Polytope of Type {15,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {15,8}
Number of vertices, edges, etc : 120, 480, 64
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {15,4}*960
3-fold quotients : {5,8}*640b
4-fold quotients : {15,4}*480
6-fold quotients : {5,4}*320
12-fold quotients : {5,4}*160
32-fold quotients : {15,2}*60
96-fold quotients : {5,2}*20
160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)( 42,137)
( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)( 50,155)
( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)( 58,147)
( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)( 66, 98)
( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)( 74,105)
( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)( 82,123)
( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)( 90,115)
( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)(162,322)
(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)(170,329)
(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)(178,347)
(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)(186,339)
(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)(194,450)
(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)(202,457)
(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)(210,475)
(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)(218,467)
(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)(226,418)
(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)(234,425)
(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)(242,443)
(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)(250,435)
(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)(258,386)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)(266,393)
(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)(274,411)
(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)(282,403)
(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)(290,354)
(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)(298,361)
(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)(306,379)
(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)(314,371)
(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)(483,484)
(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)(500,506)
(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)(516,611)
(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)(524,620)
(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)(532,634)
(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)(540,626)
(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)(548,579)
(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)(556,588)
(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)(564,602)
(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)(572,594)
(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)(644,803)
(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)(652,812)
(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)(660,826)
(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)(668,818)
(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)(676,931)
(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)(684,940)
(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)(692,954)
(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)(700,946)
(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)(708,899)
(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)(716,908)
(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)(724,922)
(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)(732,914)
(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)(740,867)
(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)(748,876)
(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)(756,890)
(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)(764,882)
(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)(772,835)
(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)(780,844)
(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)(788,858)
(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)(796,850)
(797,854)(798,853)(799,856)(800,855);;
