Overview
- Group
- SmallGroup(768,1087755)
- Rank
- 3
- Schläfli Type
- {8,12}
- Vertices, edges, …
- 32, 192, 48
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 4
- 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
12-fold
16-fold
24-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=<s0*(s1*s2)^3*s1*s0*(s2*s1)^2*s2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<s0*s1*s0*(s2*s1)^4*s0*s2*s1*s2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^3*s0*s2*s1*s2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2
24 facets
- 24 of {8}*16
16 vertex figures
- 16 of {12}*24
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^4*s2> of order 4
12 facets
- 12 of {8}*16
8 vertex figures
- 8 of {12}*24
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 4
12 facets
- 12 of {8}*16
8 vertex figures
- 8 of {12}*24
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
12 facets
- 12 of {8}*16
8 vertex figures
- 8 of {12}*24
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^3*s2> of order 4
12 facets
- 12 of {8}*16
8 vertex figures
- 8 of {12}*24
Representations
Permutation Representation (GAP)
s0 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 73, 88)( 74, 87)( 75, 86)( 76, 85)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)(128,173)(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)(136,181)(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)(144,189);; s1 := ( 1,121)( 2,122)( 3,124)( 4,123)( 5,129)( 6,130)( 7,132)( 8,131)( 9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)( 16,135)( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)( 24,139)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)( 64,171)( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)( 72,175)( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)( 80,167)( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)( 88,147)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151);; s2 := ( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 57)( 50, 59)( 51, 58)( 52, 60)( 54, 55)( 61, 69)( 62, 71)( 63, 70)( 64, 72)( 66, 67)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)( 85, 93)( 86, 95)( 87, 94)( 88, 96)( 90, 91)( 97,129)( 98,131)( 99,130)(100,132)(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)(108,124)(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)(116,140)(117,133)(118,135)(119,134)(120,136)(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)(153,169)(154,171)(155,170)(156,172)(157,189)(158,191)(159,190)(160,192)(161,185)(162,187)(163,186)(164,188)(165,181)(166,183)(167,182)(168,184);; 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*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9, 12)( 10, 11)( 13, 16)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 73, 88)( 74, 87)( 75, 86)( 76, 85)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 97,148)( 98,147)( 99,146)(100,145)(101,152)(102,151)(103,150)(104,149)(105,156)(106,155)(107,154)(108,153)(109,160)(110,159)(111,158)(112,157)(113,164)(114,163)(115,162)(116,161)(117,168)(118,167)(119,166)(120,165)(121,172)(122,171)(123,170)(124,169)(125,176)(126,175)(127,174)(128,173)(129,180)(130,179)(131,178)(132,177)(133,184)(134,183)(135,182)(136,181)(137,188)(138,187)(139,186)(140,185)(141,192)(142,191)(143,190)(144,189); s1 := Sym(192)!( 1,121)( 2,122)( 3,124)( 4,123)( 5,129)( 6,130)( 7,132)( 8,131)( 9,125)( 10,126)( 11,128)( 12,127)( 13,133)( 14,134)( 15,136)( 16,135)( 17,141)( 18,142)( 19,144)( 20,143)( 21,137)( 22,138)( 23,140)( 24,139)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)( 49,181)( 50,182)( 51,184)( 52,183)( 53,189)( 54,190)( 55,192)( 56,191)( 57,185)( 58,186)( 59,188)( 60,187)( 61,169)( 62,170)( 63,172)( 64,171)( 65,177)( 66,178)( 67,180)( 68,179)( 69,173)( 70,174)( 71,176)( 72,175)( 73,157)( 74,158)( 75,160)( 76,159)( 77,165)( 78,166)( 79,168)( 80,167)( 81,161)( 82,162)( 83,164)( 84,163)( 85,145)( 86,146)( 87,148)( 88,147)( 89,153)( 90,154)( 91,156)( 92,155)( 93,149)( 94,150)( 95,152)( 96,151); s2 := Sym(192)!( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)( 16, 24)( 18, 19)( 25, 33)( 26, 35)( 27, 34)( 28, 36)( 30, 31)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 42, 43)( 49, 57)( 50, 59)( 51, 58)( 52, 60)( 54, 55)( 61, 69)( 62, 71)( 63, 70)( 64, 72)( 66, 67)( 73, 81)( 74, 83)( 75, 82)( 76, 84)( 78, 79)( 85, 93)( 86, 95)( 87, 94)( 88, 96)( 90, 91)( 97,129)( 98,131)( 99,130)(100,132)(101,125)(102,127)(103,126)(104,128)(105,121)(106,123)(107,122)(108,124)(109,141)(110,143)(111,142)(112,144)(113,137)(114,139)(115,138)(116,140)(117,133)(118,135)(119,134)(120,136)(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)(153,169)(154,171)(155,170)(156,172)(157,189)(158,191)(159,190)(160,192)(161,185)(162,187)(163,186)(164,188)(165,181)(166,183)(167,182)(168,184); 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*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.