Overview
- Group
- SmallGroup(768,1088585)
- Rank
- 3
- Schläfli Type
- {6,48}
- Vertices, edges, …
- 8, 192, 64
- Order of s0s1s2
- 16
- Order of s0s1s2s1
- 6
- 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
96-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191);; s1 := ( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 73)( 58, 75)( 59, 74)( 60, 76)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 65, 89)( 66, 91)( 67, 90)( 68, 92)( 69, 85)( 70, 87)( 71, 86)( 72, 88)( 97,153)( 98,155)( 99,154)(100,156)(101,149)(102,151)(103,150)(104,152)(105,145)(106,147)(107,146)(108,148)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,189)(122,191)(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)(129,181)(130,183)(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)(137,173)(138,175)(139,174)(140,176)(141,169)(142,171)(143,170)(144,172);; s2 := ( 1, 98)( 2, 97)( 3, 99)( 4,100)( 5,106)( 6,105)( 7,107)( 8,108)( 9,102)( 10,101)( 11,103)( 12,104)( 13,110)( 14,109)( 15,111)( 16,112)( 17,118)( 18,117)( 19,119)( 20,120)( 21,114)( 22,113)( 23,115)( 24,116)( 25,134)( 26,133)( 27,135)( 28,136)( 29,142)( 30,141)( 31,143)( 32,144)( 33,138)( 34,137)( 35,139)( 36,140)( 37,122)( 38,121)( 39,123)( 40,124)( 41,130)( 42,129)( 43,131)( 44,132)( 45,126)( 46,125)( 47,127)( 48,128)( 49,170)( 50,169)( 51,171)( 52,172)( 53,178)( 54,177)( 55,179)( 56,180)( 57,174)( 58,173)( 59,175)( 60,176)( 61,182)( 62,181)( 63,183)( 64,184)( 65,190)( 66,189)( 67,191)( 68,192)( 69,186)( 70,185)( 71,187)( 72,188)( 73,146)( 74,145)( 75,147)( 76,148)( 77,154)( 78,153)( 79,155)( 80,156)( 81,150)( 82,149)( 83,151)( 84,152)( 85,158)( 86,157)( 87,159)( 88,160)( 89,166)( 90,165)( 91,167)( 92,168)( 93,162)( 94,161)( 95,163)( 96,164);; 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*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(192)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191); s1 := Sym(192)!( 1, 9)( 2, 11)( 3, 10)( 4, 12)( 6, 7)( 13, 21)( 14, 23)( 15, 22)( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 73)( 58, 75)( 59, 74)( 60, 76)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 65, 89)( 66, 91)( 67, 90)( 68, 92)( 69, 85)( 70, 87)( 71, 86)( 72, 88)( 97,153)( 98,155)( 99,154)(100,156)(101,149)(102,151)(103,150)(104,152)(105,145)(106,147)(107,146)(108,148)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,189)(122,191)(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)(129,181)(130,183)(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)(137,173)(138,175)(139,174)(140,176)(141,169)(142,171)(143,170)(144,172); s2 := Sym(192)!( 1, 98)( 2, 97)( 3, 99)( 4,100)( 5,106)( 6,105)( 7,107)( 8,108)( 9,102)( 10,101)( 11,103)( 12,104)( 13,110)( 14,109)( 15,111)( 16,112)( 17,118)( 18,117)( 19,119)( 20,120)( 21,114)( 22,113)( 23,115)( 24,116)( 25,134)( 26,133)( 27,135)( 28,136)( 29,142)( 30,141)( 31,143)( 32,144)( 33,138)( 34,137)( 35,139)( 36,140)( 37,122)( 38,121)( 39,123)( 40,124)( 41,130)( 42,129)( 43,131)( 44,132)( 45,126)( 46,125)( 47,127)( 48,128)( 49,170)( 50,169)( 51,171)( 52,172)( 53,178)( 54,177)( 55,179)( 56,180)( 57,174)( 58,173)( 59,175)( 60,176)( 61,182)( 62,181)( 63,183)( 64,184)( 65,190)( 66,189)( 67,191)( 68,192)( 69,186)( 70,185)( 71,187)( 72,188)( 73,146)( 74,145)( 75,147)( 76,148)( 77,154)( 78,153)( 79,155)( 80,156)( 81,150)( 82,149)( 83,151)( 84,152)( 85,158)( 86,157)( 87,159)( 88,160)( 89,166)( 90,165)( 91,167)( 92,168)( 93,162)( 94,161)( 95,163)( 96,164); 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*s0*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.