Overview
- Group
- SmallGroup(1944,956)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 18
- 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)( 4, 7)( 5, 9)( 6, 8)( 10, 20)( 11, 19)( 12, 21)( 13, 26)( 14, 25)( 15, 27)( 16, 23)( 17, 22)( 18, 24)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)( 43, 50)( 44, 49)( 45, 51)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 74)( 65, 73)( 66, 75)( 67, 80)( 68, 79)( 69, 81)( 70, 77)( 71, 76)( 72, 78)( 82,166)( 83,168)( 84,167)( 85,163)( 86,165)( 87,164)( 88,169)( 89,171)( 90,170)( 91,185)( 92,184)( 93,186)( 94,182)( 95,181)( 96,183)( 97,188)( 98,187)( 99,189)(100,176)(101,175)(102,177)(103,173)(104,172)(105,174)(106,179)(107,178)(108,180)(109,195)(110,194)(111,193)(112,192)(113,191)(114,190)(115,198)(116,197)(117,196)(118,211)(119,213)(120,212)(121,208)(122,210)(123,209)(124,214)(125,216)(126,215)(127,202)(128,204)(129,203)(130,199)(131,201)(132,200)(133,205)(134,207)(135,206)(136,221)(137,220)(138,222)(139,218)(140,217)(141,219)(142,224)(143,223)(144,225)(145,240)(146,239)(147,238)(148,237)(149,236)(150,235)(151,243)(152,242)(153,241)(154,231)(155,230)(156,229)(157,228)(158,227)(159,226)(160,234)(161,233)(162,232)(245,246)(247,250)(248,252)(249,251)(253,263)(254,262)(255,264)(256,269)(257,268)(258,270)(259,266)(260,265)(261,267)(272,273)(274,277)(275,279)(276,278)(280,290)(281,289)(282,291)(283,296)(284,295)(285,297)(286,293)(287,292)(288,294)(299,300)(301,304)(302,306)(303,305)(307,317)(308,316)(309,318)(310,323)(311,322)(312,324)(313,320)(314,319)(315,321)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)(333,413)(334,428)(335,427)(336,429)(337,425)(338,424)(339,426)(340,431)(341,430)(342,432)(343,419)(344,418)(345,420)(346,416)(347,415)(348,417)(349,422)(350,421)(351,423)(352,438)(353,437)(354,436)(355,435)(356,434)(357,433)(358,441)(359,440)(360,439)(361,454)(362,456)(363,455)(364,451)(365,453)(366,452)(367,457)(368,459)(369,458)(370,445)(371,447)(372,446)(373,442)(374,444)(375,443)(376,448)(377,450)(378,449)(379,464)(380,463)(381,465)(382,461)(383,460)(384,462)(385,467)(386,466)(387,468)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,486)(395,485)(396,484)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,477)(404,476)(405,475);; s1 := ( 1, 82)( 2, 83)( 3, 84)( 4, 88)( 5, 89)( 6, 90)( 7, 85)( 8, 86)( 9, 87)( 10, 91)( 11, 92)( 12, 93)( 13, 97)( 14, 98)( 15, 99)( 16, 94)( 17, 95)( 18, 96)( 19,100)( 20,101)( 21,102)( 22,106)( 23,107)( 24,108)( 25,103)( 26,104)( 27,105)( 28,158)( 29,159)( 30,157)( 31,155)( 32,156)( 33,154)( 34,161)( 35,162)( 36,160)( 37,139)( 38,140)( 39,141)( 40,136)( 41,137)( 42,138)( 43,142)( 44,143)( 45,144)( 46,148)( 47,149)( 48,150)( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,121)( 56,122)( 57,123)( 58,118)( 59,119)( 60,120)( 61,124)( 62,125)( 63,126)( 64,130)( 65,131)( 66,132)( 67,127)( 68,128)( 69,129)( 70,133)( 71,134)( 72,135)( 73,114)( 74,112)( 75,113)( 76,111)( 77,109)( 78,110)( 79,117)( 80,115)( 