Overview
- Group
- SmallGroup(768,1086301)
- Rank
- 3
- Schläfli Type
- {8,6}
- Vertices, edges, …
- 64, 192, 48
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
64-fold
96-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*s0*s2*(s1*s0)^2*(s2*s1*s0)^2*s1*s2> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<s0*s1*s0*(s2*(s1*s0)^2*s1)^2*s2> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s2*s1)^2*s0*s2*(s1*s0)^2*s1> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<s0*s1*(s2*(s1*s0)^2)^2*s1> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s1)^2*(s0*s2*s1)^3, s0*s1*(s2*(s1*s0)^2)^2*s1> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s0*s1)^4*s2*s1*s0*s1*s2> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1, s0*s1*(s2*(s1*s0)^2)^2*s1> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2*s1*s2, (s0*s1)^2*s2*(s1*s0)^3*s2*s1*s0*s2*s1> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^2*(s0*s2*s1)^3, (s0*s2*s1)^2*s0*s2*(s1*s0)^2*s1> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s2*s1> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, s1*s0*s2*(s1*s0)^3*s1*s2*s1> of order 4
20 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 8
12 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s2*s1, (s0*s1)^4*s2*s1*s0*s1*s2> of order 8
8 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, s1*s0*s2*(s1*s0)^3*s1*s2*s1, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 8
10 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 8
8 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s0*s2*s1)^3> of order 8
10 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s2*(s1*s0)^3*s1*s2, s1*s0*s2*(s1*s0)^3*s1*s2*s1, (s0*s1)^4*s2*s1*s0*s1*s2> of order 8
10 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1> of order 8
10 facets
8 vertex figures
- 8 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1,124)( 2,123)( 3,122)( 4,121)( 5,128)( 6,127)( 7,126)( 8,125)( 9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)( 16,117)( 17,110)( 18,109)( 19,112)( 20,111)( 21,106)( 22,105)( 23,108)( 24,107)( 25,102)( 26,101)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31,100)( 32, 99)( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)( 40,157)( 41,148)( 42,147)( 43,146)( 44,145)( 45,152)( 46,151)( 47,150)( 48,149)( 49,142)( 50,141)( 51,144)( 52,143)( 53,138)( 54,137)( 55,140)( 56,139)( 57,134)( 58,133)( 59,136)( 60,135)( 61,130)( 62,129)( 63,132)( 64,131)( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)( 72,189)( 73,180)( 74,179)( 75,178)( 76,177)( 77,184)( 78,183)( 79,182)( 80,181)( 81,174)( 82,173)( 83,176)( 84,175)( 85,170)( 86,169)( 87,172)( 88,171)( 89,166)( 90,165)( 91,168)( 92,167)( 93,162)( 94,161)( 95,164)( 