Overview
- Group
- SmallGroup(1584,672)
- Rank
- 3
- Schläfli Type
- {44,6}
- Vertices, edges, …
- 132, 396, 18
- Order of s0s1s2
- 44
- Order of s0s1s2s1
- 6
- 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
9-fold
11-fold
18-fold
22-fold
36-fold
99-fold
198-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.
Representations
Permutation Representation (GAP)
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 34, 67)( 35, 77)( 36, 76)( 37, 75)( 38, 74)( 39, 73)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 78)( 46, 88)( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)( 56, 89)( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)(142,168)(143,167)(144,177)(145,187)(146,186)(147,185)(148,184)(149,183)(150,182)(151,181)(152,180)(153,179)(154,178)(155,188)(156,198)(157,197)(158,196)(159,195)(160,194)(161,193)(162,192)(163,191)(164,190)(165,189);; s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 90)( 46, 89)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94)( 53, 93)( 54, 92)( 55, 91)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)(100,101)(102,110)(103,109)(104,108)(105,107)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,134)(123,133)(124,143)(125,142)(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(144,189)(145,188)(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,156)(157,165)(158,164)(159,163)(160,162)(177,178)(179,187)(180,186)(181,185)(182,184);; s2 := ( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)( 8,118)( 9,119)( 10,120)( 11,121)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,122)( 24,123)( 25,124)( 26,125)( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)( 32,131)( 33,132)( 34,177)( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)( 40,183)( 41,184)( 42,185)( 43,186)( 44,187)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,188)( 57,189)( 58,190)( 59,191)( 60,192)( 61,193)( 62,194)( 63,195)( 64,196)( 65,197)( 66,198)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143)( 89,155)( 90,156)( 91,157)( 92,158)( 93,159)( 94,160)( 95,161)( 96,162)( 97,163)( 98,164)( 99,165);; 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*s2*s1*s2*s0*s1*s2*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*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*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(198)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 34, 67)( 35, 77)( 36, 76)( 37, 75)( 38, 74)( 39, 73)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 78)( 46, 88)( 47, 87)( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)( 56, 89)( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)(142,168)(143,167)(144,177)(145,187)(146,186)(147,185)(148,184)(149,183)(150,182)(151,181)(152,180)(153,179)(154,178)(155,188)(156,198)(157,197)(158,196)(159,195)(160,194)(161,193)(162,192)(163,191)(164,190)(165,189); s1 := Sym(198)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 90)( 46, 89)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94)( 53, 93)( 54, 92)( 55, 91)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 78, 79)( 80, 88)( 81, 87)( 82, 86)( 83, 85)(100,101)(102,110)(103,109)(104,108)(105,107)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,134)(123,133)(124,143)(125,142)(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(144,189)(145,188)(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,156)(157,165)(158,164)(159,163)(160,162)(177,178)(179,187)(180,186)(181,185)(182,184); s2 := Sym(198)!( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)( 8,118)( 9,119)( 10,120)( 11,121)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,122)( 24,123)( 25,124)( 26,125)( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)( 32,131)( 33,132)( 34,177)( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)( 40,183)( 41,184)( 42,185)( 43,186)( 44,187)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,188)( 57,189)( 58,190)( 59,191)( 60,192)( 61,193)( 62,194)( 63,195)( 64,196)( 65,197)( 66,198)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143)( 89,155)( 90,156)( 91,157)( 92,158)( 93,159)( 94,160)( 95,161)( 96,162)( 97,163)( 98,164)( 99,165); poly := sub<Sym(198)|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*s2*s1*s2*s0*s1*s2*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*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*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.