s1 := ( 1,193)( 2,194)( 3,224)( 4,223)( 5,204)( 6,203)( 7,213)( 8,214)
( 9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)( 32,195)
( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)( 40,182)
( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)( 48,175)
( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)( 64,163)
( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)( 72,310)
( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)( 80,303)
( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)( 96,291)
( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)(104,278)
(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)(112,271)
(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)(120,281)
(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)(128,259)
(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)(136,246)
(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)(144,239)
(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)(152,249)
(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)(160,227)
(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)(328,374)
(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)(336,367)
(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)(344,377)
(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)(352,355)
(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)(392,470)
(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)(400,463)
(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)(408,473)
(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)(416,451)
(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)(426,443)
(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,674)(482,673)
(483,703)(484,704)(485,683)(486,684)(487,694)(488,693)(489,699)(490,700)
(491,677)(492,678)(493,689)(494,690)(495,687)(496,688)(497,685)(498,686)
(499,692)(500,691)(501,680)(502,679)(503,697)(504,698)(505,695)(506,696)
(507,681)(508,682)(509,701)(510,702)(511,675)(512,676)(513,642)(514,641)
(515,671)(516,672)(517,651)(518,652)(519,662)(520,661)(521,667)(522,668)
(523,645)(524,646)(525,657)(526,658)(527,655)(528,656)(529,653)(530,654)
(531,660)(532,659)(533,648)(534,647)(535,665)(536,666)(537,663)(538,664)
(539,649)(540,650)(541,669)(542,670)(543,643)(544,644)(545,770)(546,769)
(547,799)(548,800)(549,779)(550,780)(551,790)(552,789)(553,795)(554,796)
(555,773)(556,774)(557,785)(558,786)(559,783)(560,784)(561,781)(562,782)
(563,788)(564,787)(565,776)(566,775)(567,793)(568,794)(569,791)(570,792)
(571,777)(572,778)(573,797)(574,798)(575,771)(576,772)(577,738)(578,737)
(579,767)(580,768)(581,747)(582,748)(583,758)(584,757)(585,763)(586,764)
(587,741)(588,742)(589,753)(590,754)(591,751)(592,752)(593,749)(594,750)
(595,756)(596,755)(597,744)(598,743)(599,761)(600,762)(601,759)(602,760)
(603,745)(604,746)(605,765)(606,766)(607,739)(608,740)(609,706)(610,705)
(611,735)(612,736)(613,715)(614,716)(615,726)(616,725)(617,731)(618,732)
(619,709)(620,710)(621,721)(622,722)(623,719)(624,720)(625,717)(626,718)
(627,724)(628,723)(629,712)(630,711)(631,729)(632,730)(633,727)(634,728)
(635,713)(636,714)(637,733)(638,734)(639,707)(640,708)(801,834)(802,833)
(803,863)(804,864)(805,843)(806,844)(807,854)(808,853)(809,859)(810,860)
(811,837)(812,838)(813,849)(814,850)(815,847)(816,848)(817,845)(818,846)
(819,852)(820,851)(821,840)(822,839)(823,857)(824,858)(825,855)(826,856)
(827,841)(828,842)(829,861)(830,862)(831,835)(832,836)(865,930)(866,929)
(867,959)(868,960)(869,939)(870,940)(871,950)(872,949)(873,955)(874,956)
(875,933)(876,934)(877,945)(878,946)(879,943)(880,944)(881,941)(882,942)
(883,948)(884,947)(885,936)(886,935)(887,953)(888,954)(889,951)(890,952)
(891,937)(892,938)(893,957)(894,958)(895,931)(896,932)(897,898)(899,927)
(900,928)(901,907)(902,908)(903,918)(904,917)(905,923)(906,924)(909,913)
(910,914)(915,916)(919,921)(920,922);;
s2 := ( 1,491)( 2,492)( 3,489)( 4,490)( 5,496)( 6,495)( 7,494)( 8,493)
( 9,484)( 10,483)( 11,482)( 12,481)( 13,487)( 14,488)( 15,485)( 16,486)
( 17,507)( 18,508)( 19,505)( 20,506)( 21,512)( 22,511)( 23,510)( 24,509)
