Overview
- Group
- SmallGroup(1944,942)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
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*s1*s2*(s1*s0)^3*s1*s2*s1> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,167)( 83,168)( 84,166)( 85,165)( 86,163)( 87,164)( 88,169)( 89,170)( 90,171)( 91,185)( 92,186)( 93,184)( 94,183)( 95,181)( 96,182)( 97,187)( 98,188)( 99,189)(100,176)(101,177)(102,175)(103,174)(104,172)(105,173)(106,178)(107,179)(108,180)(109,194)(110,195)(111,193)(112,192)(113,190)(114,191)(115,196)(116,197)(117,198)(118,212)(119,213)(120,211)(121,210)(122,208)(123,209)(124,214)(125,215)(126,216)(127,203)(128,204)(129,202)(130,201)(131,199)(132,200)(133,205)(134,206)(135,207)(136,221)(137,222)(138,220)(139,219)(140,217)(141,218)(142,223)(143,224)(144,225)(145,239)(146,240)(147,238)(148,237)(149,235)(150,236)(151,241)(152,242)(153,243)(154,230)(155,231)(156,229)(157,228)(158,226)(159,227)(160,232)(161,233)(162,234)(247,251)(248,252)(249,250)(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)(260,265)(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)(283,296)(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)(303,304)(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)(314,319)(315,320)(325,410)(326,411)(327,409)(328,408)(329,406)(330,407)(331,412)(332,413)(333,414)(334,428)(335,429)(336,427)(337,426)(338,424)(339,425)(340,430)(341,431)(342,432)(343,419)(344,420)(345,418)(346,417)(347,415)(348,416)(349,421)(350,422)(351,423)(352,437)(353,438)(354,436)(355,435)(356,433)(357,434)(358,439)(359,440)(360,441)(361,455)(362,456)(363,454)(364,453)(365,451)(366,452)(367,457)(368,458)(369,459)(370,446)(371,447)(372,445)(373,444)(374,442)(375,443)(376,448)(377,449)(378,450)(379,464)(380,465)(381,463)(382,462)(383,460)(384,461)(385,466)(386,467)(387,468)(388,482)(389,483)(390,481)(391,480)(392,478)(393,479)(394,484)(395,485)(396,486)(397,473)(398,474)(399,472)(400,471)(401,469)(402,470)(403,475)(404,476)(405,477);; s1 := ( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)( 8, 87)( 9, 86)( 10, 92)( 11, 91)( 12, 93)( 13, 98)( 14, 97)( 15, 99)( 16, 95)( 17, 94)( 18, 96)( 19,102)( 20,101)( 21,100)( 22,108)( 23,107)( 24,106)( 25,105)( 26,104)( 27,103)( 28,157)( 29,159)( 30,158)( 31,154)( 32,156)( 33,155)( 34,160)( 35,162)( 36,161)( 37,140)( 38,139)( 39,141)( 40,137)( 41,136)( 42,138)( 43,143)( 44,142)( 45,144)( 46,150)( 47,149)( 48,148)( 49,147)( 50,146)( 51,145)( 52,153)( 53,152)( 54,151)( 55,122)( 56,121)( 57,123)( 58,119)( 59,118)( 60,120)( 61,125)( 62,124)( 63,126)( 64,132)( 65,131)( 66,130)( 67,129)( 68,128)( 69,127)( 70,135)( 71,134)( 72,133)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,115)( 80,117)( 