Overview
- Group
- SmallGroup(768,1086329)
- Rank
- 3
- Schläfli Type
- {6,8}
- Vertices, edges, …
- 48, 192, 64
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 8
- 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
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=<(s1*s0)^2*(s2*s1)^2*s0*s2*s1*s0*s1*s2> of order 2
32 facets
- 32 of {6}*12
24 vertex figures
- 24 of {8}*16
P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s1> of order 2
32 facets
- 32 of {6}*12
24 vertex figures
- 24 of {8}*16
P/N, where N=<s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 2
32 facets
- 32 of {6}*12
24 vertex figures
- 24 of {8}*16
P/N, where N=<(s1*s0)^2*s2*s1*s0*(s1*s2)^2, s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*(s2*s1)^2*s2> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<(s1*s0)^2*s2*s1*s0*(s2*s1)^2, s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s2*s1)^2, s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s1> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<(s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 4
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
Representations
Permutation Representation (GAP)
s0 := ( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 31)( 18, 32)( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)( 42, 75)( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 95)( 50, 96)( 51, 93)( 52, 94)( 53, 89)( 54, 90)( 55, 91)( 56, 92)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 83)( 62, 84)( 63, 81)( 64, 82)( 97, 98)( 99,100)(101,104)(102,103)(105,107)(106,108)(113,128)(114,127)(115,126)(116,125)(117,122)(118,121)(119,124)(120,123)(129,162)(130,161)(131,164)(132,163)(133,168)(134,167)(135,166)(136,165)(137,171)(138,172)(139,169)(140,170)(141,173)(142,174)(143,175)(144,176)(145,192)(146,191)(147,190)(148,189)(149,186)(150,185)(151,188)(152,187)(153,182)(154,181)(155,184)(156,183)(157,180)(158,179)(159,178)(160,177);; s1 := ( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 82)( 10, 81)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 88)( 16, 87)( 17, 74)( 18, 73)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 80)( 24, 79)( 25, 90)( 26, 89)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 96)( 32, 95)( 35, 37)( 36, 38)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 56)( 48, 55)( 57, 58)( 59, 62)( 60, 61)( 63, 64)( 97,161)( 98,162)( 99,165)(100,166)(101,163)(102,164)(103,167)(104,168)(105,178)(106,177)(107,182)(108,181)(109,180)(110,179)(111,184)(112,183)(113,170)(114,169)(115,174)(116,173)(117,172)(118,171)(119,176)(120,175)(121,186)(122,185)(123,190)(124,189)(125,188)(126,187)(127,192)(128,191)(131,133)(132,134)(137,146)(138,145)(139,150)(140,149)(141,148)(142,147)(143,152)(144,151)(153,154)(155,158)(156,157)(159,160);; s2 := ( 1,111)( 2,112)( 3,109)( 4,110)( 5,107)( 6,108)( 7,105)( 8,106)( 9,104)( 10,103)( 11,102)( 12,101)( 13,100)( 14, 99)( 15, 98)( 16, 97)( 17,127)( 18,128)( 19,125)( 20,126)( 21,123)( 22,124)( 23,121)( 24,122)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,143)( 34,144)( 35,141)( 36,142)( 37,139)( 38,140)( 39,137)( 40,138)( 41,136)( 42,135)( 43,134)( 44,133)( 45,132)( 46,131)( 47,130)( 48,129)( 49,159)( 50,160)( 51,157)( 52,158)( 53,155)( 54,156)( 55,153)( 56,154)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,175)( 66,176)( 67,173)( 68,174)( 69,171)( 70,172)( 71,169)( 72,170)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,191)( 82,192)( 83,189)( 84,190)( 85,187)( 86,188)( 87,185)( 88,186)( 89,184)( 90,183)( 91,182)( 92,181)( 93,180)( 94,179)( 95,178)( 96,177);; 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 31)( 18, 32)( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)( 42, 75)( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 95)( 50, 96)( 51, 93)( 52, 94)( 53, 89)( 54, 90)( 55, 91)( 56, 92)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 83)( 62, 84)( 63, 81)( 64, 82)( 97, 98)( 99,100)(101,104)(102,103)(105,107)(106,108)(113,128)(114,127)(115,126)(116,125)(117,122)(118,121)(119,124)(120,123)(129,162)(130,161)(131,164)(132,163)(133,168)(134,167)(135,166)(136,165)(137,171)(138,172)(139,169)(140,170)(141,173)(142,174)(143,175)(144,176)(145,192)(146,191)(147,190)(148,189)(149,186)(150,185)(151,188)(152,187)(153,182)(154,181)(155,184)(156,183)(157,180)(158,179)(159,178)(160,177); s1 := Sym(192)!( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 82)( 10, 81)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 88)( 16, 87)( 17, 74)( 18, 73)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 80)( 24, 79)( 25, 90)( 26, 89)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 96)( 32, 95)( 35, 37)( 36, 38)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 56)( 48, 55)( 57, 58)( 59, 62)( 60, 61)( 63, 64)( 97,161)( 98,162)( 99,165)(100,166)(101,163)(102,164)(103,167)(104,168)(105,178)(106,177)(107,182)(108,181)(109,180)(110,179)(111,184)(112,183)(113,170)(114,169)(115,174)(116,173)(117,172)(118,171)(119,176)(120,175)(121,186)(122,185)(123,190)(124,189)(125,188)(126,187)(127,192)(128,191)(131,133)(132,134)(137,146)(138,145)(139,150)(140,149)(141,148)(142,147)(143,152)(144,151)(153,154)(155,158)(156,157)(159,160); s2 := Sym(192)!( 1,111)( 2,112)( 3,109)( 4,110)( 5,107)( 6,108)( 7,105)( 8,106)( 9,104)( 10,103)( 11,102)( 12,101)( 13,100)( 14, 99)( 15, 98)( 16, 97)( 17,127)( 18,128)( 19,125)( 20,126)( 21,123)( 22,124)( 23,121)( 24,122)( 25,120)( 26,119)( 27,118)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,143)( 34,144)( 35,141)( 36,142)( 37,139)( 38,140)( 39,137)( 40,138)( 41,136)( 42,135)( 43,134)( 44,133)( 45,132)( 46,131)( 47,130)( 48,129)( 49,159)( 50,160)( 51,157)( 52,158)( 53,155)( 54,156)( 55,153)( 56,154)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)( 65,175)( 66,176)( 67,173)( 68,174)( 69,171)( 70,172)( 71,169)( 72,170)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,191)( 82,192)( 83,189)( 84,190)( 85,187)( 86,188)( 87,185)( 88,186)( 89,184)( 90,183)( 91,182)( 92,181)( 93,180)( 94,179)( 95,178)( 96,177); 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2 >;
References
None.
to this polytope.