Overview
- Group
- SmallGroup(1944,949)
- Rank
- 3
- Schläfli Type
- {6,18}
- Vertices, edges, …
- 54, 486, 162
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
9-fold
18-fold
27-fold
54-fold
81-fold
162-fold
243-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*(s2*s1)^2*s0*(s1*s2)^2> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<(s0*s2*s1)^2*(s0*(s2*s1)^2)^2> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<s0*(s2*s1)^2*s0*(s2*s1)^4> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 9
30 facets
6 vertex figures
- 6 of {18}*36
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2> of order 9
18 facets
- 18 of {6}*12
6 vertex figures
- 6 of {18}*36
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2, s0*(s1*s2)^5*s1*s0*s2> of order 9
18 facets
- 18 of {6}*12
12 vertex figures
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^4*s2> of order 9
18 facets
- 18 of {6}*12
6 vertex figures
- 6 of {18}*36
P/N, where N=<(s0*s1)^2, s0*(s1*s2)^5*s1*s0*s2> of order 9
30 facets
12 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482);; s1 := ( 1, 28)( 2, 30)( 3, 29)( 4, 31)( 5, 33)( 6, 32)( 7, 34)( 8, 36)( 9, 35)( 10, 46)( 11, 48)( 12, 47)( 13, 49)( 14, 51)( 15, 50)( 16, 52)( 17, 54)( 18, 53)( 19, 37)( 20, 39)( 21, 38)( 22, 40)( 23, 42)( 24, 41)( 25, 43)( 26, 45)( 27, 44)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 82,199)( 83,201)( 84,200)( 85,202)( 86,204)( 87,203)( 88,205)( 89,207)( 90,206)( 91,190)( 92,192)( 93,191)( 94,193)( 95,195)( 96,194)( 97,196)( 98,198)( 99,197)(100,208)(101,210)(102,209)(103,211)(104,213)(105,212)(106,214)(107,216)(108,215)(109,172)(110,174)(111,173)(112,175)(113,177)(114,176)(115,178)(116,180)(117,179)(118,163)(119,165)(120,164)(121,166)(122,168)(123,167)(124,169)(125,171)(126,170)(127,181)(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)(135,188)(136,226)(137,228)(138,227)(139,229)(140,231)(141,230)(142,232)(143,234)(144,233)(145,217)(146,219)(147,218)(148,220)(149,222)(150,221)(151,223)(152,225)(153,224)(154,235)(155,237)(156,236)(157,238)(158,240)(159,239)(160,241)(161,243)(162,242)(244,271)(245,273)(246,272)(247,274)(248,276)(249,275)(250,277)(251,279)(252,278)(253,289)(254,291)(255,290)(256,292)(257,294)(258,293)(259,295)(260,297)(261,296)(262,280)(263,282)(264,281)(265,283)(266,285)(267,284)(268,286)(269,288)(270,287)(299,300)(302,303)(305,306)(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)(315,323)(325,442)(326,444)(327,443)(328,445)(329,447)(330,446)(331,448)(332,450)(333,449)(334,433)(335,435)(336,434)(337,436)(338,438)(339,437)(340,439)(341,441)(342,440)(343,451)(344,453)(345,452)(346,454)(347,456)(348,455)(349,457)(350,459)(351,458)(352,415)(353,417)(354,416)(355,418)(356,420)(357,419)(358,421)(359,423)(360,422)(361,406)(362,408)(363,407)(364,409)(365,411)(366,410)(367,412)(368,414)(369,413)(370,424)(371,426)(372,425)(373,427)(374,429)(375,428)(376,430)(377,432)(378,431)(379,469)(380,471)(381,470)(382,472)(383,474)(384,473)(385,475)(386,477)(387,476)(388,460)(389,462)(390,461)(391,463)(392,465)(393,464)(394,466)(395,468)(396,467)(397,478)(398,480)(399,479)(400,481)(401,483)(402,482)(403,484)(404,486)(405,485);; s2 := ( 1,325)( 2,327)( 3,326)( 4,330)( 5,329)( 6,328)( 7,332)( 8,331)( 9,333)( 10,343)( 11,345)( 12,344)( 13,348)( 14,347)( 15,346)( 16,350)( 17,349)( 18,351)( 19,334)( 20,336)( 21,335)( 