Overview
- Group
- SmallGroup(1920,239472)
- Rank
- 3
- Schläfli Type
- {4,30}
- Vertices, edges, …
- 32, 480, 240
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
16-fold
20-fold
32-fold
40-fold
48-fold
80-fold
96-fold
160-fold
240-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2
140 facets
16 vertex figures
- 16 of {30}*60
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s2*s1)^11*s2> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2> of order 2
120 facets
- 120 of {4}*8
16 vertex figures
- 16 of {30}*60
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
70 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
80 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s2)^15> of order 4
60 facets
- 60 of {4}*8
12 vertex figures
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s2*s1)^11*s2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s2*s1*s0*(s2*s1)^4*s0*(s2*s1)^9*s2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
70 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
70 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
80 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4
90 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
70 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
70 facets
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^15> of order 4
60 facets
- 60 of {4}*8
10 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
60 facets
- 60 of {4}*8
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
40 facets
4 vertex figures
- 4 of {30}*60
P/N, where N=<(s0*s1)^2, (s2*s1*s0)^2*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
50 facets
4 vertex figures
- 4 of {30}*60
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
35 facets
4 vertex figures
- 4 of {30}*60
P/N, where N=<(s0*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s2)^15> of order 8
40 facets
6 vertex figures
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, (s1*s2)^15> of order 8
30 facets
- 30 of {4}*8
6 vertex figures
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s2)^15> of order 8
30 facets
- 30 of {4}*8
6 vertex figures
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
30 facets
- 30 of {4}*8
4 vertex figures
- 4 of {30}*60
P/N, where N=<(s0*s1)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 8
40 facets
4 vertex figures
- 4 of {30}*60
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^4*s0*(s2*s1)^9*s2> of order 8
30 facets
- 30 of {4}*8
4 vertex figures
- 4 of {30}*60
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 8
30 facets
- 30 of {4}*8
4 vertex figures
- 4 of {30}*60
Representations
Permutation Representation (GAP)
s0 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)( 17,505)( 18,506)( 19,507)( 20,508) ( 21,509)( 22,510)( 23,511)( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)(473,945)(474,946) (475,947)(476,948)(477,949)(478,950)(479,951)(480,952);; s1 := ( 1,241)( 2,242)( 3,244)( 4,243)( 5,246)( 6,245)( 7,247)( 8,248)( 9,256)( 10,255)( 11,253)( 12,254)( 13,251)( 14,252)( 15,250)( 16,249)( 17,305)( 18,306)( 19,308)( 20,307) ( 21,310)( 22,309)( 23,311)( 24,312)( 25,320)( 26,319)( 27,317)( 28,318)( 29,315)( 30,316)( 31,314)( 32,313)( 33,289)( 34,290)( 35,292)( 36,291)( 37,294)( 38,293)( 39,295)( 40,296)( 41,304)( 42,303)( 43,301)( 44,302)( 45,299)( 46,300)( 47,298)( 48,297)( 49,273)( 50,274)( 51,276)( 52,275)( 53,278)( 54,277)( 55,279)( 56,280)( 57,288)( 58,287)( 59,285)( 60,286)( 61,283)( 62,284)( 63,282)( 64,281)( 65,257)( 66,258)( 67,260)( 68,259)( 69,262)( 70,261)( 71,263)( 72,264)( 73,272)( 74,271)( 75,269)( 76,270)( 77,267)( 78,268)( 79,266)( 80,265)( 81,401)( 82,402)( 83,404)( 84,403)( 85,406)( 86,405)( 87,407)( 88,408)( 89,416)( 90,415)( 91,413)( 92,414)( 93,411)( 94,412)( 95,410)( 96,409)( 97,465)( 98,466)( 99,468)(100,467)(101,470)(102,469)(103,471)(104,472)(105,480)(106,479)(107,477)(108,478)(109,475)(110,476)(111,474)(112,473)(113,449)(114,450)(115,452)(116,451)(117,454)(118,453)(119,455)(120,456)(121,464)(122,463)(123,461)(124,462)(125,459)(126,460)(127,458)(128,457)(129,433)(130,434)(131,436)(132,435)(133,438)(134,437)(135,439)(136,440)(137,448)(138,447)(139,445)(140,446)(141,443)(142,444)(143,442)(144,441)(145,417)(146,418)(147,420)(148,419)(149,422)(150,421)(151,423)(152,424)(153,432)(154,431)(155,429)(156,430)(157,427)(158,428)(159,426)(160,425)(161,321)(162,322)(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,336)(170,335)(171,333)(172,334)(173,331)(174,332)(175,330)(176,329)(177,385)(178,386)(179,388)(180,387)(181,390)(182,389)(