( 25,500)( 26,499)( 27,498)( 28,497)( 29,503)( 30,504)( 31,501)( 32,502)
( 33,523)( 34,524)( 35,521)( 36,522)( 37,528)( 38,527)( 39,526)( 40,525)
( 41,516)( 42,515)( 43,514)( 44,513)( 45,519)( 46,520)( 47,517)( 48,518)
( 49,539)( 50,540)( 51,537)( 52,538)( 53,544)( 54,543)( 55,542)( 56,541)
( 57,532)( 58,531)( 59,530)( 60,529)( 61,535)( 62,536)( 63,533)( 64,534)
( 65,555)( 66,556)( 67,553)( 68,554)( 69,560)( 70,559)( 71,558)( 72,557)
( 73,548)( 74,547)( 75,546)( 76,545)( 77,551)( 78,552)( 79,549)( 80,550)
( 81,571)( 82,572)( 83,569)( 84,570)( 85,576)( 86,575)( 87,574)( 88,573)
( 89,564)( 90,563)( 91,562)( 92,561)( 93,567)( 94,568)( 95,565)( 96,566)
( 97,587)( 98,588)( 99,585)(100,586)(101,592)(102,591)(103,590)(104,589)
(105,580)(106,579)(107,578)(108,577)(109,583)(110,584)(111,581)(112,582)
(113,603)(114,604)(115,601)(116,602)(117,608)(118,607)(119,606)(120,605)
(121,596)(122,595)(123,594)(124,593)(125,599)(126,600)(127,597)(128,598)
(129,619)(130,620)(131,617)(132,618)(133,624)(134,623)(135,622)(136,621)
(137,612)(138,611)(139,610)(140,609)(141,615)(142,616)(143,613)(144,614)
(145,635)(146,636)(147,633)(148,634)(149,640)(150,639)(151,638)(152,637)
(153,628)(154,627)(155,626)(156,625)(157,631)(158,632)(159,629)(160,630)
(161,651)(162,652)(163,649)(164,650)(165,656)(166,655)(167,654)(168,653)
(169,644)(170,643)(171,642)(172,641)(173,647)(174,648)(175,645)(176,646)
(177,667)(178,668)(179,665)(180,666)(181,672)(182,671)(183,670)(184,669)
(185,660)(186,659)(187,658)(188,657)(189,663)(190,664)(191,661)(192,662)
(193,683)(194,684)(195,681)(196,682)(197,688)(198,687)(199,686)(200,685)
(201,676)(202,675)(203,674)(204,673)(205,679)(206,680)(207,677)(208,678)
(209,699)(210,700)(211,697)(212,698)(213,704)(214,703)(215,702)(216,701)
(217,692)(218,691)(219,690)(220,689)(221,695)(222,696)(223,693)(224,694)
(225,715)(226,716)(227,713)(228,714)(229,720)(230,719)(231,718)(232,717)
(233,708)(234,707)(235,706)(236,705)(237,711)(238,712)(239,709)(240,710)
(241,731)(242,732)(243,729)(244,730)(245,736)(246,735)(247,734)(248,733)
(249,724)(250,723)(251,722)(252,721)(253,727)(254,728)(255,725)(256,726)
(257,747)(258,748)(259,745)(260,746)(261,752)(262,751)(263,750)(264,749)
(265,740)(266,739)(267,738)(268,737)(269,743)(270,744)(271,741)(272,742)
(273,763)(274,764)(275,761)(276,762)(277,768)(278,767)(279,766)(280,765)
(281,756)(282,755)(283,754)(284,753)(285,759)(286,760)(287,757)(288,758)
(289,779)(290,780)(291,777)(292,778)(293,784)(294,783)(295,782)(296,781)
(297,772)(298,771)(299,770)(300,769)(301,775)(302,776)(303,773)(304,774)
(305,795)(306,796)(307,793)(308,794)(309,800)(310,799)(311,798)(312,797)
(313,788)(314,787)(315,786)(316,785)(317,791)(318,792)(319,789)(320,790)
(321,811)(322,812)(323,809)(324,810)(325,816)(326,815)(327,814)(328,813)
(329,804)(330,803)(331,802)(332,801)(333,807)(334,808)(335,805)(336,806)
(337,827)(338,828)(339,825)(340,826)(341,832)(342,831)(343,830)(344,829)
(345,820)(346,819)(347,818)(348,817)(349,823)(350,824)(351,821)(352,822)
(353,843)(354,844)(355,841)(356,842)(357,848)(358,847)(359,846)(360,845)
(361,836)(362,835)(363,834)(364,833)(365,839)(366,840)(367,837)(368,838)
(369,859)(370,860)(371,857)(372,858)(373,864)(374,863)(375,862)(376,861)
(377,852)(378,851)(379,850)(380,849)(381,855)(382,856)(383,853)(384,854)
(385,875)(386,876)(387,873)(388,874)(389,880)(390,879)(391,878)(392,877)
(393,868)(394,867)(395,866)(396,865)(397,871)(398,872)(399,869)(400,870)
(401,891)(402,892)(403,889)(404,890)(405,896)(406,895)(407,894)(408,893)
(409,884)(410,883)(411,882)(412,881)(413,887)(414,888)(415,885)(416,886)
(417,907)(418,908)(419,905)(420,906)(421,912)(422,911)(423,910)(424,909)
(425,900)(426,899)(427,898)(428,897)(429,903)(430,904)(431,901)(432,902)
(433,923)(434,924)(435,921)(436,922)(437,928)(438,927)(439,926)(440,925)
(441,916)(442,915)(443,914)(444,913)(445,919)(446,920)(447,917)(448,918)
(449,939)(450,940)(451,937)(452,938)(453,944)(454,943)(455,942)(456,941)
(457,932)(458,931)(459,930)(460,929)(461,935)(462,936)(463,933)(464,934)
(465,955)(466,956)(467,953)(468,954)(469,960)(470,959)(471,958)(472,957)
