Overview
- Group
- SmallGroup(1920,239473)
- Rank
- 3
- Schläfli Type
- {30,8}
- Vertices, edges, …
- 120, 480, 32
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 8
- 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*s2*s1*s0*(s2*s1)^2> of order 2
16 facets
- 16 of {30}*60
60 vertex figures
- 60 of {8}*16
P/N, where N=<(s0*s1)^10*s0*(s2*(s1*s0)^2)^2*s2*s1> of order 2
16 facets
- 16 of {30}*60
60 vertex figures
- 60 of {8}*16
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^11*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
8 facets
- 8 of {30}*60
40 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 77)( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74) ( 31, 76)( 32, 75)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 61)( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,221)(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,205)(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)(147,180)(148,179)(149,182)(150,181)(151,183)(152,184)(153,189)(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(245,246)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)(261,310)(262,309)(263,311)(264,312)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)(277,294)(278,293)(279,295)(280,296)(281,301)(282,302)(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)(341,470)(342,469)(343,471)(344,472)(345,477)(346,478)(347,480)(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)(357,454)(358,453)(359,455)(360,456)(361,461)(362,462)(363,464)(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)(373,438)(374,437)(375,439)(376,440)(377,445)(378,446)(379,448)(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)(389,422)(390,421)(391,423)(392,424)(393,429)(394,430)(395,432)(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(485,486)(489,493)(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,550)(502,549)(503,551)(504,552)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,534)(518,533)(519,535)(520,536)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,646)(566,645)(567,647)(568,648)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,710)(582,709)(583,711)(584,712)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,694)(598,693)(599,695)(600,696)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,678)(614,677)(615,679)(616,680)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,662)(630,661)(631,663)(632,664)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)(639,668)(640,667)(723,724)(725,726)(729,733)(730,734)(731,736)(732,735)(737,785)(738,786)(739,788)(740,787)(741,790)(742,789)(743,791)(744,792)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)(753,769)(754,770)(755,772)(756,771)(757,774)(758,773)(759,775)(760,776)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)(801,881)(802,882)(803,884)(804,883)(805,886)(806,885)(807,887)(808,888)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)(817,945)(818,946)(819,948)(820,947)(821,950)(822,949)(823,951)(824,952)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)(833,929)(834,930)(835,932)(836,931)(837,934)(838,933)(839,935)(840,936)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)(849,913)(850,914)(851,916)(852,915)(853,918)(854,917)(855,919)(856,920)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)(865,897)(866,898)(867,900)(868,899)(869,902)(870,901)(871,903)(872,904)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);; s1 := ( 1,337)( 