183,391)(184,392)(185,400)(186,399)(187,397)(188,398)(189,395)(190,396)(191,394)(192,393)(193,369)(194,370)(195,372)(196,371)(197,374)(198,373)(199,375)(200,376)(201,384)(202,383)(203,381)(204,382)(205,379)(206,380)(207,378)(208,377)(209,353)(210,354)(211,356)(212,355)(213,358)(214,357)(215,359)(216,360)(217,368)(218,367)(219,365)(220,366)(221,363)(222,364)(223,362)(224,361)(225,337)(226,338)(227,340)(228,339)(229,342)(230,341)(231,343)(232,344)(233,352)(234,351)(235,349)(236,350)(237,347)(238,348)(239,346)(240,345)(481,721)(482,722)(483,724)(484,723)(485,726)(486,725)(487,727)(488,728)(489,736)(490,735)(491,733)(492,734)(493,731)(494,732)(495,730)(496,729)(497,785)(498,786)(499,788)(500,787)(501,790)(502,789)(503,791)(504,792)(505,800)(506,799)(507,797)(508,798)(509,795)(510,796)(511,794)(512,793)(513,769)(514,770)(515,772)(516,771)(517,774)(518,773)(519,775)(520,776)(521,784)(522,783)(523,781)(524,782)(525,779)(526,780)(527,778)(528,777)(529,753)(530,754)(531,756)(532,755)(533,758)(534,757)(535,759)(536,760)(537,768)(538,767)(539,765)(540,766)(541,763)(542,764)(543,762)(544,761)(545,737)(546,738)(547,740)(548,739)(549,742)(550,741)(551,743)(552,744)(553,752)(554,751)(555,749)(556,750)(557,747)(558,748)(559,746)(560,745)(561,881)(562,882)(563,884)(564,883)(565,886)(566,885)(567,887)(568,888)(569,896)(570,895)(571,893)(572,894)(573,891)(574,892)(575,890)(576,889)(577,945)(578,946)(579,948)(580,947)(581,950)(582,949)(583,951)(584,952)(585,960)(586,959)(587,957)(588,958)(589,955)(590,956)(591,954)(592,953)(593,929)(594,930)(595,932)(596,931)(597,934)(598,933)(599,935)(600,936)(601,944)(602,943)(603,941)(604,942)(605,939)(606,940)(607,938)(608,937)(609,913)(610,914)(611,916)(612,915)(613,918)(614,917)(615,919)(616,920)(617,928)(618,927)(619,925)(620,926)(621,923)(622,924)(623,922)(624,921)(625,897)(626,898)(627,900)(628,899)(629,902)(630,901)(631,903)(632,904)(633,912)(634,911)(635,909)(636,910)(637,907)(638,908)(639,906)(640,905)(641,801)(642,802)(643,804)(644,803)(645,806)(646,805)(647,807)(648,808)(649,816)(650,815)(651,813)(652,814)(653,811)(654,812)(655,810)(656,809)(657,865)(658,866)(659,868)(660,867)(661,870)(662,869)(663,871)(664,872)(665,880)(666,879)(667,877)(668,878)(669,875)(670,876)(671,874)(672,873)(673,849)(674,850)(675,852)(676,851)(677,854)(678,853)(679,855)(680,856)(681,864)(682,863)(683,861)(684,862)(685,859)(686,860)(687,858)(688,857)(689,833)(690,834)(691,836)(692,835)(693,838)(694,837)(695,839)(696,840)(697,848)(698,847)(699,845)(700,846)(701,843)(702,844)(703,842)(704,841)(705,817)(706,818)(707,820)(708,819)(709,822)(710,821)(711,823)(712,824)(713,832)(714,831) (715,829)(716,830)(717,827)(718,828)(719,826)(720,825);; s2 := ( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)( 8,110)( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83)( 20, 82) ( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)(484,578)(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)(492,586)(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)(500,562)(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)(508,570)(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)(516,626)(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)(524,634)(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)(532,610)(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)(540,618)(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)(548,594)(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)(556,602)(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)(644,658)(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)(652,666)(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)(676,706)(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)(684,714)(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)(695,703)(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)(726,832)(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)(734,824)(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)(742,816)(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)(750,808)(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)(758,880)(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)(766,872)(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)(774,864)(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)(782,856)(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)(790,848)(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)(798,840)(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)(886,912)(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)(894,904)(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)(918,960)(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)(926,952)(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)(938,940);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(960)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)( 