Overview
- Group
- SmallGroup(768,1088551)
- Rank
- 3
- Schläfli Type
- {8,6}
- Vertices, edges, …
- 64, 192, 48
- Order of s0s1s2
- 12
- 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
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*(s2*s1)^2*s0*(s1*s2)^2> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
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*s2*s1*(s0*(s2*s1)^2)^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*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {8}*16
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s1*s0*(s1*s2)^2)^2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1*s2*s1)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*s1*s0*s2*s1*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1, (s1*s0)^2*s2*s1*s0*s1*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*s2*s1*s2> of order 4
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 30)( 6, 29)( 7, 31)( 8, 32)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 22)( 14, 21)( 15, 23)( 16, 24)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 62)( 38, 61)( 39, 63)( 40, 64)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 54)( 46, 53)( 47, 55)( 48, 56)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 94)( 70, 93)( 71, 95)( 72, 96)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 86)( 78, 85)( 79, 87)( 80, 88)( 97,122)( 98,121)( 99,123)(100,124)(101,125)(102,126)(103,128)(104,127)(105,114)(106,113)(107,115)(108,116)(109,117)(110,118)(111,120)(112,119)(129,154)(130,153)(131,155)(132,156)(133,157)(134,158)(135,160)(136,159)(137,146)(138,145)(139,147)(140,148)(141,149)(142,150)(143,152)(144,151)(161,186)(162,185)(163,187)(164,188)(165,189)(166,190)(167,192)(168,191)(169,178)(170,177)(171,179)(172,180)(173,181)(174,182)(175,184)(176,183);; s1 := ( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)( 8,102)( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)( 16,111)( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)( 24,123)( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)( 32,113)( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)( 40,166)( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)( 48,175)( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)( 56,187)( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)( 64,177)( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)( 72,134)( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)( 80,143)( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)( 88,155)( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)( 96,145);; s2 := ( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 81)( 10, 82)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 87)( 16, 88)( 17, 73)( 18, 74)( 19, 77)( 20, 78)( 21, 75)( 22, 76)( 23, 79)( 24, 80)( 25, 89)( 26, 90)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 95)( 32, 96)( 35, 37)( 36, 38)( 41, 49)( 42, 50)( 43, 53)( 44, 54)( 45, 51)( 46, 52)( 47, 55)( 48, 56)( 59, 61)( 60, 62)( 97,161)( 98,162)( 99,165)(100,166)(101,163)(102,164)(103,167)(104,168)(105,177)(106,178)(107,181)(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)(124,190)(125,187)(126,188)(127,191)(128,192)(131,133)(132,134)(137,145)(138,146)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)(156,158);; 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*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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 30)( 6, 29)( 7, 31)( 8, 32)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 22)( 14, 21)( 15, 23)( 16, 24)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 62)( 38, 61)( 39, 63)( 40, 64)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 54)( 46, 53)( 47, 55)( 48, 56)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 94)( 70, 93)( 71, 95)( 72, 96)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 86)( 78, 85)( 79, 87)( 80, 88)( 97,122)( 98,121)( 99,123)(100,124)(101,125)(102,126)(103,128)(104,127)(105,114)(106,113)(107,115)(108,116)(109,117)(110,118)(111,120)(112,119)(129,154)(130,153)(131,155)(132,156)(133,157)(134,158)(135,160)(136,159)(137,146)(138,145)(139,147)(140,148)(141,149)(142,150)(143,152)(144,151)(161,186)(162,185)(163,187)(164,188)(165,189)(166,190)(167,192)(168,191)(169,178)(170,177)(171,179)(172,180)(173,181)(174,182)(175,184)(176,183); s1 := Sym(192)!( 1, 97)( 2, 98)( 3, 99)( 4,100)( 5,103)( 6,104)( 7,101)( 8,102)( 9,108)( 10,107)( 11,106)( 12,105)( 13,110)( 14,109)( 15,112)( 16,111)( 17,128)( 18,127)( 19,126)( 20,125)( 21,122)( 22,121)( 23,124)( 24,123)( 25,118)( 26,117)( 27,120)( 28,119)( 29,116)( 30,115)( 31,114)( 32,113)( 33,161)( 34,162)( 35,163)( 36,164)( 37,167)( 38,168)( 39,165)( 40,166)( 41,172)( 42,171)( 43,170)( 44,169)( 45,174)( 46,173)( 47,176)( 48,175)( 49,192)( 50,191)( 51,190)( 52,189)( 53,186)( 54,185)( 55,188)( 56,187)( 57,182)( 58,181)( 59,184)( 60,183)( 61,180)( 62,179)( 63,178)( 64,177)( 65,129)( 66,130)( 67,131)( 68,132)( 69,135)( 70,136)( 71,133)( 72,134)( 73,140)( 74,139)( 75,138)( 76,137)( 77,142)( 78,141)( 79,144)( 80,143)( 81,160)( 82,159)( 83,158)( 84,157)( 85,154)( 86,153)( 87,156)( 88,155)( 89,150)( 90,149)( 91,152)( 92,151)( 93,148)( 94,147)( 95,146)( 96,145); s2 := Sym(192)!( 1, 65)( 2, 66)( 3, 69)( 4, 70)( 5, 67)( 6, 68)( 7, 71)( 8, 72)( 9, 81)( 10, 82)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 87)( 16, 88)( 17, 73)( 18, 74)( 19, 77)( 20, 78)( 21, 75)( 22, 76)( 23, 79)( 24, 80)( 25, 89)( 26, 90)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 95)( 32, 96)( 35, 37)( 36, 38)( 41, 49)( 42, 50)( 43, 53)( 44, 54)( 45, 51)( 46, 52)( 47, 55)( 48, 56)( 59, 61)( 60, 62)( 97,161)( 98,162)( 99,165)(100,166)(101,163)(102,164)(103,167)(104,168)(105,177)(106,178)(107,181)(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)(115,173)(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)(123,189)(124,190)(125,187)(126,188)(127,191)(128,192)(131,133)(132,134)(137,145)(138,146)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(155,157)(156,158); 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, 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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;
References
None.
to this polytope.