Overview
- Group
- SmallGroup(1872,1037)
- Rank
- 3
- Schläfli Type
- {39,6}
- Vertices, edges, …
- 156, 468, 24
- Order of s0s1s2
- 156
- 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
3-fold
4-fold
12-fold
13-fold
36-fold
39-fold
52-fold
78-fold
156-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=<s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 2
12 facets
- 12 of {39}*78
78 vertex figures
- 78 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 49)( 6, 50)( 7, 52)( 8, 51)( 9, 45)( 10, 46)( 11, 48)( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)( 67,148)( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)( 75,140)( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)( 83,132)( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)( 91,124)( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)( 99,116)(100,115)(101,109)(102,110)(103,112)(104,111);; s1 := ( 1, 57)( 2, 60)( 3, 59)( 4, 58)( 5, 53)( 6, 56)( 7, 55)( 8, 54)( 9,101)( 10,104)( 11,103)( 12,102)( 13, 97)( 14,100)( 15, 99)( 16, 98)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 81)( 30, 84)( 31, 83)( 32, 82)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 73)( 38, 76)( 39, 75)( 40, 74)( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 49, 61)( 50, 64)( 51, 63)( 52, 62)(105,109)(106,112)(107,111)(108,110)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)(127,143)(128,142)(129,137)(130,140)(131,139)(132,138)(134,136);; s2 := ( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81, 82)( 85, 86)( 89, 90)( 93, 94)( 97, 98)(101,102)(105,106)(109,110)(113,114)(117,118)(121,122)(125,126)(129,130)(133,134)(137,138)(141,142)(145,146)(149,150)(153,154);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(156)!( 3, 4)( 5, 49)( 6, 50)( 7, 52)( 8, 51)( 9, 45)( 10, 46)( 11, 48)( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)( 67,148)( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)( 75,140)( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)( 83,132)( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)( 91,124)( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)( 99,116)(100,115)(101,109)(102,110)(103,112)(104,111); s1 := Sym(156)!( 1, 57)( 2, 60)( 3, 59)( 4, 58)( 5, 53)( 6, 56)( 7, 55)( 8, 54)( 9,101)( 10,104)( 11,103)( 12,102)( 13, 97)( 14,100)( 15, 99)( 16, 98)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 81)( 30, 84)( 31, 83)( 32, 82)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 73)( 38, 76)( 39, 75)( 40, 74)( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 49, 61)( 50, 64)( 51, 63)( 52, 62)(105,109)(106,112)(107,111)(108,110)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)(120,150)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)(127,143)(128,142)(129,137)(130,140)(131,139)(132,138)(134,136); s2 := Sym(156)!( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 81, 82)( 85, 86)( 89, 90)( 93, 94)( 97, 98)(101,102)(105,106)(109,110)(113,114)(117,118)(121,122)(125,126)(129,130)(133,134)(137,138)(141,142)(145,146)(149,150)(153,154); poly := sub<Sym(156)|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*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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 >;
References
None.
to this polytope.