Overview
- Group
- SmallGroup(1944,952)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- 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.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 58)( 32, 60)( 33, 59)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 76)( 41, 78)( 42, 77)( 43, 79)( 44, 81)( 45, 80)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 82,172)( 83,174)( 84,173)( 85,175)( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)(101,183)(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)(109,226)(110,228)(111,227)(112,229)(113,231)(114,230)(115,232)(116,234)(117,233)(118,217)(119,219)(120,218)(121,220)(122,222)(123,221)(124,223)(125,225)(126,224)(127,235)(128,237)(129,236)(130,238)(131,240)(132,239)(133,241)(134,243)(135,242)(136,199)(137,201)(138,200)(139,202)(140,204)(141,203)(142,205)(143,207)(144,206)(145,190)(146,192)(147,191)(148,193)(149,195)(150,194)(151,196)(152,198)(153,197)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)(160,214)(161,216)(162,215)(245,246)(248,249)(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)(331,421)(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)(339,410)(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)(347,429)(348,428)(349,430)(350,432)(351,431)(352,469)(353,471)(354,470)(355,472)(356,474)(357,473)(358,475)(359,477)(360,476)(361,460)(362,462)(363,461)(364,463)(365,465)(366,464)(367,466)(368,468)(369,467)(370,478)(371,480)(372,479)(373,481)(374,483)(375,482)(376,484)(377,486)(378,485)(379,442)(380,444)(381,443)(382,445)(383,447)(384,446)(385,448)(386,450)(387,449)(388,433)(389,435)(390,434)(391,436)(392,438)(393,437)(394,439)(395,441)(396,440)(397,451)(398,453)(399,452)(400,454)(401,456)(402,455)(403,457)(404,459)(405,458);; s1 := ( 1,436)( 2,438)( 3,437)( 4,441)( 5,440)( 6,439)( 7,434)( 8,433)( 9,435)( 10,454)( 11,456)( 12,455)( 13,459)( 14,458)( 15,457)( 16,452)( 17,451)( 18,453)( 19,445)( 20,447)( 21,446)( 22,450)( 23,449)( 24,448)( 25,443)( 26,442)( 27,444)( 28,413)( 29,412)( 30,414)( 31,406)( 32,408)( 33,407)( 34,411)( 35,410)( 36,409)( 37,431)( 38,430)( 39,432)( 40,424)( 41,426)( 42,425)( 43,429)( 44,428)( 45,427)( 46,422)( 47,421)( 48,423)( 49,415)( 50,417)( 51,416)( 52,420)( 53,419)( 54,418)( 55,460)( 56,462)( 57,461)( 58,465)( 59,464)( 60,463)( 61,467)( 62,466)( 63,468)( 64,478)( 65,480)( 66,479)( 67,483)( 68,482)( 69,481)( 70,485)( 71,484)( 72,486)( 73,469)( 74,471)( 75,470)( 76,474)( 77,473)( 78,472)( 79,476)( 80,475)( 81,477)( 82,355)( 83,357)( 84,356)( 85,360)( 86,359)( 87,358)( 88,353)( 89,352)( 90,354)( 91,373)( 92,375)( 93,374)( 94,378)( 95,377)( 96,376)( 97,371)( 98,370)( 99,372)(100,364)(101,366)(102,365)(103,369)(104,368)(105,367)(106,362)(107,361)(108,363)(109,332)(110,331)(111,333)(112,325)(113,327)(114,326)(115,330)(116,329)(117,328)(118,350)(119,349)(120,351)(121,343)(122,345)(123,344)(124,348)(125,347)(126,346)(127,341)(128,340)(129,342)(130,334)(131,336)(132,335)(133,339)(134,338)(135,337)(136,379)(137,381)(138,380)(139,384)(140,383)(141,382)(142,386)(143,385)(144,387)(145,397)(146,399)(147,398)(148,402)(149,401)(150,400)(151,404)(152,403)(153,405)(154,388)(155,390)(156,389)(157,393)(158,392)(159,391)(160,395)(161,394)(162,396)(163,274)(164,276)(165,275)(166,279)(167,278)(168,277)(169,272)(170,271)(171,273)(172,292)(173,294)(174,293)(175,297)(176,296)(177,295)(178,290)(179,289)(180,291)(181,283)(182,285)(183,284)(184,288)(185,287)(186,286)(187,281)(188,280)(189,282)(190,251)(191,250)(192,252)(193,244)(194,246)(195,245)(196,249)(197,248)(198,247)(199,269)(200,268)(201,270)(202,262)(203,264)(204,263)(205,267)(206,266)(207,265)(208,260)(209,259)(210,261)(211,253)(212,255)(213,254)(214,258)(215,257)(216,256)(217,298)(218,300)(219,299)(220,303)(221,302)(222,301)(223,305)(224,304)(225,306)(226,316)(227,318)(228,317)(229,321)(230,320)(231,319)(232,323)(233,322)(234,324)(235,307)(236,309)(237,308)(238,312)(239,311)(240,310)(241,314)(242,313)(243,315);; s2 := ( 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);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(486)!( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 58)( 32, 60)( 33, 59)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 76)( 41, 78)( 42, 77)( 43, 79)( 44, 81)( 45, 80)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 82,172)( 83,174)( 84,173)( 85,175)( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)(101,183)(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)(109,226)(110,228)(111,227)(112,229)(113,231)(114,230)(115,232)(116,234)(117,233)(118,217)(119,219)(120,218)(121,220)(122,222)(123,221)(124,223)(125,225)(126,224)(127,235)(128,237)(129,236)(130,238)(131,240)(132,239)(133,241)(134,243)(135,242)(136,199)(137,201)(138,200)(139,202)(140,204)(141,203)(142,205)(143,207)(144,206)(145,190)(146,192)(147,191)(148,193)(149,195)(150,194)(151,196)(152,198)(153,197)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)(160,214)(161,216)(162,215)(245,246)(248,249)(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)(331,421)(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)(339,410)(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)(347,429)(348,428)(349,430)(350,432)(351,431)(352,469)(353,471)(354,470)(355,472)(356,474)(357,473)(358,475)(359,477)(360,476)(361,460)(362,462)(363,461)(364,463)(365,465)(366,464)(367,466)(368,468)(369,467)(370,478)(371,480)(372,479)(373,481)(374,483)(375,482)(376,484)(377,486)(378,485)(379,442)(380,444)(381,443)(382,445)(383,447)(384,446)(385,448)(386,450)(387,449)(388,433)(389,435)(390,434)(391,436)(392,438)(393,437)(394,439)(395,441)(396,440)(397,451)(398,453)(399,452)(400,454)(401,456)(402,455)(403,457)(404,459)(405,458); s1 := Sym(486)!( 1,436)( 2,438)( 3,437)( 4,441)( 5,440)( 6,439)( 7,434)( 8,433)( 9,435)( 10,454)( 11,456)( 12,455)( 13,459)( 14,458)( 15,457)( 16,452)( 17,451)( 18,453)( 19,445)( 20,447)( 21,446)( 22,450)( 23,449)( 24,448)( 25,443)( 26,442)( 27,444)( 28,413)( 29,412)( 30,414)( 31,406)( 32,408)( 33,407)( 34,411)( 35,410)( 36,409)( 37,431)( 38,430)( 39,432)( 40,424)( 41,426)( 42,425)( 43,429)( 44,428)( 45,427)( 46,422)( 47,421)( 48,423)( 49,415)( 50,417)( 51,416)( 52,420)( 53,419)( 54,418)( 55,460)( 56,462)( 57,461)( 58,465)( 59,464)( 60,463)( 61,467)( 62,466)( 63,468)( 64,478)( 65,480)( 66,479)( 67,483)( 68,482)( 69,481)( 70,485)( 71,484)( 72,486)( 73,469)( 74,471)( 75,470)( 76,474)( 77,473)( 78,472)( 79,476)( 80,475)( 81,477)( 82,355)( 83,357)( 84,356)( 85,360)( 86,359)( 87,358)( 88,353)( 89,352)( 90,354)( 91,373)( 92,375)( 93,374)( 94,378)( 95,377)( 96,376)( 97,371)( 98,370)( 99,372)(100,364)(101,366)(102,365)(103,369)(104,368)(105,367)(106,362)(107,361)(108,363)(109,332)(110,331)(111,333)(112,325)(113,327)(114,326)(115,330)(116,329)(117,328)(118,350)(119,349)(120,351)(121,343)(122,345)(123,344)(124,348)(125,347)(126,346)(127,341)(128,340)(129,342)(130,334)(131,336)(132,335)(133,339)(134,338)(135,337)(136,379)(137,381)(138,380)(139,384)(140,383)(141,382)(142,386)(143,385)(144,387)(145,397)(146,399)(147,398)(148,402)(149,401)(150,400)(151,404)(152,403)(153,405)(154,388)(155,390)(156,389)(157,393)(158,392)(159,391)(160,395)(161,394)(162,396)(163,274)(164,276)(165,275)(166,279)(167,278)(168,277)(169,272)(170,271)(171,273)(172,292)(173,294)(174,293)(175,297)(176,296)(177,295)(178,290)(179,289)(180,291)(181,283)(182,285)(183,284)(184,288)(185,287)(186,286)(187,281)(188,280)(189,282)(190,251)(191,250)(192,252)(193,244)(194,246)(195,245)(196,249)(197,248)(198,247)(199,269)(200,268)(201,270)(202,262)(203,264)(204,263)(205,267)(206,266)(207,265)(208,260)(209,259)(210,261)(211,253)(212,255)(213,254)(214,258)(215,257)(216,256)(217,298)(218,300)(219,299)(220,303)(221,302)(222,301)(223,305)(224,304)(225,306)(226,316)(227,318)(228,317)(229,321)(230,320)(231,319)(232,323)(233,322)(234,324)(235,307)(236,309)(237,308)(238,312)(239,311)(240,310)(241,314)(242,313)(243,315); s2 := 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); 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*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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 >;
References
None.
to this polytope.