Overview
- Group
- SmallGroup(1728,30189)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 144, 432, 48
- Order of s0s1s2
- 72
- Order of s0s1s2s1
- 12
- 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
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
144-fold
216-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 := ( 1,217)( 2,218)( 3,220)( 4,219)( 5,223)( 6,224)( 7,221)( 8,222)( 9,233)( 10,234)( 11,236)( 12,235)( 13,239)( 14,240)( 15,237)( 16,238)( 17,225)( 18,226)( 19,228)( 20,227)( 21,231)( 22,232)( 23,229)( 24,230)( 25,281)( 26,282)( 27,284)( 28,283)( 29,287)( 30,288)( 31,285)( 32,286)( 33,273)( 34,274)( 35,276)( 36,275)( 37,279)( 38,280)( 39,277)( 40,278)( 41,265)( 42,266)( 43,268)( 44,267)( 45,271)( 46,272)( 47,269)( 48,270)( 49,257)( 50,258)( 51,260)( 52,259)( 53,263)( 54,264)( 55,261)( 56,262)( 57,249)( 58,250)( 59,252)( 60,251)( 61,255)( 62,256)( 63,253)( 64,254)( 65,241)( 66,242)( 67,244)( 68,243)( 69,247)( 70,248)( 71,245)( 72,246)( 73,361)( 74,362)( 75,364)( 76,363)( 77,367)( 78,368)( 79,365)( 80,366)( 81,377)( 82,378)( 83,380)( 84,379)( 85,383)( 86,384)( 87,381)( 88,382)( 89,369)( 90,370)( 91,372)( 92,371)( 93,375)( 94,376)( 95,373)( 96,374)( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)(104,430)(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)(112,422)(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)(120,414)(121,401)(122,402)(123,404)(124,403)(125,407)(126,408)(127,405)(128,406)(129,393)(130,394)(131,396)(132,395)(133,399)(134,400)(135,397)(136,398)(137,385)(138,386)(139,388)(140,387)(141,391)(142,392)(143,389)(144,390)(145,289)(146,290)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,305)(154,306)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,297)(162,298)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,353)(170,354)(171,356)(172,355)(173,359)(174,360)(175,357)(176,358)(177,345)(178,346)(179,348)(180,347)(181,351)(182,352)(183,349)(184,350)(185,337)(186,338)(187,340)(188,339)(189,343)(190,344)(191,341)(192,342)(193,329)(194,330)(195,332)(196,331)(197,335)(198,336)(199,333)(200,334)(201,321)(202,322)(203,324)(204,323)(205,327)(206,328)(207,325)(208,326)(209,313)(210,314)(211,316)(212,315)(213,319)(214,320)(215,317)(216,318);; s1 := ( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)( 9,113)( 10,114)( 11,119)( 12,120)( 13,118)( 14,117)( 15,115)( 16,116)( 17,105)( 18,106)( 19,111)( 20,112)( 21,110)( 22,109)( 23,107)( 24,108)( 25, 73)( 26, 74)( 27, 79)( 28, 80)( 29, 78)( 30, 77)( 31, 75)( 32, 76)( 33, 89)( 34, 90)( 35, 95)( 36, 96)( 37, 94)( 38, 93)( 39, 91)( 40, 92)( 41, 81)( 42, 82)( 43, 87)( 44, 88)( 45, 86)( 46, 85)( 47, 83)( 48, 84)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)(145,169)(146,170)(147,175)(148,176)(149,174)(150,173)(151,171)(152,172)(153,185)(154,186)(155,191)(156,192)(157,190)(158,189)(159,187)(160,188)(161,177)(162,178)(163,183)(164,184)(165,182)(166,181)(167,179)(168,180)(193,209)(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)(205,206)(217,313)(218,314)(219,319)(220,320)(221,318)(222,317)(223,315)(224,316)(225,329)(226,330)(227,335)(228,336)(229,334)(230,333)(231,331)(232,332)(233,321)(234,322)(235,327)(236,328)(237,326)(238,325)(239,323)(240,324)(241,289)(242,290)(243,295)(244,296)(245,294)(246,293)(247,291)(248,292)(249,305)(250,306)(251,311)(252,312)(253,310)(254,309)(255,307)(256,308)(257,297)(258,298)(259,303)(260,304)(261,302)(262,301)(263,299)(264,300)(265,353)(266,354)(267,359)(268,360)(269,358)(270,357)(271,355)(272,356)(273,345)(274,346)(275,351)(276,352)(277,350)(278,349)(279,347)(280,348)(281,337)(282,338)(283,343)(284,344)(285,342)(286,341)(287,339)(288,340)(361,385)(362,386)(363,391)(364,392)(365,390)(366,389)(367,387)(368,388)(369,401)(370,402)(371,407)(372,408)(373,406)(374,405)(375,403)(376,404)(377,393)(378,394)(379,399)(380,400)(381,398)(382,397)(383,395)(384,396)(409,425)(410,426)(411,431)(412,432)(413,430)(414,429)(415,427)(416,428)(419,423)(420,424)(421,422);; s2 := ( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)( 18, 20)( 21, 22)( 25, 27)( 26, 28)( 29, 30)( 33, 35)( 34, 36)( 37, 38)( 41, 43)( 42, 44)( 45, 46)( 49, 51)( 50, 52)( 53, 54)( 57, 59)( 58, 60)( 61, 62)( 65, 67)( 66, 68)( 69, 70)( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)( 80,152)( 81,155)( 82,156)( 83,153)( 84,154)( 85,158)( 86,157)( 87,159)( 88,160)( 89,163)( 90,164)( 91,161)( 92,162)( 93,166)( 94,165)( 95,167)( 96,168)( 97,171)( 98,172)( 99,169)(100,170)(101,174)(102,173)(103,175)(104,176)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)(113,187)(114,188)(115,185)(116,186)(117,190)(118,189)(119,191)(120,192)(121,195)(122,196)(123,193)(124,194)(125,198)(126,197)(127,199)(128,200)(129,203)(130,204)(131,201)(132,202)(133,206)(134,205)(135,207)(136,208)(137,211)(138,212)(139,209)(140,210)(141,214)(142,213)(143,215)(144,216)(217,220)(218,219)(223,224)(225,228)(226,227)(231,232)(233,236)(234,235)(239,240)(241,244)(242,243)(247,248)(249,252)(250,251)(255,256)(257,260)(258,259)(263,264)(265,268)(266,267)(271,272)(273,276)(274,275)(279,280)(281,284)(282,283)(287,288)(289,364)(290,363)(291,362)(292,361)(293,365)(294,366)(295,368)(296,367)(297,372)(298,371)(299,370)(300,369)(301,373)(302,374)(303,376)(304,375)(305,380)(306,379)(307,378)(308,377)(309,381)(310,382)(311,384)(312,383)(313,388)(314,387)(315,386)(316,385)(317,389)(318,390)(319,392)(320,391)(321,396)(322,395)(323,394)(324,393)(325,397)(326,398)(327,400)(328,399)(329,404)(330,403)(331,402)(332,401)(333,405)(334,406)(335,408)(336,407)(337,412)(338,411)(339,410)(340,409)(341,413)(342,414)(343,416)(344,415)(345,420)(346,419)(347,418)(348,417)(349,421)(350,422)(351,424)(352,423)(353,428)(354,427)(355,426)(356,425)(357,429)(358,430)(359,432)(360,431);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(432)!( 1,217)( 2,218)( 3,220)( 4,219)( 5,223)( 6,224)( 7,221)( 8,222)( 9,233)( 10,234)( 11,236)( 12,235)( 13,239)( 14,240)( 15,237)( 16,238)( 17,225)( 18,226)( 19,228)( 20,227)( 21,231)( 22,232)( 23,229)( 24,230)( 25,281)( 26,282)( 27,284)( 28,283)( 29,287)( 30,288)( 31,285)( 32,286)( 33,273)( 34,274)( 35,276)( 36,275)( 37,279)( 38,280)( 39,277)( 40,278)( 41,265)( 42,266)( 43,268)( 44,267)( 45,271)( 46,272)( 47,269)( 48,270)( 49,257)( 50,258)( 51,260)( 52,259)( 53,263)( 54,264)( 55,261)( 56,262)( 57,249)( 58,250)( 59,252)( 60,251)( 61,255)( 62,256)( 63,253)( 64,254)( 65,241)( 66,242)( 67,244)( 68,243)( 69,247)( 70,248)( 71,245)( 72,246)( 73,361)( 74,362)( 75,364)( 76,363)( 77,367)( 78,368)( 79,365)( 80,366)( 81,377)( 82,378)( 83,380)( 84,379)( 85,383)( 86,384)( 87,381)( 88,382)( 89,369)( 90,370)( 91,372)( 92,371)( 93,375)( 94,376)( 95,373)( 96,374)( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)(104,430)(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)(112,422)(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)(120,414)(121,401)(122,402)(123,404)(124,403)(125,407)(126,408)(127,405)(128,406)(129,393)(130,394)(131,396)(132,395)(133,399)(134,400)(135,397)(136,398)(137,385)(138,386)(139,388)(140,387)(141,391)(142,392)(143,389)(144,390)(145,289)(146,290)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,305)(154,306)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,297)(162,298)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,353)(170,354)(171,356)(172,355)(173,359)(174,360)(175,357)(176,358)(177,345)(178,346)(179,348)(180,347)(181,351)(182,352)(183,349)(184,350)(185,337)(186,338)(187,340)(188,339)(189,343)(190,344)(191,341)(192,342)(193,329)(194,330)(195,332)(196,331)(197,335)(198,336)(199,333)(200,334)(201,321)(202,322)(203,324)(204,323)(205,327)(206,328)(207,325)(208,326)(209,313)(210,314)(211,316)(212,315)(213,319)(214,320)(215,317)(216,318); s1 := Sym(432)!