2,340)( 3,339)( 4,338)( 5,351)( 6,350)( 7,349)( 8,352)( 9,347)( 10,346)( 11,345)( 12,348)( 13,343)( 14,342)( 15,341)( 16,344)( 17,321)( 18,324)( 19,323)( 20,322) ( 21,335)( 22,334)( 23,333)( 24,336)( 25,331)( 26,330)( 27,329)( 28,332)( 29,327)( 30,326)( 31,325)( 32,328)( 33,385)( 34,388)( 35,387)( 36,386)( 37,399)( 38,398)( 39,397)( 40,400)( 41,395)( 42,394)( 43,393)( 44,396)( 45,391)( 46,390)( 47,389)( 48,392)( 49,369)( 50,372)( 51,371)( 52,370)( 53,383)( 54,382)( 55,381)( 56,384)( 57,379)( 58,378)( 59,377)( 60,380)( 61,375)( 62,374)( 63,373)( 64,376)( 65,353)( 66,356)( 67,355)( 68,354)( 69,367)( 70,366)( 71,365)( 72,368)( 73,363)( 74,362)( 75,361)( 76,364)( 77,359)( 78,358)( 79,357)( 80,360)( 81,257)( 82,260)( 83,259)( 84,258)( 85,271)( 86,270)( 87,269)( 88,272)( 89,267)( 90,266)( 91,265)( 92,268)( 93,263)( 94,262)( 95,261)( 96,264)( 97,241)( 98,244)( 99,243)(100,242)(101,255)(102,254)(103,253)(104,256)(105,251)(106,250)(107,249)(108,252)(109,247)(110,246)(111,245)(112,248)(113,305)(114,308)(115,307)(116,306)(117,319)(118,318)(119,317)(120,320)(121,315)(122,314)(123,313)(124,316)(125,311)(126,310)(127,309)(128,312)(129,289)(130,292)(131,291)(132,290)(133,303)(134,302)(135,301)(136,304)(137,299)(138,298)(139,297)(140,300)(141,295)(142,294)(143,293)(144,296)(145,273)(146,276)(147,275)(148,274)(149,287)(150,286)(151,285)(152,288)(153,283)(154,282)(155,281)(156,284)(157,279)(158,278)(159,277)(160,280)(161,417)(162,420)(163,419)(164,418)(165,431)(166,430)(167,429)(168,432)(169,427)(170,426)(171,425)(172,428)(173,423)(174,422)(175,421)(176,424)(177,401)(178,404)(179,403)(180,402)(181,415)(182,414)(183,413)(184,416)(185,411)(186,410)(187,409)(188,412)(189,407)(190,406)(191,405)(192,408)(193,465)(194,468)(195,467)(196,466)(197,479)(198,478)(199,477)(200,480)(201,475)(202,474)(203,473)(204,476)(205,471)(206,470)(207,469)(208,472)(209,449)(210,452)(211,451)(212,450)(213,463)(214,462)(215,461)(216,464)(217,459)(218,458)(219,457)(220,460)(221,455)(222,454)(223,453)(224,456)(225,433)(226,436)(227,435)(228,434)(229,447)(230,446)(231,445)(232,448)(233,443)(234,442)(235,441)(236,444)(237,439)(238,438)(239,437)(240,440)(481,817)(482,820)(483,819)(484,818)(485,831)(486,830)(487,829)(488,832)(489,827)(490,826)(491,825)(492,828)(493,823)(494,822)(495,821)(496,824)(497,801)(498,804)(499,803)(500,802)(501,815)(502,814)(503,813)(504,816)(505,811)(506,810)(507,809)(508,812)(509,807)(510,806)(511,805)(512,808)(513,865)(514,868)(515,867)(516,866)(517,879)(518,878)(519,877)(520,880)(521,875)(522,874)(523,873)(524,876)(525,871)(526,870)(527,869)(528,872)(529,849)(530,852)(531,851)(532,850)(533,863)(534,862)(535,861)(536,864)(537,859)(538,858)(539,857)(540,860)(541,855)(542,854)(543,853)(544,856)(545,833)(546,836)(547,835)(548,834)(549,847)(550,846)(551,845)(552,848)(553,843)(554,842)(555,841)(556,844)(557,839)(558,838)(559,837)(560,840)(561,737)(562,740)(563,739)(564,738)(565,751)(566,750)(567,749)(568,752)(569,747)(570,746)(571,745)(572,748)(573,743)(574,742)(575,741)(576,744)(577,721)(578,724)(579,723)(580,722)(581,735)(582,734)(583,733)(584,736)(585,731)(586,730)(587,729)(588,732)(589,727)(590,726)(591,725)(592,728)(593,785)(594,788)(595,787)(596,786)(597,799)(598,798)(599,797)(600,800)(601,795)(602,794)(603,793)(604,796)(605,791)(606,790)(607,789)(608,792)(609,769)(610,772)(611,771)(612,770)(613,783)(614,782)(615,781)(616,784)(617,779)(618,778)(619,777)(620,780)(621,775)(622,774)(623,773