Polytope of Type {120,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,13387)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 240, 480, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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, {60,4}*960a, {120,4}*960b
3-fold quotients : {40,4}*640a
4-fold quotients : {60,4}*480a, {120,2}*480
5-fold quotients : {24,4}*384a
6-fold quotients : {40,4}*320a, {20,4}*320, {40,4}*320b
8-fold quotients : {60,2}*240, {30,4}*240a
10-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b
12-fold quotients : {20,4}*160, {40,2}*160
15-fold quotients : {8,4}*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, {8,4}*64b, {4,4}*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)( 31,511)( 32,515)
( 33,514)( 34,513)( 35,512)( 36,521)( 37,525)( 38,524)( 39,523)( 40,522)
( 41,516)( 42,520)( 43,519)( 44,518)( 45,517)( 46,526)( 47,530)( 48,529)
( 49,528)( 50,527)( 51,536)( 52,540)( 53,539)( 54,538)( 55,537)( 56,531)
( 57,535)( 58,534)( 59,533)( 60,532)( 61,556)( 62,560)( 63,559)( 64,558)
( 65,557)( 66,566)( 67,570)( 68,569)( 69,568)( 70,567)( 71,561)( 72,565)
( 73,564)( 74,563)( 75,562)( 76,541)( 77,545)( 78,544)( 79,543)( 80,542)
( 81,551)( 82,555)( 83,554)( 84,553)( 85,552)( 86,546)( 87,550)( 88,549)
( 89,548)( 90,547)( 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)(181,706)(182,710)(183,709)(184,708)
(185,707)(186,716)(187,720)(188,719)(189,718)(190,717)(191,711)(192,715)
(193,714)(194,713)(195,712)(196,691)(197,695)(198,694)(199,693)(200,692)
(201,701)(202,705)(203,704)(204,703)(205,702)(206,696)(207,700)(208,699)
(209,698)(210,697)(211,676)(212,680)(213,679)(214,678)(215,677)(216,686)
(217,690)(218,689)(219,688)(220,687)(221,681)(222,685)(223,684)(224,683)
(225,682)(226,661)(227,665)(228,664)(229,663)(230,662)(231,671)(232,675)
(233,674)(234,673)(235,672)(236,666)(237,670)(238,669)(239,668)(240,667)
(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)(271,751)(272,755)
(273,754)(274,753)(275,752)(276,761)(277,765)(278,764)(279,763)(280,762)
(281,756)(282,760)(283,759)(284,758)(285,757)(286,766)(287,770)(288,769)
(289,768)(290,767)(291,776)(292,780)(293,779)(294,778)(295,777)(296,771)
(297,775)(298,774)(299,773)(300,772)(301,796)(302,800)(303,799)(304,798)
(305,797)(306,806)(307,810)(308,809)(309,808)(310,807)(311,801)(312,805)
(313,804)(314,803)(315,802)(316,781)(317,785)(318,784)(319,783)(320,782)
(321,791)(322,795)(323,794)(324,793)(325,792)(326,786)(327,790)(328,789)
(329,788)(330,787)(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)(421,946)(422,950)(423,949)(424,948)
(425,947)(426,956)(427,960)(428,959)(429,958)(430,957)(431,951)(432,955)
(433,954)(434,953)(435,952)(436,931)(437,935)(438,934)(439,933)(440,932)
(441,941)(442,945)(443,944)(444,943)(445,942)(446,936)(447,940)(448,939)
(449,938)(450,937)(451,916)(452,920)(453,919)(454,918)(455,917)(456,926)
(457,930)(458,929)(459,928)(460,927)(461,921)(462,925)(463,924)(464,923)
(465,922)(466,901)(467,905)(468,904)(469,903)(470,902)(471,911)(472,915)
(473,914)(474,913)(475,912)(476,906)(477,910)(478,909)(479,908)(480,907);;
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, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 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, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120)
(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)(271,337)(272,336)(273,340)(274,339)(275,338)(276,332)
(277,331)(278,335)(279,334)(280,333)(281,342)(282,341)(283,345)(284,344)
(285,343)(286,352)(287,351)(288,355)(289,354)(290,353)(291,347)(292,346)
(293,350)(294,349)(295,348)(296,357)(297,356)(298,360)(299,359)(300,358)
(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)(511,637)(512,636)(513,640)(514,639)(515,638)(516,632)
(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)(524,644)
(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)(532,646)
(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)(540,658)
(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)(571,697)(572,696)
(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)(580,693)
(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)(588,715)
(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)(596,717)
(597,716)(598,720)(599,719)(600,718)(721,922)(722,921)(723,925)(724,924)
(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)(731,927)(732,926)
(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)(739,909)(740,908)
(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)(747,911)(748,915)
(749,914)(750,913)(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)
(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)(787,856)(788,860)
(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)(795,868)(796,847)
(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)(803,845)(804,844)
(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)(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)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)
(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)(144,369)
(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)(160,415)
(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)(192,447)
(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)(216,471)
(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(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)
(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)(608,863)
(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)(616,841)
(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)(624,849)
(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)(632,887)
(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)(640,895)
(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)(648,873)
(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)(656,881)
(657,882)(658,883)(659,884)(660,885)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)(672,927)
