Polytope of Type {6,54} with group SmallGroup(1944,948)

Overview

Group: SmallGroup(1944,948)
Rank: 3
Schläfli Type: {6,54}
Vertices, edges, …: 18, 486, 162
Order of s₀s₁s₂: 54
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

{6,54}*972a

3-fold

6-fold

{6,18}*324a

9-fold

18-fold

27-fold

54-fold

{2,9}*36

81-fold

162-fold

243-fold

{2,2}*8

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)^16*s2> of order 3

54 facets

54 of {6}*12

6 vertex figures

6 of {54}*108

P/N, where N=<(s0*s1)^2> of order 3

90 facets

54 of {2}*4
36 of {6}*12

6 vertex figures

6 of {54}*108

Representations

Permutation Representation (GAP)

s0 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)( 34, 58)( 35, 59)( 36, 60)( 37, 64)( 38, 65)( 39, 66)( 40, 70)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 69)( 46, 73)( 47, 74)( 48, 75)( 49, 79)( 50, 80)( 51, 81)( 52, 76)( 53, 77)( 54, 78)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)(190,217)(191,218)(192,219)(193,223)(194,224)(195,225)(196,220)(197,221)(198,222)(199,226)(200,227)(201,228)(202,232)(203,233)(204,234)(205,229)(206,230)(207,231)(208,235)(209,236)(210,237)(211,241)(212,242)(213,243)(214,238)(215,239)(216,240)(247,250)(248,251)(249,252)(256,259)(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)(273,300)(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)(328,331)(329,332)(330,333)(337,340)(338,341)(339,342)(346,349)(347,350)(348,351)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)(373,403)(374,404)(375,405)(376,400)(377,401)(378,402)(409,412)(410,413)(411,414)(418,421)(419,422)(420,423)(427,430)(428,431)(429,432)(433,460)(434,461)(435,462)(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483);;
s1 := (  1, 28)(  2, 30)(  3, 29)(  4, 31)(  5, 33)(  6, 32)(  7, 34)(  8, 36)(  9, 35)( 10, 48)( 11, 47)( 12, 46)( 13, 51)( 14, 50)( 15, 49)( 16, 54)( 17, 53)( 18, 52)( 19, 39)( 20, 38)( 21, 37)( 22, 42)( 23, 41)( 24, 40)( 25, 45)( 26, 44)( 27, 43)( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)( 68, 77)( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 82,210)( 83,209)( 84,208)( 85,213)( 86,212)( 87,211)( 88,216)( 89,215)( 90,214)( 91,201)( 92,200)( 93,199)( 94,204)( 95,203)( 96,202)( 97,207)( 98,206)( 99,205)(100,192)(101,191)(102,190)(103,195)(104,194)(105,193)(106,198)(107,197)(108,196)(109,183)(110,182)(111,181)(112,186)(113,185)(114,184)(115,189)(116,188)(117,187)(118,174)(119,173)(120,172)(121,177)(122,176)(123,175)(124,180)(125,179)(126,178)(127,165)(128,164)(129,163)(130,168)(131,167)(132,166)(133,171)(134,170)(135,169)(136,237)(137,236)(138,235)(139,240)(140,239)(141,238)(142,243)(143,242)(144,241)(145,228)(146,227)(147,226)(148,231)(149,230)(150,229)(151,234)(152,233)(153,232)(154,219)(155,218)(156,217)(157,222)(158,221)(159,220)(160,225)(161,224)(162,223)(244,271)(245,273)(246,272)(247,274)(248,276)(249,275)(250,277)(251,279)(252,278)(253,291)(254,290)(255,289)(256,294)(257,293)(258,292)(259,297)(260,296)(261,295)(262,282)(263,281)(264,280)(265,285)(266