)(624,776)(625,753)(626,756)(627,755)(628,754)(629,767)(630,766)(631,765)(632,768)(633,763)(634,762)(635,761)(636,764)(637,759)(638,758)(639,757)(640,760)(641,897)(642,900)(643,899)(644,898)(645,911)(646,910)(647,909)(648,912)(649,907)(650,906)(651,905)(652,908)(653,903)(654,902)(655,901)(656,904)(657,881)(658,884)(659,883)(660,882)(661,895)(662,894)(663,893)(664,896)(665,891)(666,890)(667,889)(668,892)(669,887)(670,886)(671,885)(672,888)(673,945)(674,948)(675,947)(676,946)(677,959)(678,958)(679,957)(680,960)(681,955)(682,954)(683,953)(684,956)(685,951)(686,950)(687,949)(688,952)(689,929)(690,932)(691,931)(692,930)(693,943)(694,942)(695,941)(696,944)(697,939)(698,938)(699,937)(700,940)(701,935)(702,934)(703,933)(704,936)(705,913)(706,916)(707,915)(708,914)(709,927)(710,926)(711,925)(712,928)(713,923)(714,922) (715,921)(716,924)(717,919)(718,918)(719,917)(720,920);; s2 := ( 1,727)( 2,728)( 3,725)( 4,726)( 5,723)( 6,724)( 7,721)( 8,722)( 9,733)( 10,734)( 11,735)( 12,736)( 13,729)( 14,730)( 15,731)( 16,732)( 17,743)( 18,744)( 19,741)( 20,742) ( 21,739)( 22,740)( 23,737)( 24,738)( 25,749)( 26,750)( 27,751)( 28,752)( 29,745)( 30,746)( 31,747)( 32,748)( 33,759)( 34,760)( 35,757)( 36,758)( 37,755)( 38,756)( 39,753)( 40,754)( 41,765)( 42,766)( 43,767)( 44,768)( 45,761)( 46,762)( 47,763)( 48,764)( 49,775)( 50,776)( 51,773)( 52,774)( 53,771)( 54,772)( 55,769)( 56,770)( 57,781)( 58,782)( 59,783)( 60,784)( 61,777)( 62,778)( 63,779)( 64,780)( 65,791)( 66,792)( 67,789)( 68,790)( 69,787)( 70,788)( 71,785)( 72,786)( 73,797)( 74,798)( 75,799)( 76,800)( 77,793)( 78,794)( 79,795)( 80,796)( 81,807)( 82,808)( 83,805)( 84,806)( 85,803)( 86,804)( 87,801)( 88,802)( 89,813)( 90,814)( 91,815)( 92,816)( 93,809)( 94,810)( 95,811)( 96,812)( 97,823)( 98,824)( 99,821)(100,822)(101,819)(102,820)(103,817)(104,818)(105,829)(106,830)(107,831)(108,832)(109,825)(110,826)(111,827)(112,828)(113,839)(114,840)(115,837)(116,838)(117,835)(118,836)(119,833)(120,834)(121,845)(122,846)(123,847)(124,848)(125,841)(126,842)(127,843)(128,844)(129,855)(130,856)(131,853)(132,854)(133,851)(134,852)(135,849)(136,850)(137,861)(138,862)(139,863)(140,864)(141,857)(142,858)(143,859)(144,860)(145,871)(146,872)(147,869)(148,870)(149,867)(150,868)(151,865)(152,866)(153,877)(154,878)(155,879)(156,880)(157,873)(158,874)(159,875)(160,876)(161,887)(162,888)(163,885)(164,886)(165,883)(166,884)(167,881)(168,882)(169,893)(170,894)(171,895)(172,896)(173,889)(174,890)(175,891)(176,892)(177,903)(178,904)(179,901)(180,902)(181,899)(182,900)(183,897)(184,898)(185,909)(186,910)(187,911)(188,912)(189,905)(190,906)(191,907)(192,908)(193,919)(194,920)(195,917)(196,918)(197,915)(198,916)(199,913)(200,914)(201,925)(202,926)(203,927)(204,928)(205,921)(206,922)(207,923)(208,924)(209,935)(210,936)(211,933)(212,934)(213,931)(214,932)(215,929)(216,930)(217,941)(218,942)(219,943)(220,944)(221,937)(222,938)(223,939)(224,940)(225,951)(226,952)(227,949)(228,950)(229,947)(230,948)(231,945)(232,946)(233,957)(234,958)(235,959)(236,960)(237,953)(238,954)(239,955)(240,956)(241,487)(242,488)(243,485)(244,486)(245,483)(246,484)(247,481)(248,482)(249,493)(250,494)(251,495)(252,496)(253,489)(254,490)(255,491)(256,492)(257,503)(258,504)(259,501)(260,502)(261,499)(262,500)(263,497)(264,498)(265,509)(266,510)(267,511)(268,512)(269,505)(270,506)(271,507)(272,508)(273,519)(274,520)(275,517)(276,518)(277,515)(278,516)(279,513)(280,514)(281,525)(282,526)(283,527)(284,528