(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)(688,913)
(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)(696,951)
(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)(704,959)
(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)(712,937)
(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)(720,945);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 31,511)
( 32,515)( 33,514)( 34,513)( 35,512)( 36,521)( 37,525)( 38,524)( 39,523)
( 40,522)( 41,516)( 42,520)( 43,519)( 44,518)( 45,517)( 46,526)( 47,530)
( 48,529)( 49,528)( 50,527)( 51,536)( 52,540)( 53,539)( 54,538)( 55,537)
( 56,531)( 57,535)( 58,534)( 59,533)( 60,532)( 61,556)( 62,560)( 63,559)
( 64,558)( 65,557)( 66,566)( 67,570)( 68,569)( 69,568)( 70,567)( 71,561)
( 72,565)( 73,564)( 74,563)( 75,562)( 76,541)( 77,545)( 78,544)( 79,543)
( 80,542)( 81,551)( 82,555)( 83,554)( 84,553)( 85,552)( 86,546)( 87,550)
( 88,549)( 89,548)( 90,547)( 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)(181,706)(182,710)(183,709)
(184,708)(185,707)(186,716)(187,720)(188,719)(189,718)(190,717)(191,711)
(192,715)(193,714)(194,713)(195,712)(196,691)(197,695)(198,694)(199,693)
(200,692)(201,701)(202,705)(203,704)(204,703)(205,702)(206,696)(207,700)
(208,699)(209,698)(210,697)(211,676)(212,680)(213,679)(214,678)(215,677)
(216,686)(217,690)(218,689)(219,688)(220,687)(221,681)(222,685)(223,684)
(224,683)(225,682)(226,661)(227,665)(228,664)(229,663)(230,662)(231,671)
(232,675)(233,674)(234,673)(235,672)(236,666)(237,670)(238,669)(239,668)
(240,667)(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)(271,751)
(272,755)(273,754)(274,753)(275,752)(276,761)(277,765)(278,764)(279,763)
(280,762)(281,756)(282,760)(283,759)(284,758)(285,757)(286,766)(287,770)
(288,769)(289,768)(290,767)(291,776)(292,780)(293,779)(294,778)(295,777)
(296,771)(297,775)(298,774)(299,773)(300,772)(301,796)(302,800)(303,799)
(304,798)(305,797)(306,806)(307,810)(308,809)(309,808)(310,807)(311,801)
(312,805)(313,804)(314,803)(315,802)(316,781)(317,785)(318,784)(319,783)
(320,782)(321,791)(322,795)(323,794)(324,793)(325,792)(326,786)(327,790)
(328,789)(329,788)(330,787)(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)(421,946)(422,950)(423,949)
(424,948)(425,947)(426,956)(427,960)(428,959)(429,958)(430,957)(431,951)
(432,955)(433,954)(434,953)(435,952)(436,931)(437,935)(438,934)(439,933)
(440,932)(441,941)(442,945)(443,944)(444,943)(445,942)(446,936)(447,940)
(448,939)(449,938)(450,937)(451,916)(452,920)(453,919)(454,918)(455,917)
(456,926)(457,930)(458,929)(459,928)(460,927)(461,921)(462,925)(463,924)
(464,923)(465,922)(466,901)(467,905)(468,904)(469,903)(470,902)(471,911)
(472,915)(473,914)(474,913)(475,912)(476,906)(477,910)(478,909)(479,908)
(480,907);
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, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 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, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120)(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)(271,337)(272,336)(273,340)(274,339)(275,338)
(276,332)(277,331)(278,335)(279,334)(280,333)(281,342)(282,341)(283,345)
(284,344)(285,343)(286,352)(287,351)(288,355)(289,354)(290,353)(291,347)
(292,346)(293,350)(294,349)(295,348)(296,357)(297,356)(298,360)(299,359)
(300,358)(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)(511,637)(512,636)(513,640)(514,639)(515,638)
(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)
(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)
(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)
(540,658)(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)(571,697)
(572,696)(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)
(580,693)(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)
(588,715)(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)
(596,717)(597,716)(598,720)(599,719)(600,718)(721,922)(722,921)(723,925)
(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)(731,927)
(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)(739,909)
(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)(747,911)
(748,915)(749,914)(750,913)(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)(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)(787,856)
(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)(795,868)
(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)(803,845)
(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)(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)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)
(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)
(144,369)(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)
(160,415)(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)
(192,447)(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,471)(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)
(232,457)(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(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)(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)
(608,863)(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)
(616,841)(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)
(624,849)(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)
(632,887)(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)
(640,895)(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)
(648,873)(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)
(656,881)(657,882)(658,883)(659,884)(660,885)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)
(672,927)(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)
(688,913)(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,951)(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)
(704,959)(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)
(712,937)(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)
(720,945);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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