17,505)( 18,506)( 19,507) ( 20,508)( 21,509)( 22,510)( 23,511)( 24,512)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)(121,593)(122,594)(123,595)(124,596)(125,597)(126,598)(127,599)(128,600)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,609)(138,610)(139,611)(140,612)(141,613)(142,614)(143,615)(144,616)(145,633)(146,634)(147,635)(148,636)(149,637)(150,638)(151,639)(152,640)(153,625)(154,626)(155,627)(156,628)(157,629)(158,630)(159,631)(160,632)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,641)(170,642)(171,643)(172,644)(173,645)(174,646)(175,647)(176,648)(177,665)(178,666)(179,667)(180,668)(181,669)(182,670)(183,671)(184,672)(185,657)(186,658)(187,659)(188,660)(189,661)(190,662)(191,663)(192,664)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,673)(202,674)(203,675)(204,676)(205,677)(206,678)(207,679)(208,680)(209,697)(210,698)(211,699)(212,700)(213,701)(214,702)(215,703)(216,704)(217,689)(218,690)(219,691)(220,692)(221,693)(222,694)(223,695)(224,696)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,705)(234,706)(235,707)(236,708)(237,709)(238,710)(239,711)(240,712)(241,729)(242,730)(243,731)(244,732)(245,733)(246,734)(247,735)(248,736)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,833)(362,834)(363,835)(364,836)(365,837)(366,838)(367,839)(368,840)(369,857)(370,858)(371,859)(372,860)(373,861)(374,862)(375,863)(376,864)(377,849)(378,850)(379,851)(380,852)(381,853)(382,854)(383,855)(384,856)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,865)(394,866)(395,867)(396,868)(397,869)(398,870)(399,871)(400,872)(401,889)(402,890)(403,891)(404,892)(405,893)(406,894)(407,895)(408,896)(409,881)(410,882)(411,883)(412,884)(413,885)(414,886)(415,887)(416,888)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,897)(426,898)(427,899)(428,900)(429,901)(430,902)(431,903)(432,904)(433,921)(434,922)(435,923)(436,924)(437,925)(438,926)(439,927)(440,928)(441,913)(442,914)(443,915)(444,916)(445,917)(446,918)(447,919)(448,920)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,929)(458,930)(459,931)(460,932)(461,933)(462,934)(463,935)(464,936)(465,953)(466,954)(467,955)(468,956)(469,957)(470,958)(471,959)(472,960)(473,945) (474,946)(475,947)(476,948)(477,949)(478,950)(479,951)(480,952); s1 := Sym(960)!( 1,241)( 2,242)( 3,244)( 4,243)( 5,246)( 6,245)( 7,247)( 8,248)( 9,256)( 10,255)( 11,253)( 12,254)( 13,251)( 14,252)( 15,250)( 16,249)( 17,305)( 18,306)( 19,308) ( 20,307)( 21,310)( 22,309)( 23,311)( 24,312)( 25,320)( 26,319)( 27,317)( 28,318)( 29,315)( 30,316)( 31,314)( 32,313)( 33,289)( 34,290)( 35,292)( 36,291)( 37,294)( 38,293)( 39,295)( 40,296)( 41,304)( 42,303)( 43,301)( 44,302)( 45,299)( 46,300)( 47,298)( 48,297)( 49,273)( 50,274)( 51,276)( 52,275)( 53,278)( 54,277)( 55,279)( 56,280)( 57,288)( 58,287)( 59,285)( 60,286)( 61,283)( 62,284)( 63,282)( 64,281)( 65,257)( 66,258)( 67,260)( 68,259)( 69,262)( 70,261)( 71,263)( 72,264)( 73,272)( 74,271)( 75,269)( 76,270)( 77,267)( 78,268)( 79,266)( 80,265)( 81,401)( 82,402)( 83,404)( 84,403)( 85,406)( 86,405)( 87,407)( 88,408)( 89,416)( 90,415)( 91,413)( 92,414)( 93,411)( 94,412)( 95,410)( 96,409)( 97,465)( 98,466)( 99,468)(100,467)(101,470)(102,469)(103,471)(104,472)(105,480)(106,479)(107,477)(108,478)(109,475)(110,476)(111,474)(112,473)(113,449)(114,450)(115,452)(116,451)(117,454)(118,453)(119,455)(120,456)(121,464)(122,463)(123,461)(124,462)(125,459)(126,460)(127,458)(128,457)(129,433)(130,434)(131,436)(132,435)(133,438)(134,437)(135,439)(136,440)(137,448)(138,447)(139,445)(140,446)(141,443)(142,444)(143,442)(144,441)(145,417)(146,418)(147,420)(148,419)(149,422)(150,421)(151,423)(152,424)(153,432)(154,431)(155,429)(156,430)(157,427)(158,428)(159,426)(160,425)(161,321)(162,322)(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,336)(170,335)(171,333)(172,334)(173,331)(174,332)(175,330)(176,329)(177,385)(178,386)(179,388)(180,387)(181,390)(182,389)(183,391)(184,392)(185,400)(186,399)(187,397)(188,398)(189,395)(190,396)(191,394)(192,393)(193,369)(194,370)(195,372)(196,371)(197,374)(198,373)(199,375)(200,376)(201,384)(202,383)(203,381)(204,382)(205,379)(206,380)(207,378)(208,377)(209,353)(210,354)(211,356)(212,355)(213,358)(214,357)(215,359)(216,360