Overview
- Group
- SmallGroup(1512,485)
- Rank
- 3
- Schläfli Type
- {42,18}
- Vertices, edges, …
- 42, 378, 18
- Order of s0s1s2
- 126
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
7-fold
9-fold
14-fold
21-fold
27-fold
42-fold
54-fold
63-fold
126-fold
189-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 := ( 4, 19)( 5, 20)( 6, 21)( 7, 16)( 8, 17)( 9, 18)( 10, 13)( 11, 14)( 12, 15)( 22, 43)( 23, 44)( 24, 45)( 25, 61)( 26, 62)( 27, 63)( 28, 58)( 29, 59)( 30, 60)( 31, 55)( 32, 56)( 33, 57)( 34, 52)( 35, 53)( 36, 54)( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 67, 82)( 68, 83)( 69, 84)( 70, 79)( 71, 80)( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 85,106)( 86,107)( 87,108)( 88,124)( 89,125)( 90,126)( 91,121)( 92,122)( 93,123)( 94,118)( 95,119)( 96,120)( 97,115)( 98,116)( 99,117)(100,112)(101,113)(102,114)(103,109)(104,110)(105,111)(130,145)(131,146)(132,147)(133,142)(134,143)(135,144)(136,139)(137,140)(138,141)(148,169)(149,170)(150,171)(151,187)(152,188)(153,189)(154,184)(155,185)(156,186)(157,181)(158,182)(159,183)(160,178)(161,179)(162,180)(163,175)(164,176)(165,177)(166,172)(167,173)(168,174);; s1 := ( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)( 8, 42)( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 64,152)( 65,151)( 66,153)( 67,149)( 68,148)( 69,150)( 70,167)( 71,166)( 72,168)( 73,164)( 74,163)( 75,165)( 76,161)( 77,160)( 78,162)( 79,158)( 80,157)( 81,159)( 82,155)( 83,154)( 84,156)( 85,131)( 86,130)( 87,132)( 88,128)( 89,127)( 90,129)( 91,146)( 92,145)( 93,147)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,137)(101,136)(102,138)(103,134)(104,133)(105,135)(106,173)(107,172)(108,174)(109,170)(110,169)(111,171)(112,188)(113,187)(114,189)(115,185)(116,184)(117,186)(118,182)(119,181)(120,183)(121,179)(122,178)(123,180)(124,176)(125,175)(126,177);; s2 := ( 1, 64)( 2, 66)( 3, 65)( 4, 67)( 5, 69)( 6, 68)( 7, 70)( 8, 72)( 9, 71)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)( 16, 79)( 17, 81)( 18, 80)( 19, 82)( 20, 84)( 21, 83)( 22,106)( 23,108)( 24,107)( 25,109)( 26,111)( 27,110)( 28,112)( 29,114)( 30,113)( 31,115)( 32,117)( 33,116)( 34,118)( 35,120)( 36,119)( 37,121)( 38,123)( 39,122)( 40,124)( 41,126)( 42,125)( 43, 85)( 44, 87)( 45, 86)( 46, 88)( 47, 90)( 48, 89)( 49, 91)( 50, 93)( 51, 92)( 52, 94)( 53, 96)( 54, 95)( 55, 97)( 56, 99)( 57, 98)( 58,100)( 59,102)( 60,101)( 61,103)( 62,105)( 63,104)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)(145,146)(148,170)(149,169)(150,171)(151,173)(152,172)(153,174)(154,176)(155,175)(156,177)(157,179)(158,178)(159,180)(160,182)(161,181)(162,183)(163,185)(164,184)(165,186)(166,188)(167,187)(168,189);; 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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(189)!( 4, 19)( 5, 20)( 6, 21)( 7, 16)( 8, 17)( 9, 18)( 10, 13)( 11, 14)( 12, 15)( 22, 43)( 23, 44)( 24, 45)( 25, 61)( 26, 62)( 27, 63)( 28, 58)( 29, 59)( 30, 60)( 31, 55)( 32, 56)( 33, 57)( 34, 52)( 35, 53)( 36, 54)( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 67, 82)( 68, 83)( 69, 84)( 70, 79)( 71, 80)( 72, 81)( 73, 76)( 74, 77)( 75, 78)( 85,106)( 86,107)( 87,108)( 88,124)( 89,125)( 90,126)( 91,121)( 92,122)( 93,123)( 94,118)( 95,119)( 96,120)( 97,115)( 98,116)( 99,117)(100,112)(101,113)(102,114)(103,109)(104,110)(105,111)(130,145)(131,146)(132,147)(133,142)(134,143)(135,144)(136,139)(137,140)(138,141)(148,169)(149,170)(150,171)(151,187)(152,188)(153,189)(154,184)(155,185)(156,186)(157,181)(158,182)(159,183)(160,178)(161,179)(162,180)(163,175)(164,176)(165,177)(166,172)(167,173)(168,174); s1 := Sym(189)!( 1, 25)( 2, 27)( 3, 26)( 4, 22)( 5, 24)( 6, 23)( 7, 40)( 8, 42)( 9, 41)( 10, 37)( 11, 39)( 12, 38)( 13, 34)( 14, 36)( 15, 35)( 16, 31)( 17, 33)( 18, 32)( 19, 28)( 20, 30)( 21, 29)( 43, 46)( 44, 48)( 45, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 64,152)( 65,151)( 66,153)( 67,149)( 68,148)( 69,150)( 70,167)( 71,166)( 72,168)( 73,164)( 74,163)( 75,165)( 76,161)( 77,160)( 78,162)( 79,158)( 80,157)( 81,159)( 82,155)( 83,154)( 84,156)( 85,131)( 86,130)( 87,132)( 88,128)( 89,127)( 90,129)( 91,146)( 92,145)( 93,147)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,137)(101,136)(102,138)(103,134)(104,133)(105,135)(106,173)(107,172)(108,174)(109,170)(110,169)(111,171)(112,188)(113,187)(114,189)(115,185)(116,184)(117,186)(118,182)(119,181)(120,183)(121,179)(122,178)(123,180)(124,176)(125,175)(126,177); s2 := Sym(189)!( 1, 64)( 2, 66)( 3, 65)( 4, 67)( 5, 69)( 6, 68)( 7, 70)( 8, 72)( 9, 71)( 10, 73)( 11, 75)( 12, 74)( 13, 76)( 14, 78)( 15, 77)( 16, 79)( 17, 81)( 18, 80)( 19, 82)( 20, 84)( 21, 83)( 22,106)( 23,108)( 24,107)( 25,109)( 26,111)( 27,110)( 28,112)( 29,114)( 30,113)( 31,115)( 32,117)( 33,116)( 34,118)( 35,120)( 36,119)( 37,121)( 38,123)( 39,122)( 40,124)( 41,126)( 42,125)( 43, 85)( 44, 87)( 45, 86)( 46, 88)( 47, 90)( 48, 89)( 49, 91)( 50, 93)( 51, 92)( 52, 94)( 53, 96)( 54, 95)( 55, 97)( 56, 99)( 57, 98)( 58,100)( 59,102)( 60,101)( 61,103)( 62,105)( 63,104)(127,128)(130,131)(133,134)(136,137)(139,140)(142,143)(145,146)(148,170)(149,169)(150,171)(151,173)(152,172)(153,174)(154,176)(155,175)(156,177)(157,179)(158,178)(159,180)(160,182)(161,181)(162,183)(163,185)(164,184)(165,186)(166,188)(167,187)(168,189); poly := sub<Sym(189)|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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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.