(473,948)(474,947)(475,946)(476,945)(477,951)(478,952)(479,949)(480,950);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*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)!( 5, 8)( 6, 7)( 9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)
( 42,137)( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)
( 50,155)( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)
( 58,147)( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)
( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)
( 74,105)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)
( 82,123)( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)
( 90,115)( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)
(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)
(170,329)(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)
(178,347)(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)
(186,339)(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)
(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)
(202,457)(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)
(210,475)(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)
(218,467)(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)
(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)
(234,425)(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)
(242,443)(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)
(250,435)(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)
(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)
(266,393)(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)
(274,411)(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)
(282,403)(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)
(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)
(298,361)(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)
(306,379)(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)
(314,371)(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(481,482)
(483,484)(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)
(500,506)(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)
(516,611)(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)
(524,620)(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)
(532,634)(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)
(540,626)(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)
(548,579)(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)
(556,588)(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)
(564,602)(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)
(572,594)(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)
(644,803)(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)
(652,812)(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)
(660,826)(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)
(668,818)(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)
(676,931)(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)
(684,940)(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)
(692,954)(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)
(700,946)(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)
(708,899)(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)
(716,908)(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)
(724,922)(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)
(732,914)(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)
(740,867)(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)
(748,876)(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)
(756,890)(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)
(764,882)(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)
(772,835)(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)
(780,844)(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)
(788,858)(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)
(796,850)(797,854)(798,853)(799,856)(800,855);
s1 := Sym(960)!( 1,193)( 2,194)( 3,224)( 4,223)( 5,204)( 6,203)( 7,213)
( 8,214)( 9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)
( 24,217)( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)
( 32,195)( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)