96,163)(193,316)(194,315)(195,314)(196,313)(197,320)(198,319)(199,318)(200,317)(201,308)(202,307)(203,306)(204,305)(205,312)(206,311)(207,310)(208,309)(209,302)(210,301)(211,304)(212,303)(213,298)(214,297)(215,300)(216,299)(217,294)(218,293)(219,296)(220,295)(221,290)(222,289)(223,292)(224,291)(225,348)(226,347)(227,346)(228,345)(229,352)(230,351)(231,350)(232,349)(233,340)(234,339)(235,338)(236,337)(237,344)(238,343)(239,342)(240,341)(241,334)(242,333)(243,336)(244,335)(245,330)(246,329)(247,332)(248,331)(249,326)(250,325)(251,328)(252,327)(253,322)(254,321)(255,324)(256,323)(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)(264,381)(265,372)(266,371)(267,370)(268,369)(269,376)(270,375)(271,374)(272,373)(273,366)(274,365)(275,368)(276,367)(277,362)(278,361)(279,364)(280,363)(281,358)(282,357)(283,360)(284,359)(285,354)(286,353)(287,356)(288,355);; s1 := ( 3, 4)( 5, 6)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 79)( 42, 80)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 73)( 48, 74)( 49, 92)( 50, 91)( 51, 89)( 52, 90)( 53, 95)( 54, 96)( 55, 94)( 56, 93)( 57, 83)( 58, 84)( 59, 82)( 60, 81)( 61, 88)( 62, 87)( 63, 85)( 64, 86)( 97,103)( 98,104)( 99,102)(100,101)(107,108)(109,110)(113,126)(114,125)(115,127)(116,128)(117,121)(118,122)(119,124)(120,123)(129,167)(130,168)(131,166)(132,165)(133,164)(134,163)(135,161)(136,162)(137,169)(138,170)(139,172)(140,171)(141,174)(142,173)(143,175)(144,176)(145,190)(146,189)(147,191)(148,192)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,178)(158,177)(159,179)(160,180)(195,196)(197,198)(201,207)(202,208)(203,206)(204,205)(209,220)(210,219)(211,217)(212,218)(213,223)(214,224)(215,222)(216,221)(225,257)(226,258)(227,260)(228,259)(229,262)(230,261)(231,263)(232,264)(233,271)(234,272)(235,270)(236,269)(237,268)(238,267)(239,265)(240,266)(241,284)(242,283)(243,281)(244,282)(245,287)(246,288)(247,286)(248,285)(249,275)(250,276)(251,274)(252,273)(253,280)(254,279)(255,277)(256,278)(289,295)(290,296)(291,294)(292,293)(299,300)(301,302)(305,318)(306,317)(307,319)(308,320)(309,313)(310,314)(311,316)(312,315)(321,359)(322,360)(323,358)(324,357)(325,356)(326,355)(327,353)(328,354)(329,361)(330,362)(331,364)(332,363)(333,366)(334,365)(335,367)(336,368)(337,382)(338,381)(339,383)(340,384)(341,377)(342,378)(343,380)(344,379)(345,373)(346,374)(347,376)(348,375)(349,370)(350,369)(351,371)(352,372);; s2 := ( 1,286)( 2,288)( 3,285)( 4,287)( 5,283)( 6,281)( 7,284)( 8,282)( 9,271)( 10,269)( 11,272)( 12,270)( 13,266)( 14,268)( 15,265)( 16,267)( 17,273)( 18,275)( 19,274)( 20,276)( 21,280)( 22,278)( 23,279)( 24,277)( 25,262)( 26,264)( 27,261)( 28,263)( 29,259)( 30,257)( 31,260)( 32,258)( 33,254)( 34,256)( 35,253)( 36,255)( 37,251)( 38,249)( 39,252)( 40,250)( 41,239)( 42,237)( 43,240)( 44,238)( 45,234)( 46,236)( 47,233)( 48,235)( 49,241)( 50,243)( 51,242)( 52,244)( 53,248)( 54,246)( 55,247)( 56,245)( 57,230)( 58,232)( 59,229)( 60,231)( 61,227)( 62,225)( 63,228)( 64,226)( 65,222)( 66,224)( 67,221)( 68,223)( 69,219)( 70,217)( 71,220)( 72,218)( 73,207)( 74,205)( 75,208)( 76,206)( 77,202)( 78,204)( 79,201)( 80,203)( 81,209)( 82,211)( 83,210)( 84,212)( 85,216)( 86,214)( 87,215)( 88,213)( 89,198)( 90,200)( 91,197)( 92,199)( 93,195)( 94,193)( 95,196)( 96,194)( 97,380)( 98,378)( 