81,116)(163,166)(164,167)(165,168)(172,175)(173,176)(174,177)(181,184)(182,185)(183,186)(190,243)(191,241)(192,242)(193,240)(194,238)(195,239)(196,237)(197,235)(198,236)(199,224)(200,225)(201,223)(202,221)(203,222)(204,220)(205,218)(206,219)(207,217)(208,233)(209,234)(210,232)(211,230)(212,231)(213,229)(214,227)(215,228)(216,226)(244,325)(245,326)(246,327)(247,331)(248,332)(249,333)(250,328)(251,329)(252,330)(253,334)(254,335)(255,336)(256,340)(257,341)(258,342)(259,337)(260,338)(261,339)(262,343)(263,344)(264,345)(265,349)(266,350)(267,351)(268,346)(269,347)(270,348)(271,401)(272,402)(273,400)(274,398)(275,399)(276,397)(277,404)(278,405)(279,403)(280,382)(281,383)(282,384)(283,379)(284,380)(285,381)(286,385)(287,386)(288,387)(289,391)(290,392)(291,393)(292,388)(293,389)(294,390)(295,394)(296,395)(297,396)(298,364)(299,365)(300,366)(301,361)(302,362)(303,363)(304,367)(305,368)(306,369)(307,373)(308,374)(309,375)(310,370)(311,371)(312,372)(313,376)(314,377)(315,378)(316,357)(317,355)(318,356)(319,354)(320,352)(321,353)(322,360)(323,358)(324,359)(406,409)(407,410)(408,411)(415,418)(416,419)(417,420)(424,427)(425,428)(426,429)(433,486)(434,484)(435,485)(436,483)(437,481)(438,482)(439,480)(440,478)(441,479)(442,467)(443,468)(444,466)(445,464)(446,465)(447,463)(448,461)(449,462)(450,460)(451,476)(452,477)(453,475)(454,473)(455,474)(456,472)(457,470)(458,471)(459,469);; s2 := ( 1,271)( 2,272)( 3,273)( 4,278)( 5,279)( 6,277)( 7,276)( 8,274)( 9,275)( 10,288)( 11,286)( 12,287)( 13,283)( 14,284)( 15,285)( 16,281)( 17,282)( 18,280)( 19,293)( 20,294)( 21,292)( 22,291)( 23,289)( 24,290)( 25,295)( 26,296)( 27,297)( 28,244)( 29,245)( 30,246)( 31,251)( 32,252)( 33,250)( 34,249)( 35,247)( 36,248)( 37,261)( 38,259)( 39,260)( 40,256)( 41,257)( 42,258)( 43,254)( 44,255)( 45,253)( 46,266)( 47,267)( 48,265)( 49,264)( 50,262)( 51,263)( 52,268)( 53,269)( 54,270)( 55,298)( 56,299)( 57,300)( 58,305)( 59,306)( 60,304)( 61,303)( 62,301)( 63,302)( 64,315)( 65,313)( 66,314)( 67,310)( 68,311)( 69,312)( 70,308)( 71,309)( 72,307)( 73,320)( 74,321)( 75,319)( 76,318)( 77,316)( 78,317)( 79,322)( 80,323)( 81,324)( 82,438)( 83,436)( 84,437)( 85,433)( 86,434)( 87,435)( 88,440)( 89,441)( 90,439)( 91,443)( 92,444)( 93,442)( 94,450)( 95,448)( 96,449)( 97,445)( 98,446)( 99,447)(100,457)(101,458)(102,459)(103,455)(104,456)(105,454)(106,453)(107,451)(108,452)(109,409)(110,410)(111,411)(112,407)(113,408)(114,406)(115,414)(116,412)(117,413)(118,417)(119,415)(120,416)(121,421)(122,422)(123,423)(124,419)(125,420)(126,418)(127,431)(128,432)(129,430)(130,429)(131,427)(132,428)(133,424)(134,425)(135,426)(136,464)(137,465)(138,463)(139,462)(140,460)(141,461)(142,466)(143,467)(144,468)(145,469)(146,470)(147,471)(148,476)(149,477)(150,475)(151,474)(152,472)(153,473)(154,486)(155,484)(156,485)(157,481)(158,482)(159,483)(160,479)(161,480)(162,478)(163,357)(164,355)(165,356)(166,352)(167,353)(168,354)(169,359)(170,360)(171,358)(172,362)(173,363)(174,361)(175,369)(176,367)(177,368)(178,364)(179,365)(180,366)(181,376)(182,377)(183,378)(184,374)(185,375)(186,373)(187,372)(188,370)(189,371)(190,328)(191,329)(192,330)(193,326)(194,327)(195,325)(196,333)(197,331)(198,332)(199,336)(200,334)(201,335)(202,340)(203,341)(204,342)(205,338)(206,339)(207,337)(208,350)(209,351)(210,349)(211,348)(212,346)(213,347)(214,343)(215,344)(216,345)(217,383)(218,384)(219,382)(220,381)(221,379)(222,380)(223,385)(224,386)(225,387)(226,388)(227,389)(228,390)(229,395)(230,396)(231,394)(232,393)(233,391)(234,392)(235,405)(236,403)(237,404)(238,400)(239,401)(240,402)(241,398)(242,399)(243,397);; 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,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0,
