Overview
- Group
- SmallGroup(768,1088009)
- 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
48-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=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> 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*s0*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=<(s1*s0)^2*s2*s1*s0*s1*s2> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s1)^4, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s1*s0)^2*s1*s2*s1*s0*s1*s2*s1> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s2*s1*s0*s2*(s1*s0)^2*s1*s2*s1> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
16 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s1*s2*s1, (s0*(s1*s2)^2*s1)^2> of order 8
8 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<(s0*s1)^4, s0*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*(s1*s0)^3*(s2*s1)^2> of order 8
8 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<(s0*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
12 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<(s0*s1)^4, (s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^2*s2*s1> of order 8
8 facets
8 vertex figures
- 8 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 16)( 2, 15)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 65, 80)( 66, 79)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 97,160)( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,192)(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,185)(137,184)(138,183)(139,182)(140,181)(141,180)(142,179)(143,178)(144,177);; s1 := ( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,101)( 6,102)( 7,104)( 8,103)( 9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)( 24,135)( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)( 32,137)( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)( 40,119)( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)( 48,121)( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)( 56,151)( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)( 64,153)( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)( 72,183)( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)( 80,185)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)( 96,169);; s2 := ( 1, 33)( 2, 35)( 3, 34)( 4, 36)( 5, 44)( 6, 42)( 7, 43)( 8, 41)( 9, 40)( 10, 38)( 11, 39)( 12, 37)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 28)( 22, 26)( 23, 27)( 24, 25)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 92)( 54, 90)( 55, 91)( 56, 89)( 57, 88)( 58, 86)( 59, 87)( 60, 85)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 78, 79)( 97,129)( 98,131)( 99,130)(100,132)(101,140)(102,138)(103,139)(104,137)(105,136)(106,134)(107,135)(108,133)(109,141)(110,143)(111,142)(112,144)(114,115)(117,124)(118,122)(119,123)(120,121)(126,127)(145,177)(146,179)(147,178)(148,180)(149,188)(150,186)(151,187)(152,185)(153,184)(154,182)(155,183)(156,181)(157,189)(158,191)(159,190)(160,192)(162,163)(165,172)(166,170)(167,171)(168,169)(174,175);; 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,
s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 1, 16)( 2, 15)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 65, 80)( 66, 79)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 97,160)( 98,159)( 99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,192)(130,191)(131,190)(132,189)(133,188)(134,187)(135,186)(136,185)(137,184)(138,183)(139,182)(140,181)(141,180)(142,179)(143,178)(144,177); s1 := Sym(192)!( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,101)( 6,102)( 7,104)( 8,103)( 9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)( 24,135)( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)( 32,137)( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)( 40,119)( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)( 48,121)( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)( 56,151)( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)( 64,153)( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)( 72,183)( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)( 80,185)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)( 96,169); s2 := Sym(192)!( 1, 33)( 2, 35)( 3, 34)( 4, 36)( 5, 44)( 6, 42)( 7, 43)( 8, 41)( 9, 40)( 10, 38)( 11, 39)( 12, 37)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 28)( 22, 26)( 23, 27)( 24, 25)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 92)( 54, 90)( 55, 91)( 56, 89)( 57, 88)( 58, 86)( 59, 87)( 60, 85)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 78, 79)( 97,129)( 98,131)( 99,130)(100,132)(101,140)(102,138)(103,139)(104,137)(105,136)(106,134)(107,135)(108,133)(109,141)(110,143)(111,142)(112,144)(114,115)(117,124)(118,122)(119,123)(120,121)(126,127)(145,177)(146,179)(147,178)(148,180)(149,188)(150,186)(151,187)(152,185)(153,184)(154,182)(155,183)(156,181)(157,189)(158,191)(159,190)(160,192)(162,163)(165,172)(166,170)(167,171)(168,169)(174,175); poly := sub<Sym(192)|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, s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.