99,379)(100,377)(101,381)(102,383)(103,382)(104,384)(105,361)(106,363)(107,362)(108,364)(109,368)(110,366)(111,367)(112,365)(113,375)(114,373)(115,376)(116,374)(117,370)(118,372)(119,369)(120,371)(121,356)(122,354)(123,355)(124,353)(125,357)(126,359)(127,358)(128,360)(129,348)(130,346)(131,347)(132,345)(133,349)(134,351)(135,350)(136,352)(137,329)(138,331)(139,330)(140,332)(141,336)(142,334)(143,335)(144,333)(145,343)(146,341)(147,344)(148,342)(149,338)(150,340)(151,337)(152,339)(153,324)(154,322)(155,323)(156,321)(157,325)(158,327)(159,326)(160,328)(161,316)(162,314)(163,315)(164,313)(165,317)(166,319)(167,318)(168,320)(169,297)(170,299)(171,298)(172,300)(173,304)(174,302)(175,303)(176,301)(177,311)(178,309)(179,312)(180,310)(181,306)(182,308)(183,305)(184,307)(185,292)(186,290)(187,291)(188,289)(189,293)(190,295)(191,294)(192,296);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(384)!( 1,124)( 2,123)( 3,122)( 4,121)( 5,128)( 6,127)( 7,126)( 8,125)( 9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)( 16,117)( 17,110)( 18,109)( 19,112)( 20,111)( 21,106)( 22,105)( 23,108)( 24,107)( 25,102)( 26,101)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31,100)( 32, 99)( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)( 40,157)( 41,148)( 42,147)( 43,146)( 44,145)( 45,152)( 46,151)( 47,150)( 48,149)( 49,142)( 50,141)( 51,144)( 52,143)( 53,138)( 54,137)( 55,140)( 56,139)( 57,134)( 58,133)( 59,136)( 60,135)( 61,130)( 62,129)( 63,132)( 64,131)( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)( 72,189)( 73,180)( 74,179)( 75,178)( 76,177)( 77,184)( 78,183)( 79,182)( 80,181)( 81,174)( 82,173)( 83,176)( 84,175)( 85,170)( 86,169)( 87,172)( 88,171)( 89,166)( 90,165)( 91,168)( 92,167)( 93,162)( 94,161)( 95,164)( 96,163)(193,316)(194,315)(195,314)(196,313)(197,320)(198,319)(199,318)(200,317)(201,308)(202,307)(203,306)(204,305)(205,312)(206,311)(207,310)(208,309)(209,302)(210,301)(211,304)(212,303)(213,298)(214,297)(215,300)(216,299)(217,294)(218,293)(219,296)(220,295)(221,290)(222,289)(223,292)(224,291)(225,348)(226,347)(227,346)(228,345)(229,352)(230,351)(231,350)(232,349)(233,340)(234,339)(235,338)(236,337)(237,344)(238,343)(239,342)(240,341)(241,334)(242,333)(243,336)(244,335)(245,330)(246,329)(247,332)(248,331)(249,326)(250,325)(251,328)(252,327)(253,322)(254,321)(255,324)(256,323)(257,380)(258,379)(259,378)(260,377)(261,384)(262,383)(263,382)(264,381)(265,372)(266,371)(267,370)(268,369)(269,376)(270,375)(271,374)(272,373)(273,366)(274,365)(275,368)(276,367)(277,362)(278,361)(279,364)(280,363)(281,358)(282,357)(283,360)(284,359)(285,354)(286,353)(287,356)(288,355); s1 := Sym(384)!