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)( 4, 7)( 5, 9)( 6, 8)( 10, 20)( 11, 19)( 12, 21)( 13, 26)( 14, 25)( 15, 27)( 16, 23)( 17, 22)( 18, 24)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 47)( 38, 46)( 39, 48)( 40, 53)( 41, 52)( 42, 54)( 43, 50)( 44, 49)( 45, 51)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 74)( 65, 73)( 66, 75)( 67, 80)( 68, 79)( 69, 81)( 70, 77)( 71, 76)( 72, 78)( 82,166)( 83,168)( 84,167)( 85,163)( 86,165)( 87,164)( 88,169)( 89,171)( 90,170)( 91,185)( 92,184)( 93,186)( 94,182)( 95,181)( 96,183)( 97,188)( 98,187)( 99,189)(100,176)(101,175)(102,177)(103,173)(104,172)(105,174)(106,179)(107,178)(108,180)(109,195)(110,194)(111,193)(112,192)(113,191)(114,190)(115,198)(116,197)(117,196)(118,211)(119,213)(120,212)(121,208)(122,210)(123,209)(124,214)(125,216)(126,215)(127,202)(128,204)(129,203)(130,199)(131,201)(132,200)(133,205)(134,207)(135,206)(136,221)(137,220)(138,222)(139,218)(140,217)(141,219)(142,224)(143,223)(144,225)(145,240)(146,239)(147,238)(148,237)(149,236)(150,235)(151,243)(152,242)(153,241)(154,231)(155,230)(156,229)(157,228)(158,227)(159,226)(160,234)(161,233)(162,232)(245,246)(247,250)(248,252)(249,251)(253,263)(254,262)(255,264)(256,269)(257,268)(258,270)(259,266)(260,265)(261,267)(272,273)(274,277)(275,279)(276,278)(280,290)(281,289)(282,291)(283,296)(284,295)(285,297)(286,293)(287,292)(288,294)(299,300)(301,304)(302,306)(303,305)(307,317)(308,316)(309,318)(310,323)(311,322)(312,324)(313,320)(314,319)(315,321)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)(333,413)(334,428)(335,427)(336,429)(337,425)(338,424)(339,426)(340,431)(341,430)(342,432)(343,419)(344,418)(345,420)(346,416)(347,415)(348,417)(349,422)(350,421)(351,423)(352,438)(353,437)(354,436)(355,435)(356,434)(357,433)(358,441)(359,440)(360,439)(361,454)(362,456)(363,455)(364,451)(365,453)(366,452)(367,457)(368,459)(369,458)(370,445)(371,447)(372,446)(373,442)(374,444)(375,443)(376,448)(377,450)(378,449)(379,464)(380,463)(381,465)(382,461)(383,460)(384,462)(385,467)(386,466)(387,468)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,486)(395,485)(396,484)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,477)(404,476)(405,475); s1 := Sym(486)!( 1, 82)( 2, 83)( 3, 84)( 4, 88)( 5, 89)( 6, 90)( 7, 85)( 8, 86)( 9, 87)( 10, 91)( 11, 92)( 12, 93)( 13, 97)( 14, 98)( 15, 99)( 16, 94)( 17, 95)( 18, 96)( 19,100)( 20,101)( 21,102)( 22,106)( 23,107)( 24,108)( 25,103)( 26,104)( 27,105)( 28,158)( 29,159)( 30,157)( 31,155)( 32,156)( 33,154)( 34,161)( 35,162)( 36,160)( 37,139)( 38,140)( 39,141)( 40,136)( 41,137)( 42,138)( 43,142)( 44,143)( 45,144)( 46,148)( 47,149)( 48,150)( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,121)( 56,122)( 57,123)( 58,118)( 59,119)( 60,120)( 61,124)( 62,125)( 63,126)( 64,130)( 65,131)( 66,132)( 67,127)( 68,128)( 69,129)( 70,133)( 71,134)( 72,135)( 73,114)( 74,112)( 75,113)( 76,111)( 77,109)( 78,110)( 79,117)( 80,115)( 