)(285,521)(286,522)(287,523)(288,524)(289,535)(290,536)(291,533)(292,534)(293,531)(294,532)(295,529)(296,530)(297,541)(298,542)(299,543)(300,544)(301,537)(302,538)(303,539)(304,540)(305,551)(306,552)(307,549)(308,550)(309,547)(310,548)(311,545)(312,546)(313,557)(314,558)(315,559)(316,560)(317,553)(318,554)(319,555)(320,556)(321,567)(322,568)(323,565)(324,566)(325,563)(326,564)(327,561)(328,562)(329,573)(330,574)(331,575)(332,576)(333,569)(334,570)(335,571)(336,572)(337,583)(338,584)(339,581)(340,582)(341,579)(342,580)(343,577)(344,578)(345,589)(346,590)(347,591)(348,592)(349,585)(350,586)(351,587)(352,588)(353,599)(354,600)(355,597)(356,598)(357,595)(358,596)(359,593)(360,594)(361,605)(362,606)(363,607)(364,608)(365,601)(366,602)(367,603)(368,604)(369,615)(370,616)(371,613)(372,614)(373,611)(374,612)(375,609)(376,610)(377,621)(378,622)(379,623)(380,624)(381,617)(382,618)(383,619)(384,620)(385,631)(386,632)(387,629)(388,630)(389,627)(390,628)(391,625)(392,626)(393,637)(394,638)(395,639)(396,640)(397,633)(398,634)(399,635)(400,636)(401,647)(402,648)(403,645)(404,646)(405,643)(406,644)(407,641)(408,642)(409,653)(410,654)(411,655)(412,656)(413,649)(414,650)(415,651)(416,652)(417,663)(418,664)(419,661)(420,662)(421,659)(422,660)(423,657)(424,658)(425,669)(426,670)(427,671)(428,672)(429,665)(430,666)(431,667)(432,668)(433,679)(434,680)(435,677)(436,678)(437,675)(438,676)(439,673)(440,674)(441,685)(442,686)(443,687)(444,688)(445,681)(446,682)(447,683)(448,684)(449,695)(450,696)(451,693)(452,694)(453,691)(454,692)(455,689)(456,690)(457,701)(458,702)(459,703)(460,704)(461,697)(462,698)(463,699)(464,700)(465,711)(466,712)(467,709)(468,710)(469,707)(470,708)(471,705)(472,706)(473,717)(474,718) (475,719)(476,720)(477,713)(478,714)(479,715)(480,716);; 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*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*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*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)!( 3, 4)( 5, 6)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 77)( 26, 78)( 27, 80)( 28, 79)( 29, 73) ( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 61)( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,221)(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,205)(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)(147,180)(148,179)(149,182)(150,181)(151,183)(152,184)(153,189)(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(245,246)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)(261,310)(262,309)(263,311)(264,312)(265,317)(266,318)(267,320)(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)(277,294)(278,293)(279,295)(280,296)(281,301)(282,302)(283,304)(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)(341,470)(342,469)(343,471)(344,472)(345,477)(346,478)(347,480)(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)(357,454)(358,453)(359,455)(360,456)(361,461)(362,462)(363,464)(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)(373,438)(374,437)(375,439)(376,440)(377,445)(378,446)(379,448)(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)(389,422)(390,421)(391,423)(392,424)(393,429)(394,430)(395,432)(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(485,486)(489,493)(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,550)(502,549)(503,551)(504,552)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,534)(518,533)(519,535)(520,536)