( 1, 97)( 2, 98)( 3,103)( 4,104)( 5,102)( 6,101)( 7, 99)( 8,100)( 9,113)( 10,114)( 11,119)( 12,120)( 13,118)( 14,117)( 15,115)( 16,116)( 17,105)( 18,106)( 19,111)( 20,112)( 21,110)( 22,109)( 23,107)( 24,108)( 25, 73)( 26, 74)( 27, 79)( 28, 80)( 29, 78)( 30, 77)( 31, 75)( 32, 76)( 33, 89)( 34, 90)( 35, 95)( 36, 96)( 37, 94)( 38, 93)( 39, 91)( 40, 92)( 41, 81)( 42, 82)( 43, 87)( 44, 88)( 45, 86)( 46, 85)( 47, 83)( 48, 84)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)(145,169)(146,170)(147,175)(148,176)(149,174)(150,173)(151,171)(152,172)(153,185)(154,186)(155,191)(156,192)(157,190)(158,189)(159,187)(160,188)(161,177)(162,178)(163,183)(164,184)(165,182)(166,181)(167,179)(168,180)(193,209)(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)(205,206)(217,313)(218,314)(219,319)(220,320)(221,318)(222,317)(223,315)(224,316)(225,329)(226,330)(227,335)(228,336)(229,334)(230,333)(231,331)(232,332)(233,321)(234,322)(235,327)(236,328)(237,326)(238,325)(239,323)(240,324)(241,289)(242,290)(243,295)(244,296)(245,294)(246,293)(247,291)(248,292)(249,305)(250,306)(251,311)(252,312)(253,310)(254,309)(255,307)(256,308)(257,297)(258,298)(259,303)(260,304)(261,302)(262,301)(263,299)(264,300)(265,353)(266,354)(267,359)(268,360)(269,358)(270,357)(271,355)(272,356)(273,345)(274,346)(275,351)(276,352)(277,350)(278,349)(279,347)(280,348)(281,337)(282,338)(283,343)(284,344)(285,342)(286,341)(287,339)(288,340)(361,385)(362,386)(363,391)(364,392)(365,390)(366,389)(367,387)(368,388)(369,401)(370,402)(371,407)(372,408)(373,406)(374,405)(375,403)(376,404)(377,393)(378,394)(379,399)(380,400)(381,398)(382,397)(383,395)(384,396)(409,425)(410,426)(411,431)(412,432)(413,430)(414,429)(415,427)(416,428)(419,423)(420,424)(421,422); s2 := Sym(432)!( 1, 3)( 2, 4)( 5, 6)( 9, 11)( 10, 12)( 13, 14)( 17, 19)( 18, 20)( 21, 22)( 25, 27)( 26, 28)( 29, 30)( 33, 35)( 34, 36)( 37, 38)( 41, 43)( 42, 44)( 45, 46)( 49, 51)( 50, 52)( 53, 54)( 57, 59)( 58, 60)( 61, 62)( 65, 67)( 66, 68)( 69, 70)( 73,147)( 74,148)( 75,145)( 76,146)( 77,150)( 78,149)( 79,151)( 80,152)( 81,155)( 82,156)( 83,153)( 84,154)( 85,158)( 86,157)( 87,159)( 88,160)( 89,163)( 90,164)( 91,161)( 92,162)( 93,166)( 94,165)( 95,167)( 96,168)( 97,171)( 98,172)( 99,169)(100,170)(101,174)(102,173)(103,175)(104,176)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)(113,187)(114,188)(115,185)(116,186)(117,190)(118,189)(119,191)(120,192)(121,195)(122,196)(123,193)(124,194)(125,198)(126,197)(127,199)(128,200)(129,203)(130,204)(131,201)(132,202)(133,206)(134,205)(135,207)(136,208)(137,211)(138,212)(139,209)(140,210)(141,214)(142,213)(143,215)(144,216)(217,220)(218,219)(223,224)(225,228)(226,227)(231,232)(233,236)(234,235)(239,240)(241,244)(242,243)(247,248)(249,252)(250,251)(255,256)(257,260)(258,259)(263,264)(265,268)(266,267)(271,272)(273,276)(274,275)(279,280)(281,284)(282,283)(287,288)(289,364)(290,363)(291,362)(292,361)(293,365)(294,366)(295,368)(296,367)(297,372)(298,371)(299,370)(300,369)(301,373)(302,374)(303,376)(304,375)(305,380)(306,379)(307,378)(308,377)(309,381)(310,382)(311,384)(312,383)(313,388)(314,387)(315,386)(316,385)(317,389)(318,390)(319,392)(320,391)(321,396)(322,395)(323,394)(324,393)(325,397)(326,398)(327,400)(328,399)(329,404)(330,403)(331,402)(332,401)(333,405)(334,406)(335,408)(336,407)(337,412)(338,411)(339,410)(340,409)(341,413)(342,414)(343,416)(344,415)(345,420)(346,419)(347,418)(348,417)(349,421)(350,422)(351,424)(352,423)(353,428)(354,427)(355,426)(356,425)(357,429)(358,430)(359,432)(360,431); poly := sub<Sym(432)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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*s0*s1 >;
References
None.
to this polytope.