,284)(267,283)(268,288)(269,287)(270,286)(299,300)(302,303)(305,306)(307,318)(308,317)(309,316)(310,321)(311,320)(312,319)(313,324)(314,323)(315,322)(325,453)(326,452)(327,451)(328,456)(329,455)(330,454)(331,459)(332,458)(333,457)(334,444)(335,443)(336,442)(337,447)(338,446)(339,445)(340,450)(341,449)(342,448)(343,435)(344,434)(345,433)(346,438)(347,437)(348,436)(349,441)(350,440)(351,439)(352,426)(353,425)(354,424)(355,429)(356,428)(357,427)(358,432)(359,431)(360,430)(361,417)(362,416)(363,415)(364,420)(365,419)(366,418)(367,423)(368,422)(369,421)(370,408)(371,407)(372,406)(373,411)(374,410)(375,409)(376,414)(377,413)(378,412)(379,480)(380,479)(381,478)(382,483)(383,482)(384,481)(385,486)(386,485)(387,484)(388,471)(389,470)(390,469)(391,474)(392,473)(393,472)(394,477)(395,476)(396,475)(397,462)(398,461)(399,460)(400,465)(401,464)(402,463)(403,468)(404,467)(405,466);;
s2 := (  1,325)(  2,327)(  3,326)(  4,331)(  5,333)(  6,332)(  7,328)(  8,330)(  9,329)( 10,345)( 11,344)( 12,343)( 13,351)( 14,350)( 15,349)( 16,348)( 17,347)( 18,346)( 19,336)( 20,335)( 21,334)( 22,342)( 23,341)( 24,340)( 25,339)( 26,338)( 27,337)( 28,355)( 29,357)( 30,356)( 31,352)( 32,354)( 33,353)( 34,358)( 35,360)( 36,359)( 37,375)( 38,374)( 39,373)( 40,372)( 41,371)( 42,370)( 43,378)( 44,377)( 45,376)( 46,366)( 47,365)( 48,364)( 49,363)( 50,362)( 51,361)( 52,369)( 53,368)( 54,367)( 55,385)( 56,387)( 57,386)( 58,382)( 59,384)( 60,383)( 61,379)( 62,381)( 63,380)( 64,405)( 65,404)( 66,403)( 67,402)( 68,401)( 69,400)( 70,399)( 71,398)( 72,397)( 73,396)( 74,395)( 75,394)( 76,393)( 77,392)( 78,391)( 79,390)( 80,389)( 81,388)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)( 88,247)( 89,249)( 90,248)( 91,264)( 92,263)( 93,262)( 94,270)( 95,269)( 96,268)( 97,267)( 98,266)( 99,265)(100,255)(101,254)(102,253)(103,261)(104,260)(105,259)(106,258)(107,257)(108,256)(109,274)(110,276)(111,275)(112,271)(113,273)(114,272)(115,277)(116,279)(117,278)(118,294)(119,293)(120,292)(121,291)(122,290)(123,289)(124,297)(125,296)(126,295)(127,285)(128,284)(129,283)(130,282)(131,281)(132,280)(133,288)(134,287)(135,286)(136,304)(137,306)(138,305)(139,301)(140,303)(141,302)(142,298)(143,300)(144,299)(145,324)(146,323)(147,322)(148,321)(149,320)(150,319)(151,318)(152,317)(153,316)(154,315)(155,314)(156,313)(157,312)(158,311)(159,310)(160,309)(161,308)(162,307)(163,426)(164,425)(165,424)(166,432)(167,431)(168,430)(169,429)(170,428)(171,427)(172,417)(173,416)(174,415)(175,423)(176,422)(177,421)(178,420)(179,419)(180,418)(181,408)(182,407)(183,406)(184,414)(185,413)(186,412)(187,411)(188,410)(189,409)(190,456)(191,455)(192,454)(193,453)(194,452)(195,451)(196,459)(197,458)(198,457)(199,447)(200,446)(201,445)(202,444)(203,443)(204,442)(205,450)(206,449)(207,448)(208,438)(209,437)(210,436)(211,435)(212,434)(213,433)(214,441)(215,440)(216,439)(217,486)(218,485)(219,484)(220,483)(221,482)(222,481)(223,480)(224,479)(225,478)(226,477)(227,476)(228,475)(229,474)(230,473)(231,472)(232,471)(233,470)(234,469)(235,468)(236,467)(237,466)(238,465)(239,464)(240,463)(241,462)(242,461)(243,460);;