22,339)( 23,338)( 24,337)( 25,341)( 26,340)( 27,342)( 28,387)( 29,386)( 30,385)( 31,380)( 32,379)( 33,381)( 34,382)( 35,384)( 36,383)( 37,405)( 38,404)( 39,403)( 40,398)( 41,397)( 42,399)( 43,400)( 44,402)( 45,401)( 46,396)( 47,395)( 48,394)( 49,389)( 50,388)( 51,390)( 52,391)( 53,393)( 54,392)( 55,356)( 56,355)( 57,357)( 58,358)( 59,360)( 60,359)( 61,354)( 62,353)( 63,352)( 64,374)( 65,373)( 66,375)( 67,376)( 68,378)( 69,377)( 70,372)( 71,371)( 72,370)( 73,365)( 74,364)( 75,366)( 76,367)( 77,369)( 78,368)( 79,363)( 80,362)( 81,361)( 82,244)( 83,246)( 84,245)( 85,249)( 86,248)( 87,247)( 88,251)( 89,250)( 90,252)( 91,262)( 92,264)( 93,263)( 94,267)( 95,266)( 96,265)( 97,269)( 98,268)( 99,270)(100,253)(101,255)(102,254)(103,258)(104,257)(105,256)(106,260)(107,259)(108,261)(109,306)(110,305)(111,304)(112,299)(113,298)(114,300)(115,301)(116,303)(117,302)(118,324)(119,323)(120,322)(121,317)(122,316)(123,318)(124,319)(125,321)(126,320)(127,315)(128,314)(129,313)(130,308)(131,307)(132,309)(133,310)(134,312)(135,311)(136,275)(137,274)(138,276)(139,277)(140,279)(141,278)(142,273)(143,272)(144,271)(145,293)(146,292)(147,294)(148,295)(149,297)(150,296)(151,291)(152,290)(153,289)(154,284)(155,283)(156,285)(157,286)(158,288)(159,287)(160,282)(161,281)(162,280)(163,415)(164,417)(165,416)(166,420)(167,419)(168,418)(169,422)(170,421)(171,423)(172,406)(173,408)(174,407)(175,411)(176,410)(177,409)(178,413)(179,412)(180,414)(181,424)(182,426)(183,425)(184,429)(185,428)(186,427)(187,431)(188,430)(189,432)(190,477)(191,476)(192,475)(193,470)(194,469)(195,471)(196,472)(197,474)(198,473)(199,468)(200,467)(201,466)(202,461)(203,460)(204,462)(205,463)(206,465)(207,464)(208,486)(209,485)(210,484)(211,479)(212,478)(213,480)(214,481)(215,483)(216,482)(217,446)(218,445)(219,447)(220,448)(221,450)(222,449)(223,444)(224,443)(225,442)(226,437)(227,436)(228,438)(229,439)(230,441)(231,440)(232,435)(233,434)(234,433)(235,455)(236,454)(237,456)(238,457)(239,459)(240,458)(241,453)(242,452)(243,451);; 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*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(486)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482); s1 := Sym(486)!( 1, 28)( 2, 30)( 3, 29)( 4, 31)( 5, 33)( 6, 32)( 7, 34)( 8, 36)( 9, 35)( 10, 46)( 11, 48)( 12, 47)( 13, 49)( 14, 51)( 15, 50)( 16, 52)( 17, 54)( 18, 53)( 19, 37)( 20, 39)( 21, 38)( 22, 40)( 23, 42)( 24, 41)( 25, 43)( 26, 45)( 27, 44)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 82,199)( 83,201)( 84,200)( 85,202)( 86,204)( 87,203)( 88,205)( 89,207)( 90,206)( 91,190)( 92,192)( 93,191)( 94,193)( 95,195)( 96,194)( 97,196)( 98,198)( 99,197)(100,208)(101,210)(102,209)(103,211)(104,213)(105,212)(106,214)(107,216)(108,215)(109,172)(110,174)(111,173)(112,175)(113,177)(114,176)(115,178)(116,180)(117,179)(118,163)(119,165)(120,164)(121,166)(122,168)(123,167)(124,169)(125,171)(126,170)(127,181)(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)(135,188)(136,226)(137,228)(138,227)(139,229)(140,231)(141,230)(142,232)(143,234)(144,233)(145,217)(146,219)(147,218)(148,220)(149,222)(150,221)(151,223)(152,225)(153,224)(154,235)(155,237)(156,236)(157,238)(158,240)(159,239)(160,241)(161,243)(162,242)(244,271)(245,273)(246,272)(247,274)(248,276)(249,275)(250,277)(251,279)(252,278)(253,289)(254,291)(255,290)(256,292)(257,294)(258,293)(259,295