( 3, 4)( 5, 6)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 79)( 42, 80)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 73)( 48, 74)( 49, 92)( 50, 91)( 51, 89)( 52, 90)( 53, 95)( 54, 96)( 55, 94)( 56, 93)( 57, 83)( 58, 84)( 59, 82)( 60, 81)( 61, 88)( 62, 87)( 63, 85)( 64, 86)( 97,103)( 98,104)( 99,102)(100,101)(107,108)(109,110)(113,126)(114,125)(115,127)(116,128)(117,121)(118,122)(119,124)(120,123)(129,167)(130,168)(131,166)(132,165)(133,164)(134,163)(135,161)(136,162)(137,169)(138,170)(139,172)(140,171)(141,174)(142,173)(143,175)(144,176)(145,190)(146,189)(147,191)(148,192)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,178)(158,177)(159,179)(160,180)(195,196)(197,198)(201,207)(202,208)(203,206)(204,205)(209,220)(210,219)(211,217)(212,218)(213,223)(214,224)(215,222)(216,221)(225,257)(226,258)(227,260)(228,259)(229,262)(230,261)(231,263)(232,264)(233,271)(234,272)(235,270)(236,269)(237,268)(238,267)(239,265)(240,266)(241,284)(242,283)(243,281)(244,282)(245,287)(246,288)(247,286)(248,285)(249,275)(250,276)(251,274)(252,273)(253,280)(254,279)(255,277)(256,278)(289,295)(290,296)(291,294)(292,293)(299,300)(301,302)(305,318)(306,317)(307,319)(308,320)(309,313)(310,314)(311,316)(312,315)(321,359)(322,360)(323,358)(324,357)(325,356)(326,355)(327,353)(328,354)(329,361)(330,362)(331,364)(332,363)(333,366)(334,365)(335,367)(336,368)(337,382)(338,381)(339,383)(340,384)(341,377)(342,378)(343,380)(344,379)(345,373)(346,374)(347,376)(348,375)(349,370)(350,369)(351,371)(352,372); s2 := Sym(384)!( 1,286)( 2,288)( 3,285)( 4,287)( 5,283)( 6,281)( 7,284)( 8,282)( 9,271)( 10,269)( 11,272)( 12,270)( 13,266)( 14,268)( 15,265)( 16,267)( 17,273)( 18,275)( 19,274)( 20,276)( 21,280)( 22,278)( 23,279)( 24,277)( 25,262)( 26,264)( 27,261)( 28,263)( 29,259)( 30,257)( 31,260)( 32,258)( 33,254)( 34,256)( 35,253)( 36,255)( 37,251)( 38,249)( 39,252)( 40,250)( 41,239)( 42,237)( 43,240)( 44,238)( 45,234)( 46,236)( 47,233)( 48,235)( 49,241)( 50,243)( 51,242)( 52,244)( 53,248)( 54,246)( 55,247)( 56,245)( 57,230)( 58,232)( 59,229)( 60,231)( 61,227)( 62,225)( 63,228)( 64,226)( 65,222)( 66,224)( 67,221)( 68,223)( 69,219)( 70,217)( 71,220)( 72,218)( 73,207)( 74,205)( 75,208)( 76,206)( 77,202)( 78,204)( 79,201)( 80,203)( 81,209)( 82,211)( 83,210)( 84,212)( 85,216)( 86,214)( 87,215)( 88,213)( 89,198)( 90,200)( 91,197)( 92,199)( 93,195)( 94,193)( 95,196)( 96,194)( 97,380)( 98,378)( 99,379)(100,377)(101,381)(102,383)(103,382)(104,384)(105,361)(106,363)(107,362)(108,364)(109,368)(110,366)(111,367)(112,365)(113,375)(114,373)(115,376)(116,374)(117,370)(118,372)(119,369)(120,371)(121,356)(122,354)(123,355)(124,353)(125,357)(126,359)(127,358)(128,360)(129,348)(130,346)(131,347)(132,345)(133,349)(134,351)(135,350)(136,352)(137,329)(138,331)(139,330)(140,332)(141,336)(142,334)(143,335)(144,333)(145,343)(146,341)(147,344)(148,342)(149,338)(150,340)(151,337)(152,339)(153,324)(154,322)(155,323)(156,321)(157,325)(158,327)(159,326)(160,328)(161,316)(162,314)(163,315)(164,313)(165,317)(166,319)(167,318)(168,320)(169,297)(170,299)(171,298)(172,300)(173,304)(174,302)(175,303)(176,301)(177,311)(178,309)(179,312)(180,310)(181,306)(182,308)(183,305)(184,307)(185,292)(186,290)(187,291)(188,289)(189,293)(190,295)(191,294)(192,296); poly := sub<Sym(384)|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*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.