)(217,368)(218,367)(219,365)(220,366)(221,363)(222,364)(223,362)(224,361)(225,337)(226,338)(227,340)(228,339)(229,342)(230,341)(231,343)(232,344)(233,352)(234,351)(235,349)(236,350)(237,347)(238,348)(239,346)(240,345)(481,721)(482,722)(483,724)(484,723)(485,726)(486,725)(487,727)(488,728)(489,736)(490,735)(491,733)(492,734)(493,731)(494,732)(495,730)(496,729)(497,785)(498,786)(499,788)(500,787)(501,790)(502,789)(503,791)(504,792)(505,800)(506,799)(507,797)(508,798)(509,795)(510,796)(511,794)(512,793)(513,769)(514,770)(515,772)(516,771)(517,774)(518,773)(519,775)(520,776)(521,784)(522,783)(523,781)(524,782)(525,779)(526,780)(527,778)(528,777)(529,753)(530,754)(531,756)(532,755)(533,758)(534,757)(535,759)(536,760)(537,768)(538,767)(539,765)(540,766)(541,763)(542,764)(543,762)(544,761)(545,737)(546,738)(547,740)(548,739)(549,742)(550,741)(551,743)(552,744)(553,752)(554,751)(555,749)(556,750)(557,747)(558,748)(559,746)(560,745)(561,881)(562,882)(563,884)(564,883)(565,886)(566,885)(567,887)(568,888)(569,896)(570,895)(571,893)(572,894)(573,891)(574,892)(575,890)(576,889)(577,945)(578,946)(579,948)(580,947)(581,950)(582,949)(583,951)(584,952)(585,960)(586,959)(587,957)(588,958)(589,955)(590,956)(591,954)(592,953)(593,929)(594,930)(595,932)(596,931)(597,934)(598,933)(599,935)(600,936)(601,944)(602,943)(603,941)(604,942)(605,939)(606,940)(607,938)(608,937)(609,913)(610,914)(611,916)(612,915)(613,918)(614,917)(615,919)(616,920)(617,928)(618,927)(619,925)(620,926)(621,923)(622,924)(623,922)(624,921)(625,897)(626,898)(627,900)(628,899)(629,902)(630,901)(631,903)(632,904)(633,912)(634,911)(635,909)(636,910)(637,907)(638,908)(639,906)(640,905)(641,801)(642,802)(643,804)(644,803)(645,806)(646,805)(647,807)(648,808)(649,816)(650,815)(651,813)(652,814)(653,811)(654,812)(655,810)(656,809)(657,865)(658,866)(659,868)(660,867)(661,870)(662,869)(663,871)(664,872)(665,880)(666,879)(667,877)(668,878)(669,875)(670,876)(671,874)(672,873)(673,849)(674,850)(675,852)(676,851)(677,854)(678,853)(679,855)(680,856)(681,864)(682,863)(683,861)(684,862)(685,859)(686,860)(687,858)(688,857)(689,833)(690,834)(691,836)(692,835)(693,838)(694,837)(695,839)(696,840)(697,848)(698,847)(699,845)(700,846)(701,843)(702,844)(703,842)(704,841)(705,817)(706,818)(707,820)(708,819)(709,822)(710,821)(711,823)(712,824)(713,832) (714,831)(715,829)(716,830)(717,827)(718,828)(719,826)(720,825); s2 := Sym(960)!( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)( 8,110)( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83) ( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)(484,578)(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)(492,586)(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)(500,562)(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)(508,570)(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)(516,626)(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)(524,634)(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)(532,610)(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)(540,618)(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)(548,594)(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)(556,602)(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)(644,658)(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)(652,666)(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)(676,706)(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)(684,714)(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)(695,703)(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)(726,832)(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)(734,824)(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)(742,816)(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)(750,808)(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)(758,880)(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)(766,872)(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)(774,864)(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)(782,856)(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)(790,848)(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)(798,840)(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)(886,912)(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)(894,904)(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)(918,960)(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)(926,952)(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)(938,940); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References
None.
to this polytope.