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,646)(566,645)(567,647)(568,648)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,710)(582,709)(583,711)(584,712)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,694)(598,693)(599,695)(600,696)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,678)(614,677)(615,679)(616,680)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,662)(630,661)(631,663)(632,664)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)(639,668)(640,667)(723,724)(725,726)(729,733)(730,734)(731,736)(732,735)(737,785)(738,786)(739,788)(740,787)(741,790)(742,789)(743,791)(744,792)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)(753,769)(754,770)(755,772)(756,771)(757,774)(758,773)(759,775)(760,776)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)(801,881)(802,882)(803,884)(804,883)(805,886)(806,885)(807,887)(808,888)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)(817,945)(818,946)(819,948)(820,947)(821,950)(822,949)(823,951)(824,952)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)(833,929)(834,930)(835,932)(836,931)(837,934)(838,933)(839,935)(840,936)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)(849,913)(850,914)(851,916)(852,915)(853,918)(854,917)(855,919)(856,920)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)(865,897)(866,898)(867,900)(868,899)(869,902)(870,901)(871,903)(872,904)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907); s1 := Sym(960)!( 1,337)( 2,340)( 3,339)( 4,338)( 5,351)( 6,350)( 7,349)( 8,352)( 9,347)( 10,346)( 11,345)( 12,348)( 13,343)( 14,342)( 15,341)( 16,344)( 17,321)( 18,324)( 19,323) ( 20,322)( 21,335)( 22,334)( 23,333)( 24,336)( 25,331)( 26,330)( 27,329)( 28,332)( 29,327)( 30,326)( 31,325)( 32,328)( 33,385)( 34,388)( 35,387)( 36,386)( 37,399)( 38,398)( 39,397)( 40,400)( 41,395)( 42,394)( 43,393)( 44,396)( 45,391)( 46,390)( 47,389)( 48,392)( 49,369)( 50,372)( 51,371)( 52,370)( 53,383)( 54,382)( 55,381)( 56,384)( 57,379)( 58,378)( 59,377)( 60,380)( 61,375)( 62,374)( 63,373)( 64,376)( 65,353)( 66,356)( 67,355)( 68,354)( 69,367)( 70,366)( 71,365)( 72,368)( 73,363)( 74,362)( 75,361)( 76,364)( 77,359)( 78,358)( 79,357)( 80,360)( 81,257)( 82,260)( 83,259)( 84,258)( 85,271)( 86,270)( 87,269)( 88,272)( 89,267)( 90,266)( 91,265)( 92,268)( 93,263)( 94,262)( 95,261)( 96,264)( 97,241)( 98,244)( 99,243)(100,242)(101,255)(102,254)(103,253)(104,256)(105,251)(106,250)(107,249)(108,252)(109,247)(110,246)(111,245)(112,248)(113,305)(114,308)(115,307)(116,306)(117,319)(118,318)(119,317)(120,320)(121,315)(122,314)(123,313)(124,316)(125,311)(126,310)(127,309)(128,312)(129,289)(130,292)(131,291)(132,290)(133,303)(134,302)(135,301)(136,304)(137,299)(138,298)(139,297)(140,300)(141,295)(142,294)(143,293)(144,296)(145,273)(146,276)(147,275)(148,274)(149,287)(150,286)(151,285)(152,288)(153,283)(154,282)(155,281)(156,284)(157,279)(158,278)(159,277)(160,280)(161,417)(162,420)(163,419)(164,418)(165,431)(166,430)(167,429)(168,432)(169,427)(170,426)(171,425)(172,428)(173,423)(174,422)(175,421)(176,424)(177,401)(178,404)(179,403)(180,402)(181,415)(182,414)(183,413)(184,416)(185,411)(186,410)(187,409)(188,412)(189,407)(190,406)(191,405)(192,408)(193,465)(194,468)(195,467)(196,466)(197,479)(198,478)(199,477)(200,480)(201,475)(202,474)(203,473)(204,476)(205,471)(206,470)(207,469)(208,472)(209,449)(210,452)(211,451)(212,450)(213,463)(214,462)(215,461)(216,464)(217,459)(218,458)(219,457)(220,460)(221,455)(222,454)(223,453)(224