81,116)(163,167)(164,166)(165,168)(169,170)(172,177)(173,176)(174,175)(178,180)(181,184)(182,186)(183,185)(188,189)(190,242)(191,241)(192,243)(193,239)(194,238)(195,240)(196,236)(197,235)(198,237)(199,225)(200,224)(201,223)(202,222)(203,221)(204,220)(205,219)(206,218)(207,217)(208,232)(209,234)(210,233)(211,229)(212,231)(213,230)(214,226)(215,228)(216,227)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)(252,329)(253,335)(254,334)(255,336)(256,341)(257,340)(258,342)(259,338)(260,337)(261,339)(262,345)(263,344)(264,343)(265,351)(266,350)(267,349)(268,348)(269,347)(270,346)(271,400)(272,402)(273,401)(274,397)(275,399)(276,398)(277,403)(278,405)(279,404)(280,383)(281,382)(282,384)(283,380)(284,379)(285,381)(286,386)(287,385)(288,387)(289,393)(290,392)(291,391)(292,390)(293,389)(294,388)(295,396)(296,395)(297,394)(298,365)(299,364)(300,366)(301,362)(302,361)(303,363)(304,368)(305,367)(306,369)(307,375)(308,374)(309,373)(310,372)(311,371)(312,370)(313,378)(314,377)(315,376)(316,355)(317,357)(318,356)(319,352)(320,354)(321,353)(322,358)(323,360)(324,359)(406,410)(407,409)(408,411)(412,413)(415,420)(416,419)(417,418)(421,423)(424,427)(425,429)(426,428)(431,432)(433,485)(434,484)(435,486)(436,482)(437,481)(438,483)(439,479)(440,478)(441,480)(442,468)(443,467)(444,466)(445,465)(446,464)(447,463)(448,462)(449,461)(450,460)(451,475)(452,477)(453,476)(454,472)(455,474)(456,473)(457,469)(458,471)(459,470);; s2 := ( 1,271)( 2,273)( 3,272)( 4,277)( 5,279)( 6,278)( 7,274)( 8,276)( 9,275)( 10,288)( 11,287)( 12,286)( 13,285)( 14,284)( 15,283)( 16,282)( 17,281)( 18,280)( 19,293)( 20,292)( 21,294)( 22,290)( 23,289)( 24,291)( 25,296)( 26,295)( 27,297)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)( 33,251)( 34,247)( 35,249)( 36,248)( 37,261)( 38,260)( 39,259)( 40,258)( 41,257)( 42,256)( 43,255)( 44,254)( 45,253)( 46,266)( 47,265)( 48,267)( 49,263)( 50,262)( 51,264)( 52,269)( 53,268)( 54,270)( 55,299)( 56,298)( 57,300)( 58,305)( 59,304)( 60,306)( 61,302)( 62,301)( 63,303)( 64,313)( 65,315)( 66,314)( 67,310)( 68,312)( 69,311)( 70,307)( 71,309)( 72,308)( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,324)( 80,323)( 81,322)( 82,437)( 83,436)( 84,438)( 85,434)( 86,433)( 87,435)( 88,440)( 89,439)( 90,441)( 91,442)( 92,444)( 93,443)( 94,448)( 95,450)( 96,449)( 97,445)( 98,447)( 99,446)(100,459)(101,458)(102,457)(103,456)(104,455)(105,454)(106,453)(107,452)(108,451)(109,410)(110,409)(111,411)(112,407)(113,406)(114,408)(115,413)(116,412)(117,414)(118,415)(119,417)(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,432)(128,431)(129,430)(130,429)(131,428)(132,427)(133,426)(134,425)(135,424)(136,465)(137,464)(138,463)(139,462)(140,461)(141,460)(142,468)(143,467)(144,466)(145,470)(146,469)(147,471)(148,476)(149,475)(150,477)(151,473)(152,472)(153,474)(154,484)(155,486)(156,485)(157,481)(158,483)(159,482)(160,478)(161,480)(162,479)(163,356)(164,355)(165,357)(166,353)(167,352)(168,354)(169,359)(170,358)(171,360)(172,361)(173,363)(174,362)(175,367)(176,369)(177,368)(178,364)(179,366)(180,365)(181,378)(182,377)(183,376)(184,375)(185,374)(186,373)(187,372)(188,371)(189,370)(190,329)(191,328)(192,330)(193,326)(194,325)(195,327)(196,332)(197,331)(198,333)(199,334)(200,336)(201,335)(202,340)(203,342)(204,341)(205,337)(206,339)(207,338)(208,351)(209,350)(210,349)(211,348)(212,347)(213,346)(214,345)(215,344)(216,343)(217,384)(218,383)(219,382)(220,381)(221,380)(222,379)(223,387)(224,386)(225,385)(226,389)(227,388)(228,390)(229,395)(230,394)(231,396)(232,392)(233,391)(234,393)(235,403)(236,405)(237,404)(238,400)(239,402)(240,401)(241,397)(242,399)(243,398);; 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(486)!( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 82,167)( 83,168)( 84,166)( 85,165)( 86,163)( 87,164)( 88,169)( 89,170)( 90,171)( 91,185)( 92,186)( 93,184)( 94,183)( 95,181)( 96,182)( 97,187)( 98,188)( 99,189)(100,176)(101,177)(102,175)(103,174)(104,172)(105,173)(106,178)(107,179)(108,180)(109,194)(110,195)(111,193)(112,192)(113,190)(114,191)(115,196)(116,197)(117,198)(118,212)(119,213)(120,211)(121,210)(122,208)(123,209)(124,214)(125,215)(126,216)(127,203)(128,204)(129,202)(130,201)(131,199)(132,200)(133,205)(134,206)(135,207)(136,221)(137,222)(138,220)(139,219)(140,217)(141,218)(142,223)(143,224)(144,225)(145,239)(146,240)(147,238)(148,237)(149,235)(150,236)(151,241)(152,242)(153,243)(154,230)(155,231)(156,229)(157,228)(158,226)(159,227)(160,232)(161,233)(162,234)(247,251)(248,252)(249,250)(253,262)(254,263)(255,264)(256,269)(257,270)(258,268)(259,267)(260,265)(261,266)(274,278)(275,279)(276,277)(280,289)(281,290)(282,291)(283,296)(284,297)(285,295)(286,294)(287,292)(288,293)(301,305)(302,306)(303,304)(307,316)(308,317)(309,318)(310,323)(311,324)(312,322)(313,321)(314,319)(315,320)(325,410)(326,411)(327,409)(328,408)(329,406)(330,407)(331,412)(332,413)(333,414)(334,428)(335,429)(336,427)(337,426)(338,424)(339,425)(340,430)(341,431)(342,432)(343,419)(344,420)(345,418)(346,417)(347,415)(348,416)(349,421)(350,422)(351,423)(352,437)(353,438)(354,436)(355,435)(356,433)(357,434)(358,439)(359,440)(360,441)(361,455)(362,456)(363,454)(364,453)(365,451)(366,452)(367,457)(368,458)(369,459)(370,446)(371,447)(372,445)(373,444)(374,442)(375,443)(376,448)(377,449)(378,450)(379,464)(380,465)(381,463)(382,462)(383,460)(384,461)(385,466)(386,467)(387,468)(388,482)(389,483)(390,481)(391,480)(392,478)(393,479)(394,484)(395,485)(396,486)(397,473)(398,474)(399,472)(400,471)(401,469)(402,470)(403,475)(404,476)(405,477); s1 := Sym(486)!( 1, 82)( 2, 84)( 3, 83)( 4, 88)( 5, 90)( 6, 89)( 7, 85)( 8, 87)( 9, 86)( 10, 92)( 11, 91)( 12, 93)( 13, 98)( 14, 97)( 15, 99)( 16, 95)( 17, 94)( 18, 96)( 19,102)( 20,101)( 21,100)( 22,108)( 23,107)( 24,106)( 25,105)( 26,104)( 27,103)( 28,157)( 29,159)( 30,158)( 31,154)( 32,156)( 33,155)( 34,160)( 35,162)( 36,161)( 37,140)( 38,139)( 39,141)( 40,137)( 41,136)( 42,138)( 43,143)( 44,142)( 45,144)( 46,150)( 47,149)( 48,148)( 49,147)( 50,146)( 51,145)( 52,153)( 53,152)( 54,151)( 55,122)( 56,121)( 57,123)( 58,119)( 59,118)( 60,120)( 61,125)( 62,124)( 63,126)( 64,132)( 65,131)( 66,130)( 67,129)( 68,128)( 69,127)( 70,135)( 71,134)( 72,133)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,115)( 80,117)( 81,116)(163,167)(164,166)(165,168)(169,170)(172,177)(173,176)(174,175)(178,180)(181,184)(182,186)(183,185)(188,189)(190,242)(191,241)(192,243)(193,239)(194,238)(195,240)(196,236)(197,235)(198,237)(199,225)(200,224)(201,223)(202,222)(203,221)(204,220)(205,219)(206,218)(207,217)(208,232)(209,234)(210,233)(211,229)(212,231)(213,230)(214,226)(215,228)(216,227)(244,325)(245,327)(246,326)(247,331)(248,333)(249,332)(250,328)(251,330)(252,329)(253,335)(254,334)(255,336)(256,341)(257,340)(258,342)(259,338)(260,337)(261,339)(262,345)(263,