( 40,182)( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)
( 48,175)( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)
( 64,163)( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)
( 72,310)( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)
( 80,303)( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)
( 96,291)( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)
(104,278)(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)
(112,271)(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)
(120,281)(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)
(128,259)(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)
(136,246)(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)
(144,239)(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)
(152,249)(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)
(160,227)(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)
(328,374)(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)
(336,367)(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)
(344,377)(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)
(352,355)(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)
(392,470)(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)
(400,463)(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)
(408,473)(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)
(416,451)(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)
(426,443)(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,674)
(482,673)(483,703)(484,704)(485,683)(486,684)(487,694)(488,693)(489,699)
(490,700)(491,677)(492,678)(493,689)(494,690)(495,687)(496,688)(497,685)
(498,686)(499,692)(500,691)(501,680)(502,679)(503,697)(504,698)(505,695)
(506,696)(507,681)(508,682)(509,701)(510,702)(511,675)(512,676)(513,642)
(514,641)(515,671)(516,672)(517,651)(518,652)(519,662)(520,661)(521,667)
(522,668)(523,645)(524,646)(525,657)(526,658)(527,655)(528,656)(529,653)
(530,654)(531,660)(532,659)(533,648)(534,647)(535,665)(536,666)(537,663)
(538,664)(539,649)(540,650)(541,669)(542,670)(543,643)(544,644)(545,770)
(546,769)(547,799)(548,800)(549,779)(550,780)(551,790)(552,789)(553,795)
(554,796)(555,773)(556,774)(557,785)(558,786)(559,783)(560,784)(561,781)
(562,782)(563,788)(564,787)(565,776)(566,775)(567,793)(568,794)(569,791)
(570,792)(571,777)(572,778)(573,797)(574,798)(575,771)(576,772)(577,738)
(578,737)(579,767)(580,768)(581,747)(582,748)(583,758)(584,757)(585,763)
(586,764)(587,741)(588,742)(589,753)(590,754)(591,751)(592,752)(593,749)
(594,750)(595,756)(596,755)(597,744)(598,743)(599,761)(600,762)(601,759)
(602,760)(603,745)(604,746)(605,765)(606,766)(607,739)(608,740)(609,706)
(610,705)(611,735)(612,736)(613,715)(614,716)(615,726)(616,725)(617,731)
(618,732)(619,709)(620,710)(621,721)(622,722)(623,719)(624,720)(625,717)
(626,718)(627,724)(628,723)(629,712)(630,711)(631,729)(632,730)(633,727)
(634,728)(635,713)(636,714)(637,733)(638,734)(639,707)(640,708)(801,834)
(802,833)(803,863)(804,864)(805,843)(806,844)(807,854)(808,853)(809,859)
(810,860)(811,837)(812,838)(813,849)(814,850)(815,847)(816,848)(817,845)
(818,846)(819,852)(820,851)(821,840)(822,839)(823,857)(824,858)(825,855)
(826,856)(827,841)(828,842)(829,861)(830,862)(831,835)(832,836)(865,930)
(866,929)(867,959)(868,960)(869,939)(870,940)(871,950)(872,949)(873,955)
(874,956)(875,933)(876,934)(877,945)(878,946)(879,943)(880,944)(881,941)
(882,942)(883,948)(884,947)(885,936)(886,935)(887,953)(888,954)(889,951)
(890,952)(891,937)(892,938)(893,957)(894,958)(895,931)(896,932)(897,898)
(899,927)(900,928)(901,907)(902,908)(903,918)(904,917)(905,923)(906,924)
(909,913)(910,914)(915,916)(919,921)(920,922);
s2 := Sym(960)!( 1,491)( 2,492)( 3,489)( 4,490)( 5,496)( 6,495)( 7,494)
( 8,493)( 9,484)( 10,483)( 11,482)( 12,481)( 13,487)( 14,488)( 15,485)
( 16,486)( 17,507)( 18,508)( 19,505)( 20,506)( 21,512)( 22,511)( 23,510)
( 24,509)( 25,500)( 26,499)( 27,498)( 28,497)( 29,503)( 30,504)( 31,501)
( 32,502)( 33,523)( 34,524)( 35,521)( 36,522)( 37,528)( 38,527)( 39,526)
( 40,525)( 41,516)( 42,515)( 43,514)( 44,513)( 45,519)( 46,520)( 47,517)