)(260,297)(261,296)(262,280)(263,282)(264,281)(265,283)(266,285)(267,284)(268,286)(269,288)(270,287)(299,300)(302,303)(305,306)(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)(315,323)(325,442)(326,444)(327,443)(328,445)(329,447)(330,446)(331,448)(332,450)(333,449)(334,433)(335,435)(336,434)(337,436)(338,438)(339,437)(340,439)(341,441)(342,440)(343,451)(344,453)(345,452)(346,454)(347,456)(348,455)(349,457)(350,459)(351,458)(352,415)(353,417)(354,416)(355,418)(356,420)(357,419)(358,421)(359,423)(360,422)(361,406)(362,408)(363,407)(364,409)(365,411)(366,410)(367,412)(368,414)(369,413)(370,424)(371,426)(372,425)(373,427)(374,429)(375,428)(376,430)(377,432)(378,431)(379,469)(380,471)(381,470)(382,472)(383,474)(384,473)(385,475)(386,477)(387,476)(388,460)(389,462)(390,461)(391,463)(392,465)(393,464)(394,466)(395,468)(396,467)(397,478)(398,480)(399,479)(400,481)(401,483)(402,482)(403,484)(404,486)(405,485); s2 := Sym(486)!( 1,325)( 2,327)( 3,326)( 4,330)( 5,329)( 6,328)( 7,332)( 8,331)( 9,333)( 10,343)( 11,345)( 12,344)( 13,348)( 14,347)( 15,346)( 16,350)( 17,349)( 18,351)( 19,334)( 20,336)( 21,335)( 22,339)( 23,338)( 24,337)( 25,341)( 26,340)( 27,342)( 28,387)( 29,386)( 30,385)( 31,380)( 32,379)( 33,381)( 34,382)( 35,384)( 36,383)( 37,405)( 38,404)( 39,403)( 40,398)( 41,397)( 42,399)( 43,400)( 44,402)( 45,401)( 46,396)( 47,395)( 48,394)( 49,389)( 50,388)( 51,390)( 52,391)( 53,393)( 54,392)( 55,356)( 56,355)( 57,357)( 58,358)( 59,360)( 60,359)( 61,354)( 62,353)( 63,352)( 64,374)( 65,373)( 66,375)( 67,376)( 68,378)( 69,377)( 70,372)( 71,371)( 72,370)( 73,365)( 74,364)( 75,366)( 76,367)( 77,369)( 78,368)( 79,363)( 80,362)( 81,361)( 82,244)( 83,246)( 84,245)( 85,249)( 86,248)( 87,247)( 88,251)( 89,250)( 90,252)( 91,262)( 92,264)( 93,263)( 94,267)( 95,266)( 96,265)( 97,269)( 98,268)( 99,270)(100,253)(101,255)(102,254)(103,258)(104,257)(105,256)(106,260)(107,259)(108,261)(109,306)(110,305)(111,304)(112,299)(113,298)(114,300)(115,301)(116,303)(117,302)(118,324)(119,323)(120,322)(121,317)(122,316)(123,318)(124,319)(125,321)(126,320)(127,315)(128,314)(129,313)(130,308)(131,307)(132,309)(133,310)(134,312)(135,311)(136,275)(137,274)(138,276)(139,277)(140,279)(141,278)(142,273)(143,272)(144,271)(145,293)(146,292)(147,294)(148,295)(149,297)(150,296)(151,291)(152,290)(153,289)(154,284)(155,283)(156,285)(157,286)(158,288)(159,287)(160,282)(161,281)(162,280)(163,415)(164,417)(165,416)(166,420)(167,419)(168,418)(169,422)(170,421)(171,423)(172,406)(173,408)(174,407)(175,411)(176,410)(177,409)(178,413)(179,412)(180,414)(181,424)(182,426)(183,425)(184,429)(185,428)(186,427)(187,431)(188,430)(189,432)(190,477)(191,476)(192,475)(193,470)(194,469)(195,471)(196,472)(197,474)(198,473)(199,468)(200,467)(201,466)(202,461)(203,460)(204,462)(205,463)(206,465)(207,464)(208,486)(209,485)(210,484)(211,479)(212,478)(213,480)(214,481)(215,483)(216,482)(217,446)(218,445)(219,447)(220,448)(221,450)(222,449)(223,444)(224,443)(225,442)(226,437)(227,436)(228,438)(229,439)(230,441)(231,440)(232,435)(233,434)(234,433)(235,455)(236,454)(237,456)(238,457)(239,459)(240,458)(241,453)(242,452)(243,451); poly := sub<Sym(486)|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*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*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 >;
References
None.
to this polytope.