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*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(486)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)( 34, 58)( 35, 59)( 36, 60)( 37, 64)( 38, 65)( 39, 66)( 40, 70)( 41, 71)( 42, 72)( 43, 67)( 44, 68)( 45, 69)( 46, 73)( 47, 74)( 48, 75)( 49, 79)( 50, 80)( 51, 81)( 52, 76)( 53, 77)( 54, 78)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(109,136)(110,137)(111,138)(112,142)(113,143)(114,144)(115,139)(116,140)(117,141)(118,145)(119,146)(120,147)(121,151)(122,152)(123,153)(124,148)(125,149)(126,150)(127,154)(128,155)(129,156)(130,160)(131,161)(132,162)(133,157)(134,158)(135,159)(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)(190,217)(191,218)(192,219)(193,223)(194,224)(195,225)(196,220)(197,221)(198,222)(199,226)(200,227)(201,228)(202,232)(203,233)(204,234)(205,229)(206,230)(207,231)(208,235)(209,236)(210,237)(211,241)(212,242)(213,243)(214,238)(215,239)(216,240)(247,250)(248,251)(249,252)(256,259)(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)(273,300)(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)(328,331)(329,332)(330,333)(337,340)(338,341)(339,342)(346,349)(347,350)(348,351)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)(373,403)(374,404)(375,405)(376,400)(377,401)(378,402)(409,412)(410,413)(411,414)(418,421)(419,422)(420,423)(427,430)(428,431)(429,432)(433,460)(434,461)(435,462)(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483);
s1 := Sym(486)!(  1, 28)(  2, 30)(  3, 29)(  4, 31)(  5, 33)(  6, 32)(  7, 34)(  8, 36)(  9, 35)( 10, 48)( 11, 47)( 12, 46)( 13, 51)( 14, 50)( 15, 49)( 16, 54)( 17, 53)( 18, 52)( 19, 39)( 20, 38)( 21, 37)( 22, 42)( 23, 41)( 24, 40)( 25, 45)( 26, 44)( 27, 43)( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)( 68, 77)( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 82,210)( 83,209)( 84,208)( 85,213)( 86,212)( 87,211)( 88,216)( 89,215)( 90,214)( 91,201)( 92,200)( 93,199)( 94,204)( 95,203)( 96,202)( 97,207)( 98,206)( 99,205)(100,192)(101,191)(102,190)(103,195)(104,194)(105,193)(106,198)(107,197)(108,196)(109,183)(110,182)(111,181)(112,186)(113,185)(114,184)(115,189)(116,188)(117,187)(118,174)(119,173)(120,172)(121,177)(122,176)(123,175)(124,180)(125,179)(126,178)(127,165)(128,164)(129,163)(130,168)(131,167)(132,166)(133,171)(134,170)(135,169)(136,237)(137,236)(138,235)(139,240)(140,239)(141,238)(142,243)(143,242)(144,241)(145,228)(146,227)(147,226)(148,231)(149,230)(150,229)(151,234)(152,233)(153,232)(154,219)(155,218)(156,217)(157,222)(158,221)(159,220)(160,225)(161,224)(162,223)(244,271)(245,273)(246,272)(247,274)(248,276)(249,275)(250,277)(251,279)(252,278)(253,291)(254,290)(255,289)(256,294)(257,293)(258,292)(259,297)(260,296)(261,295)(262,282)(263,281)(264,280)(265,285)(266,284)(267,283)(268,288)(269,287)(270,286)(299,300)(302,303)(305,306)(307,318)(308,317)(309,316)(310,321)(311,320)(312,319)(313,324)(314,323)(315,322)(325,453)(326,452)(327,451)(328