( 48,518)( 49,539)( 50,540)( 51,537)( 52,538)( 53,544)( 54,543)( 55,542)
( 56,541)( 57,532)( 58,531)( 59,530)( 60,529)( 61,535)( 62,536)( 63,533)
( 64,534)( 65,555)( 66,556)( 67,553)( 68,554)( 69,560)( 70,559)( 71,558)
( 72,557)( 73,548)( 74,547)( 75,546)( 76,545)( 77,551)( 78,552)( 79,549)
( 80,550)( 81,571)( 82,572)( 83,569)( 84,570)( 85,576)( 86,575)( 87,574)
( 88,573)( 89,564)( 90,563)( 91,562)( 92,561)( 93,567)( 94,568)( 95,565)
( 96,566)( 97,587)( 98,588)( 99,585)(100,586)(101,592)(102,591)(103,590)
(104,589)(105,580)(106,579)(107,578)(108,577)(109,583)(110,584)(111,581)
(112,582)(113,603)(114,604)(115,601)(116,602)(117,608)(118,607)(119,606)
(120,605)(121,596)(122,595)(123,594)(124,593)(125,599)(126,600)(127,597)
(128,598)(129,619)(130,620)(131,617)(132,618)(133,624)(134,623)(135,622)
(136,621)(137,612)(138,611)(139,610)(140,609)(141,615)(142,616)(143,613)
(144,614)(145,635)(146,636)(147,633)(148,634)(149,640)(150,639)(151,638)
(152,637)(153,628)(154,627)(155,626)(156,625)(157,631)(158,632)(159,629)
(160,630)(161,651)(162,652)(163,649)(164,650)(165,656)(166,655)(167,654)
(168,653)(169,644)(170,643)(171,642)(172,641)(173,647)(174,648)(175,645)
(176,646)(177,667)(178,668)(179,665)(180,666)(181,672)(182,671)(183,670)
(184,669)(185,660)(186,659)(187,658)(188,657)(189,663)(190,664)(191,661)
(192,662)(193,683)(194,684)(195,681)(196,682)(197,688)(198,687)(199,686)
(200,685)(201,676)(202,675)(203,674)(204,673)(205,679)(206,680)(207,677)
(208,678)(209,699)(210,700)(211,697)(212,698)(213,704)(214,703)(215,702)
(216,701)(217,692)(218,691)(219,690)(220,689)(221,695)(222,696)(223,693)
(224,694)(225,715)(226,716)(227,713)(228,714)(229,720)(230,719)(231,718)
(232,717)(233,708)(234,707)(235,706)(236,705)(237,711)(238,712)(239,709)
(240,710)(241,731)(242,732)(243,729)(244,730)(245,736)(246,735)(247,734)
(248,733)(249,724)(250,723)(251,722)(252,721)(253,727)(254,728)(255,725)
(256,726)(257,747)(258,748)(259,745)(260,746)(261,752)(262,751)(263,750)
(264,749)(265,740)(266,739)(267,738)(268,737)(269,743)(270,744)(271,741)
(272,742)(273,763)(274,764)(275,761)(276,762)(277,768)(278,767)(279,766)
(280,765)(281,756)(282,755)(283,754)(284,753)(285,759)(286,760)(287,757)
(288,758)(289,779)(290,780)(291,777)(292,778)(293,784)(294,783)(295,782)
(296,781)(297,772)(298,771)(299,770)(300,769)(301,775)(302,776)(303,773)
(304,774)(305,795)(306,796)(307,793)(308,794)(309,800)(310,799)(311,798)
(312,797)(313,788)(314,787)(315,786)(316,785)(317,791)(318,792)(319,789)
(320,790)(321,811)(322,812)(323,809)(324,810)(325,816)(326,815)(327,814)
(328,813)(329,804)(330,803)(331,802)(332,801)(333,807)(334,808)(335,805)
(336,806)(337,827)(338,828)(339,825)(340,826)(341,832)(342,831)(343,830)
(344,829)(345,820)(346,819)(347,818)(348,817)(349,823)(350,824)(351,821)
(352,822)(353,843)(354,844)(355,841)(356,842)(357,848)(358,847)(359,846)
(360,845)(361,836)(362,835)(363,834)(364,833)(365,839)(366,840)(367,837)
(368,838)(369,859)(370,860)(371,857)(372,858)(373,864)(374,863)(375,862)
(376,861)(377,852)(378,851)(379,850)(380,849)(381,855)(382,856)(383,853)
(384,854)(385,875)(386,876)(387,873)(388,874)(389,880)(390,879)(391,878)
(392,877)(393,868)(394,867)(395,866)(396,865)(397,871)(398,872)(399,869)
(400,870)(401,891)(402,892)(403,889)(404,890)(405,896)(406,895)(407,894)
(408,893)(409,884)(410,883)(411,882)(412,881)(413,887)(414,888)(415,885)
(416,886)(417,907)(418,908)(419,905)(420,906)(421,912)(422,911)(423,910)
(424,909)(425,900)(426,899)(427,898)(428,897)(429,903)(430,904)(431,901)
(432,902)(433,923)(434,924)(435,921)(436,922)(437,928)(438,927)(439,926)
(440,925)(441,916)(442,915)(443,914)(444,913)(445,919)(446,920)(447,917)
(448,918)(449,939)(450,940)(451,937)(452,938)(453,944)(454,943)(455,942)
(456,941)(457,932)(458,931)(459,930)(460,929)(461,935)(462,936)(463,933)
(464,934)(465,955)(466,956)(467,953)(468,954)(469,960)(470,959)(471,958)
(472,957)(473,948)(474,947)(475,946)(476,945)(477,951)(478,952)(479,949)
(480,950);
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*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*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