)
(713,935)(714,934)(715,933)(716,942)(717,941)(718,945)(719,944)(720,943);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*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)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,571)( 92,572)( 93,573)( 94,574)( 95,575)
( 96,576)( 97,577)( 98,578)( 99,579)(100,580)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,586)(107,587)(108,588)(109,589)(110,590)(111,591)
(112,592)(113,593)(114,594)(115,595)(116,596)(117,597)(118,598)(119,599)
(120,600)(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)(181,706)(182,707)(183,708)
(184,709)(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)
(192,717)(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)
(200,695)(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)
(208,703)(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)
(216,681)(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)
(224,689)(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)
(232,667)(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)
(240,675)(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)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,811)(332,812)(333,813)(334,814)(335,815)
(336,816)(337,817)(338,818)(339,819)(340,820)(341,821)(342,822)(343,823)
(344,824)(345,825)(346,826)(347,827)(348,828)(349,829)(350,830)(351,831)
(352,832)(353,833)(354,834)(355,835)(356,836)(357,837)(358,838)(359,839)
(360,840)(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)(421,946)(422,947)(423,948)
(424,949)(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)
(432,957)(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)
(440,935)(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)
(448,943)(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)
(456,921)(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)
(464,929)(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)
(472,907)(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)
(480,915);
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)(721,916)
(722,920)(723,919)(724,918)(725,917)(726,926)(727,930)(728,929)(729,928)
(730,927)(731,921)(732,925)(733,924)(734,923)(735,922)(736,901)(737,905)
(738,904)(739,903)(740,902)(741,911)(742,915)(743,914)(744,913)(745,912)
(746,906)(747,910)(748,909)(749,908)(750,907)(751,931)(752,935)(753,934)
(754,933)(755,932)(756,941)(757,945)(758,944)(759,943)(760,942)(761,936)
(762,940)(763,939)(764,938)(765,937)(766,946)(767,950)(768,949)(769,948)
(770,947)(771,956)(772,960)(773,959)(774,958)(775,957)(776,951)(777,955)
(778,954)(779,953)(780,952)(781,856)(782,860)(783,859)(784,858)(785,857)
(786,866)(787,870)(788,869)(789,868)(790,867)(791,861)(792,865)(793,864)
(794,863)(795,862)(796,841)(797,845)(798,844)(799,843)(800,842)(801,851)
(802,855)(803,854)(804,853)(805,852)(806,846)(807,850)(808,849)(809,848)
(810,847)(811,871)(812,875)(813,874)(814,873)(815,872)(816,881)(817,885)
(818,884)(819,883)(820,882)(821,876)(822,880)(823,879)(824,878)(825,877)
(826,886)(827,890)(828,889)(829,888)(830,887)(831,896)(832,900)(833,899)
(834,898)(835,897)(836,891)(837,895)(838,894)(839,893)(840,892);
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)(121,382)(122,381)(123,385)(124,384)(125,383)(126,377)(127,376)
(128,380)(129,379)(130,378)(131,387)(132,386)(133,390)(134,389)(135,388)
(136,367)(137,366)(138,370)(139,369)(140,368)(141,362)(142,361)(143,365)
(144,364)(145,363)(146,372)(147,371)(148,375)(149,374)(150,373)(151,412)
(152,411)(153,415)(154,414)(155,413)(156,407)(157,406)(158,410)(159,409)
(160,408)(161,417)(162,416)(163,420)(164,419)(165,418)(166,397)(167,396)
(168,400)(169,399)(170,398)(171,392)(172,391)(173,395)(174,394)(175,393)
(176,402)(177,401)(178,405)(179,404)(180,403)(181,442)(182,441)(183,445)
(184,444)(185,443)(186,437)(187,436)(188,440)(189,439)(190,438)(191,447)
(192,446)(193,450)(194,449)(195,448)(196,427)(197,426)(198,430)(199,429)
(200,428)(201,422)(202,421)(203,425)(204,424)(205,423)(206,432)(207,431)
(208,435)(209,434)(210,433)(211,472)(212,471)(213,475)(214,474)(215,473)
(216,467)(217,466)(218,470)(219,469)(220,468)(221,477)(222,476)(223,480)
(224,479)(225,478)(226,457)(227,456)(228,460)(229,459)(230,458)(231,452)
(232,451)(233,455)(234,454)(235,453)(236,462)(237,461)(238,465)(239,464)
(240,463)(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)(601,862)(602,861)(603,865)(604,864)(605,863)(606,857)(607,856)
(608,860)(609,859)(610,858)(611,867)(612,866)(613,870)(614,869)(615,868)
(616,847)(617,846)(618,850)(619,849)(620,848)(621,842)(622,841)(623,845)
(624,844)(625,843)(626,852)(627,851)(628,855)(629,854)(630,853)(631,892)
(632,891)(633,895)(634,894)(635,893)(636,887)(637,886)(638,890)(639,889)
(640,888)(641,897)(642,896)(643,900)(644,899)(645,898)(646,877)(647,876)
(648,880)(649,879)(650,878)(651,872)(652,871)(653,875)(654,874)(655,873)
(656,882)(657,881)(658,885)(659,884)(660,883)(661,922)(662,921)(663,925)
(664,924)(665,923)(666,917)(667,916)(668,920)(669,919)(670,918)(671,927)
(672,926)(673,930)(674,929)(675,928)(676,907)(677,906)(678,910)(679,909)
(680,908)(681,902)(682,901)(683,905)(684,904)(685,903)(686,912)(687,911)
(688,915)(689,914)(690,913)(691,952)(692,951)(693,955)(694,954)(695,953)
(696,947)(697,946)(698,950)(699,949)(700,948)(701,957)(702,956)(703,960)
(704,959)(705,958)(706,937)(707,936)(708,940)(709,939)(710,938)(711,932)
(712,931)(713,935)(714,934)(715,933)(716,942)(717,941)(718,945)(719,944)
(720,943);
poly := sub<Sym(960)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*s1*s2 >;
References : None.
to this polytope