,456)(225,433)(226,436)(227,435)(228,434)(229,447)(230,446)(231,445)(232,448)(233,443)(234,442)(235,441)(236,444)(237,439)(238,438)(239,437)(240,440)(481,817)(482,820)(483,819)(484,818)(485,831)(486,830)(487,829)(488,832)(489,827)(490,826)(491,825)(492,828)(493,823)(494,822)(495,821)(496,824)(497,801)(498,804)(499,803)(500,802)(501,815)(502,814)(503,813)(504,816)(505,811)(506,810)(507,809)(508,812)(509,807)(510,806)(511,805)(512,808)(513,865)(514,868)(515,867)(516,866)(517,879)(518,878)(519,877)(520,880)(521,875)(522,874)(523,873)(524,876)(525,871)(526,870)(527,869)(528,872)(529,849)(530,852)(531,851)(532,850)(533,863)(534,862)(535,861)(536,864)(537,859)(538,858)(539,857)(540,860)(541,855)(542,854)(543,853)(544,856)(545,833)(546,836)(547,835)(548,834)(549,847)(550,846)(551,845)(552,848)(553,843)(554,842)(555,841)(556,844)(557,839)(558,838)(559,837)(560,840)(561,737)(562,740)(563,739)(564,738)(565,751)(566,750)(567,749)(568,752)(569,747)(570,746)(571,745)(572,748)(573,743)(574,742)(575,741)(576,744)(577,721)(578,724)(579,723)(580,722)(581,735)(582,734)(583,733)(584,736)(585,731)(586,730)(587,729)(588,732)(589,727)(590,726)(591,725)(592,728)(593,785)(594,788)(595,787)(596,786)(597,799)(598,798)(599,797)(600,800)(601,795)(602,794)(603,793)(604,796)(605,791)(606,790)(607,789)(608,792)(609,769)(610,772)(611,771)(612,770)(613,783)(614,782)(615,781)(616,784)(617,779)(618,778)(619,777)(620,780)(621,775)(622,774)(623,773)(624,776)(625,753)(626,756)(627,755)(628,754)(629,767)(630,766)(631,765)(632,768)(633,763)(634,762)(635,761)(636,764)(637,759)(638,758)(639,757)(640,760)(641,897)(642,900)(643,899)(644,898)(645,911)(646,910)(647,909)(648,912)(649,907)(650,906)(651,905)(652,908)(653,903)(654,902)(655,901)(656,904)(657,881)(658,884)(659,883)(660,882)(661,895)(662,894)(663,893)(664,896)(665,891)(666,890)(667,889)(668,892)(669,887)(670,886)(671,885)(672,888)(673,945)(674,948)(675,947)(676,946)(677,959)(678,958)(679,957)(680,960)(681,955)(682,954)(683,953)(684,956)(685,951)(686,950)(687,949)(688,952)(689,929)(690,932)(691,931)(692,930)(693,943)(694,942)(695,941)(696,944)(697,939)(698,938)(699,937)(700,940)(701,935)(702,934)(703,933)(704,936)(705,913)(706,916)(707,915)(708,914)(709,927)(710,926)(711,925)(712,928)(713,923) (714,922)(715,921)(716,924)(717,919)(718,918)(719,917)(720,920); s2 := Sym(960)!( 1,727)( 2,728)( 3,725)( 4,726)( 5,723)( 6,724)( 7,721)( 8,722)( 9,733)( 10,734)( 11,735)( 12,736)( 13,729)( 14,730)( 15,731)( 16,732)( 17,743)( 18,744)( 19,741) ( 20,742)( 21,739)( 22,740)( 23,737)( 24,738)( 25,749)( 26,750)( 27,751)( 28,752)( 29,745)( 30,746)( 31,747)( 32,748)( 33,759)( 34,760)( 35,757)( 36,758)( 37,755)( 38,756)( 39,753)( 40,754)( 41,765)( 42,766)( 43,767)( 44,768)( 45,761)( 46,762)( 47,763)( 48,764)( 49,775)( 50,776)( 51,773)( 52,774)( 53,771)( 54,772)( 55,769)( 56,770)( 57,781)( 58,782)( 59,783)( 60,784)( 61,777)( 62,778)( 63,779)( 64,780)( 65,791)( 66,792)( 67,789)( 68,790)( 69,787)( 70,788)( 71,785)( 72,786)( 73,797)( 74,798)( 75,799)( 76,800)( 77,793)( 78,794)( 79,795)( 80,796)( 81,807)( 82,808)( 83,805)( 84,806)( 85,803)( 86,804)( 87,801)( 88,802)( 89,813)( 90,814)( 91,815)( 92,816)( 93,809)( 94,810)( 95,811)( 96,812)( 97,823)( 98,824)( 