Overview
- Group
- SmallGroup(768,1088585)
- Rank
- 3
- Schläfli Type
- {16,6}
- Vertices, edges, …
- 64, 192, 24
- Order of s0s1s2
- 48
- 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*(s2*s1)^2*s0*(s1*s2)^2> of order 2
12 facets
- 12 of {16}*32
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 2
12 facets
- 12 of {16}*32
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s1)^4*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 2
12 facets
- 12 of {16}*32
32 vertex figures
- 32 of {6}*12
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 4
6 facets
- 6 of {16}*32
16 vertex figures
- 16 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*s1)^6*s0*s2*s1*s0*s1*s2> of order 4
6 facets
- 6 of {16}*32
16 vertex figures
- 16 of {6}*12
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, 40)( 26, 39)( 27, 38)( 28, 37)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 80)( 54, 79)( 55, 78)( 56, 77)( 57, 84)( 58, 83)( 59, 82)( 60, 81)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 96)( 70, 95)( 71, 94)( 72, 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)(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)(128,185)(129,192)(130,191)(131,190)(132,189)(133,172)(134,171)(135,170)(136,169)(137,176)(138,175)(139,174)(140,173)(141,180)(142,179)(143,178)(144,177);; s1 := ( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,105)( 6,106)( 7,108)( 8,107)( 9,101)( 10,102)( 11,104)( 12,103)( 13,109)( 14,110)( 15,112)( 16,111)( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)( 24,115)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,169)( 50,170)( 51,172)( 52,171)( 53,177)( 54,178)( 55,180)( 56,179)( 57,173)( 58,174)( 59,176)( 60,175)( 61,181)( 62,182)( 63,184)( 64,183)( 65,189)( 66,190)( 67,192)( 68,191)( 69,185)( 70,186)( 71,188)( 72,187)( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)( 80,155)( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)( 88,159)( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)( 96,163);; 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)( 97,105)( 98,107)( 99,106)(100,108)(102,103)(109,117)(110,119)(111,118)(112,120)(114,115)(121,129)(122,131)(123,130)(124,132)(126,127)(133,141)(134,143)(135,142)(136,144)(138,139)(145,153)(146,155)(147,154)(148,156)(150,151)(157,165)(158,167)(159,166)(160,168)(162,163)(169,177)(170,179)(171,178)(172,180)(174,175)(181,189)(182,191)(183,190)(184,192)(186,187);; 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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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, 40)( 26, 39)( 27, 38)( 28, 37)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 80)( 54, 79)( 55, 78)( 56, 77)( 57, 84)( 58, 83)( 59, 82)( 60, 81)( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 96)( 70, 95)( 71, 94)( 72, 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)(121,184)(122,183)(123,182)(124,181)(125,188)(126,187)(127,186)(128,185)(129,192)(130,191)(131,190)(132,189)(133,172)(134,171)(135,170)(136,169)(137,176)(138,175)(139,174)(140,173)(141,180)(142,179)(143,178)(144,177); s1 := Sym(192)!( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,105)( 6,106)( 7,108)( 8,107)( 9,101)( 10,102)( 11,104)( 12,103)( 13,109)( 14,110)( 15,112)( 16,111)( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)( 24,115)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,169)( 50,170)( 51,172)( 52,171)( 53,177)( 54,178)( 55,180)( 56,179)( 57,173)( 58,174)( 59,176)( 60,175)( 61,181)( 62,182)( 63,184)( 64,183)( 65,189)( 66,190)( 67,192)( 68,191)( 69,185)( 70,186)( 71,188)( 72,187)( 73,145)( 74,146)( 75,148)( 76,147)( 77,153)( 78,154)( 79,156)( 80,155)( 81,149)( 82,150)( 83,152)( 84,151)( 85,157)( 86,158)( 87,160)( 88,159)( 89,165)( 90,166)( 91,168)( 92,167)( 93,161)( 94,162)( 95,164)( 96,163); 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)( 97,105)( 98,107)( 99,106)(100,108)(102,103)(109,117)(110,119)(111,118)(112,120)(114,115)(121,129)(122,131)(123,130)(124,132)(126,127)(133,141)(134,143)(135,142)(136,144)(138,139)(145,153)(146,155)(147,154)(148,156)(150,151)(157,165)(158,167)(159,166)(160,168)(162,163)(169,177)(170,179)(171,178)(172,180)(174,175)(181,189)(182,191)(183,190)(184,192)(186,187); 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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.