344)(264,343)(265,351)(266,350)(267,349)(268,348)(269,347)(270,346)(271,400)(272,402)(273,401)(274,397)(275,399)(276,398)(277,403)(278,405)(279,404)(280,383)(281,382)(282,384)(283,380)(284,379)(285,381)(286,386)(287,385)(288,387)(289,393)(290,392)(291,391)(292,390)(293,389)(294,388)(295,396)(296,395)(297,394)(298,365)(299,364)(300,366)(301,362)(302,361)(303,363)(304,368)(305,367)(306,369)(307,375)(308,374)(309,373)(310,372)(311,371)(312,370)(313,378)(314,377)(315,376)(316,355)(317,357)(318,356)(319,352)(320,354)(321,353)(322,358)(323,360)(324,359)(406,410)(407,409)(408,411)(412,413)(415,420)(416,419)(417,418)(421,423)(424,427)(425,429)(426,428)(431,432)(433,485)(434,484)(435,486)(436,482)(437,481)(438,483)(439,479)(440,478)(441,480)(442,468)(443,467)(444,466)(445,465)(446,464)(447,463)(448,462)(449,461)(450,460)(451,475)(452,477)(453,476)(454,472)(455,474)(456,473)(457,469)(458,471)(459,470); s2 := Sym(486)!( 1,271)( 2,273)( 3,272)( 4,277)( 5,279)( 6,278)( 7,274)( 8,276)( 9,275)( 10,288)( 11,287)( 12,286)( 13,285)( 14,284)( 15,283)( 16,282)( 17,281)( 18,280)( 19,293)( 20,292)( 21,294)( 22,290)( 23,289)( 24,291)( 25,296)( 26,295)( 27,297)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)( 33,251)( 34,247)( 35,249)( 36,248)( 37,261)( 38,260)( 39,259)( 40,258)( 41,257)( 42,256)( 43,255)( 44,254)( 45,253)( 46,266)( 47,265)( 48,267)( 49,263)( 50,262)( 51,264)( 52,269)( 53,268)( 54,270)( 55,299)( 56,298)( 57,300)( 58,305)( 59,304)( 60,306)( 61,302)( 62,301)( 63,303)( 64,313)( 65,315)( 66,314)( 67,310)( 68,312)( 69,311)( 70,307)( 71,309)( 72,308)( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,324)( 80,323)( 81,322)( 82,437)( 83,436)( 84,438)( 85,434)( 86,433)( 87,435)( 88,440)( 89,439)( 90,441)( 91,442)( 92,444)( 93,443)( 94,448)( 95,450)( 96,449)( 97,445)( 98,447)( 99,446)(100,459)(101,458)(102,457)(103,456)(104,455)(105,454)(106,453)(107,452)(108,451)(109,410)(110,409)(111,411)(112,407)(113,406)(114,408)(115,413)(116,412)(117,414)(118,415)(119,417)(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,432)(128,431)(129,430)(130,429)(131,428)(132,427)(133,426)(134,425)(135,424)(136,465)(137,464)(138,463)(139,462)(140,461)(141,460)(142,468)(143,467)(144,466)(145,470)(146,469)(147,471)(148,476)(149,475)(150,477)(151,473)(152,472)(153,474)(154,484)(155,486)(156,485)(157,481)(158,483)(159,482)(160,478)(161,480)(162,479)(163,356)(164,355)(165,357)(166,353)(167,352)(168,354)(169,359)(170,358)(171,360)(172,361)(173,363)(174,362)(175,367)(176,369)(177,368)(178,364)(179,366)(180,365)(181,378)(182,377)(183,376)(184,375)(185,374)(186,373)(187,372)(188,371)(189,370)(190,329)(191,328)(192,330)(193,326)(194,325)(195,327)(196,332)(197,331)(198,333)(199,334)(200,336)(201,335)(202,340)(203,342)(204,341)(205,337)(206,339)(207,338)(208,351)(209,350)(210,349)(211,348)(212,347)(213,346)(214,345)(215,344)(216,343)(217,384)(218,383)(219,382)(220,381)(221,380)(222,379)(223,387)(224,386)(225,385)(226,389)(227,388)(228,390)(229,395)(230,394)(231,396)(232,392)(233,391)(234,393)(235,403)(236,405)(237,404)(238,400)(239,402)(240,401)(241,397)(242,399)(243,398); 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.