99,821)(100,822)(101,819)(102,820)(103,817)(104,818)(105,829)(106,830)(107,831)(108,832)(109,825)(110,826)(111,827)(112,828)(113,839)(114,840)(115,837)(116,838)(117,835)(118,836)(119,833)(120,834)(121,845)(122,846)(123,847)(124,848)(125,841)(126,842)(127,843)(128,844)(129,855)(130,856)(131,853)(132,854)(133,851)(134,852)(135,849)(136,850)(137,861)(138,862)(139,863)(140,864)(141,857)(142,858)(143,859)(144,860)(145,871)(146,872)(147,869)(148,870)(149,867)(150,868)(151,865)(152,866)(153,877)(154,878)(155,879)(156,880)(157,873)(158,874)(159,875)(160,876)(161,887)(162,888)(163,885)(164,886)(165,883)(166,884)(167,881)(168,882)(169,893)(170,894)(171,895)(172,896)(173,889)(174,890)(175,891)(176,892)(177,903)(178,904)(179,901)(180,902)(181,899)(182,900)(183,897)(184,898)(185,909)(186,910)(187,911)(188,912)(189,905)(190,906)(191,907)(192,908)(193,919)(194,920)(195,917)(196,918)(197,915)(198,916)(199,913)(200,914)(201,925)(202,926)(203,927)(204,928)(205,921)(206,922)(207,923)(208,924)(209,935)(210,936)(211,933)(212,934)(213,931)(214,932)(215,929)(216,930)(217,941)(218,942)(219,943)(220,944)(221,937)(222,938)(223,939)(224,940)(225,951)(226,952)(227,949)(228,950)(229,947)(230,948)(231,945)(232,946)(233,957)(234,958)(235,959)(236,960)(237,953)(238,954)(239,955)(240,956)(241,487)(242,488)(243,485)(244,486)(245,483)(246,484)(247,481)(248,482)(249,493)(250,494)(251,495)(252,496)(253,489)(254,490)(255,491)(256,492)(257,503)(258,504)(259,501)(260,502)(261,499)(262,500)(263,497)(264,498)(265,509)(266,510)(267,511)(268,512)(269,505)(270,506)(271,507)(272,508)(273,519)(274,520)(275,517)(276,518)(277,515)(278,516)(279,513)(280,514)(281,525)(282,526)(283,527)(284,528)(285,521)(286,522)(287,523)(288,524)(289,535)(290,536)(291,533)(292,534)(293,531)(294,532)(295,529)(296,530)(297,541)(298,542)(299,543)(300,544)(301,537)(302,538)(303,539)(304,540)(305,551)(306,552)(307,549)(308,550)(309,547)(310,548)(311,545)(312,546)(313,557)(314,558)(315,559)(316,560)(317,553)(318,554)(319,555)(320,556)(321,567)(322,568)(323,565)(324,566)(325,563)(326,564)(327,561)(328,562)(329,573)(330,574)(331,575)(332,576)(333,569)(334,570)(335,571)(336,572)(337,583)(338,584)(339,581)(340,582)(341,579)(342,580)(343,577)(344,578)(345,589)(346,590)(347,591)(348,592)(349,585)(350,586)(351,587)(352,588)(353,599)(354,600)(355,597)(356,598)(357,595)(358,596)(359,593)(360,594)(361,605)(362,606)(363,607)(364,608)(365,601)(366,602)(367,603)(368,604)(369,615)(370,616)(371,613)(372,614)(373,611)(374,612)(375,609)(376,610)(377,621)(378,622)(379,623)(380,624)(381,617)(382,618)(383,619)(384,620)(385,631)(386,632)(387,629)(388,630)(389,627)(390,628)(391,625)(392,626)(393,637)(394,638)(395,639)(396,640)(397,633)(398,634)(399,635)(400,636)(401,647)(402,648)(403,645)(404,646)(405,643)(406,644)(407,641)(408,642)(409,653)(410,654)(411,655)(412,656)(413,649)(414,650)(415,651)(416,652)(417,663)(418,664)(419,661)(420,662)(421,659)(422,660)(423,657)(424,658)(425,669)(426,670)(427,671)(428,672)(429,665)(430,666)(431,667)(432,668)(433,679)(434,680)(435,677)(436,678)(437,675)(438,676)(439,673)(440,674)(441,685)(442,686)(443,687)(444,688)(445,681)(446,682)(447,683)(448,684)(449,695)(450,696)(451,693)(452,694)(453,691)(454,692)(455,689)(456,690)(457,701)(458,702)(459,703)(460,704)(461,697)(462,698)(463,699)(464,700)(465,711)(466,712)(467,709)(468,710)(469,707)(470,708)(471,705)(472,706)(473,717) (474,718)(475,719)(476,720)(477,713)(478,714)(479,715)(480,716); 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*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*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*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.