,456)(329,455)(330,454)(331,459)(332,458)(333,457)(334,444)(335,443)(336,442)(337,447)(338,446)(339,445)(340,450)(341,449)(342,448)(343,435)(344,434)(345,433)(346,438)(347,437)(348,436)(349,441)(350,440)(351,439)(352,426)(353,425)(354,424)(355,429)(356,428)(357,427)(358,432)(359,431)(360,430)(361,417)(362,416)(363,415)(364,420)(365,419)(366,418)(367,423)(368,422)(369,421)(370,408)(371,407)(372,406)(373,411)(374,410)(375,409)(376,414)(377,413)(378,412)(379,480)(380,479)(381,478)(382,483)(383,482)(384,481)(385,486)(386,485)(387,484)(388,471)(389,470)(390,469)(391,474)(392,473)(393,472)(394,477)(395,476)(396,475)(397,462)(398,461)(399,460)(400,465)(401,464)(402,463)(403,468)(404,467)(405,466);
s2 := Sym(486)!(  1,325)(  2,327)(  3,326)(  4,331)(  5,333)(  6,332)(  7,328)(  8,330)(  9,329)( 10,345)( 11,344)( 12,343)( 13,351)( 14,350)( 15,349)( 16,348)( 17,347)( 18,346)( 19,336)( 20,335)( 21,334)( 22,342)( 23,341)( 24,340)( 25,339)( 26,338)( 27,337)( 28,355)( 29,357)( 30,356)( 31,352)( 32,354)( 33,353)( 34,358)( 35,360)( 36,359)( 37,375)( 38,374)( 39,373)( 40,372)( 41,371)( 42,370)( 43,378)( 44,377)( 45,376)( 46,366)( 47,365)( 48,364)( 49,363)( 50,362)( 51,361)( 52,369)( 53,368)( 54,367)( 55,385)( 56,387)( 57,386)( 58,382)( 59,384)( 60,383)( 61,379)( 62,381)( 63,380)( 64,405)( 65,404)( 66,403)( 67,402)( 68,401)( 69,400)( 70,399)( 71,398)( 72,397)( 73,396)( 74,395)( 75,394)( 76,393)( 77,392)( 78,391)( 79,390)( 80,389)( 81,388)( 82,244)( 83,246)( 84,245)( 85,250)( 86,252)( 87,251)( 88,247)( 89,249)( 90,248)( 91,264)( 92,263)( 93,262)( 94,270)( 95,269)( 96,268)( 97,267)( 98,266)( 99,265)(100,255)(101,254)(102,253)(103,261)(104,260)(105,259)(106,258)(107,257)(108,256)(109,274)(110,276)(111,275)(112,271)(113,273)(114,272)(115,277)(116,279)(117,278)(118,294)(119,293)(120,292)(121,291)(122,290)(123,289)(124,297)(125,296)(126,295)(127,285)(128,284)(129,283)(130,282)(131,281)(132,280)(133,288)(134,287)(135,286)(136,304)(137,306)(138,305)(139,301)(140,303)(141,302)(142,298)(143,300)(144,299)(145,324)(146,323)(147,322)(148,321)(149,320)(150,319)(151,318)(152,317)(153,316)(154,315)(155,314)(156,313)(157,312)(158,311)(159,310)(160,309)(161,308)(162,307)(163,426)(164,425)(165,424)(166,432)(167,431)(168,430)(169,429)(170,428)(171,427)(172,417)(173,416)(174,415)(175,423)(176,422)(177,421)(178,420)(179,419)(180,418)(181,408)(182,407)(183,406)(184,414)(185,413)(186,412)(187,411)(188,410)(189,409)(190,456)(191,455)(192,454)(193,453)(194,452)(195,451)(196,459)(197,458)(198,457)(199,447)(200,446)(201,445)(202,444)(203,443)(204,442)(205,450)(206,449)(207,448)(208,438)(209,437)(210,436)(211,435)(212,434)(213,433)(214,441)(215,440)(216,439)(217,486)(218,485)(219,484)(220,483)(221,482)(222,481)(223,480)(224,479)(225,478)(226,477)(227,476)(228,475)(229,474)(230,473)(231,472)(232,471)(233,470)(234,469)(235,468)(236,467)(237,466)(238,465)(239,464)(240,463)(241,462)(242,461)(243,460);
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*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.