81,116)(163,166)(164,167)(165,168)(172,175)(173,176)(174,177)(181,184)(182,185)(183,186)(190,243)(191,241)(192,242)(193,240)(194,238)(195,239)(196,237)(197,235)(198,236)(199,224)(200,225)(201,223)(202,221)(203,222)(204,220)(205,218)(206,219)(207,217)(208,233)(209,234)(210,232)(211,230)(212,231)(213,229)(214,227)(215,228)(216,226)(244,325)(245,326)(246,327)(247,331)(248,332)(249,333)(250,328)(251,329)(252,330)(253,334)(254,335)(255,336)(256,340)(257,341)(258,342)(259,337)(260,338)(261,339)(262,343)(263,344)(264,345)(265,349)(266,350)(267,351)(268,346)(269,347)(270,348)(271,401)(272,402)(273,400)(274,398)(275,399)(276,397)(277,404)(278,405)(279,403)(280,382)(281,383)(282,384)(283,379)(284,380)(285,381)(286,385)(287,386)(288,387)(289,391)(290,392)(291,393)(292,388)(293,389)(294,390)(295,394)(296,395)(297,396)(298,364)(299,365)(300,366)(301,361)(302,362)(303,363)(304,367)(305,368)(306,369)(307,373)(308,374)(309,375)(310,370)(311,371)(312,372)(313,376)(314,377)(315,378)(316,357)(317,355)(318,356)(319,354)(320,352)(321,353)(322,360)(323,358)(324,359)(406,409)(407,410)(408,411)(415,418)(416,419)(417,420)(424,427)(425,428)(426,429)(433,486)(434,484)(435,485)(436,483)(437,481)(438,482)(439,480)(440,478)(441,479)(442,467)(443,468)(444,466)(445,464)(446,465)(447,463)(448,461)(449,462)(450,460)(451,476)(452,477)(453,475)(454,473)(455,474)(456,472)(457,470)(458,471)(459,469); s2 := Sym(486)!( 1,271)( 2,272)( 3,273)( 4,278)( 5,279)( 6,277)( 7,276)( 8,274)( 9,275)( 10,288)( 11,286)( 12,287)( 13,283)( 14,284)( 15,285)( 16,281)( 17,282)( 18,280)( 19,293)( 20,294)( 21,292)( 22,291)( 23,289)( 24,290)( 25,295)( 26,296)( 27,297)( 28,244)( 29,245)( 30,246)( 31,251)( 32,252)( 33,250)( 34,249)( 35,247)( 36,248)( 37,261)( 38,259)( 39,260)( 40,256)( 41,257)( 42,258)( 43,254)( 44,255)( 45,253)( 46,266)( 47,267)( 48,265)( 49,264)( 50,262)( 51,263)( 52,268)( 53,269)( 54,270)( 55,298)( 56,299)( 57,300)( 58,305)( 59,306)( 60,304)( 61,303)( 62,301)( 63,302)( 64,315)( 65,313)( 66,314)( 67,310)( 68,311)( 69,312)( 70,308)( 71,309)( 72,307)( 73,320)( 74,321)( 75,319)( 76,318)( 77,316)( 78,317)( 79,322)( 80,323)( 81,324)( 82,438)( 83,436)( 84,437)( 85,433)( 86,434)( 87,435)( 88,440)( 89,441)( 90,439)( 91,443)( 92,444)( 93,442)( 94,450)( 95,448)( 96,449)( 97,445)( 98,446)( 99,447)(100,457)(101,458)(102,459)(103,455)(104,456)(105,454)(106,453)(107,451)(108,452)(109,409)(110,410)(111,411)(112,407)(113,408)(114,406)(115,414)(116,412)(117,413)(118,417)(119,415)(120,416)(121,421)(122,422)(123,423)(124,419)(125,420)(126,418)(127,431)(128,432)(129,430)(130,429)(131,427)(132,428)(133,424)(134,425)(135,426)(136,464)(137,465)(138,463)(139,462)(140,460)(141,461)(142,466)(143,467)(144,468)(145,469)(146,470)(147,471)(148,476)(149,477)(150,475)(151,474)(152,472)(153,473)(154,486)(155,484)(156,485)(157,481)(158,482)(159,483)(160,479)(161,480)(162,478)(163,357)(164,355)(165,356)(166,352)(167,353)(168,354)(169,359)(170,360)(171,358)(172,362)(173,363)(174,361)(175,369)(176,367)(177,368)(178,364)(179,365)(180,366)(181,376)(182,377)(183,378)(184,374)(185,375)(186,373)(187,372)(188,370)(189,371)(190,328)(191,329)(192,330)(193,326)(194,327)(195,325)(196,333)(197,331)(198,332)(199,336)(200,334)(201,335)(202,340)(203,341)(204,342)(205,338)(206,339)(207,337)(208,350)(209,351)(210,349)(211,348)(212,346)(213,347)(214,343)(215,344)(216,345)(217,383)(218,384)(219,382)(220,381)(221,379)(222,380)(223,385)(224,386)(225,387)(226,388)(227,389)(228,390)(229,395)(230,396)(231,394)(232,393)(233,391)(234,392)(235,405)(236,403)(237,404)(238,400)(239,401)(240,402)(241,398)(242,399)(243,397); 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, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 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.