Overview
- Group
- SmallGroup(1872,1037)
- Rank
- 3
- Schläfli Type
- {6,39}
- Vertices, edges, …
- 24, 468, 156
- 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=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 2
78 facets
- 78 of {6}*12
12 vertex figures
- 12 of {39}*78
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 83, 84)( 87, 88)( 91, 92)( 95, 96)( 99,100)(103,104)(107,108)(111,112)(115,116)(119,120)(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(147,148)(151,152)(155,156);; s1 := ( 2, 4)( 5, 49)( 6, 52)( 7, 51)( 8, 50)( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 41)( 14, 44)( 15, 43)( 16, 42)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 21, 33)( 22, 36)( 23, 35)( 24, 34)( 25, 29)( 26, 32)( 27, 31)( 28, 30)( 53,105)( 54,108)( 55,107)( 56,106)( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)( 64,150)( 65,145)( 66,148)( 67,147)( 68,146)( 69,141)( 70,144)( 71,143)( 72,142)( 73,137)( 74,140)( 75,139)( 76,138)( 77,133)( 78,136)( 79,135)( 80,134)( 81,129)( 82,132)( 83,131)( 84,130)( 85,125)( 86,128)( 87,127)( 88,126)( 89,121)( 90,124)( 91,123)( 92,122)( 93,117)( 94,120)( 95,119)( 96,118)( 97,113)( 98,116)( 99,115)(100,114)(101,109)(102,112)(103,111)(104,110);; s2 := ( 1, 58)( 2, 57)( 3, 59)( 4, 60)( 5, 54)( 6, 53)( 7, 55)( 8, 56)( 9,102)( 10,101)( 11,103)( 12,104)( 13, 98)( 14, 97)( 15, 99)( 16,100)( 17, 94)( 18, 93)( 19, 95)( 20, 96)( 21, 90)( 22, 89)( 23, 91)( 24, 92)( 25, 86)( 26, 85)( 27, 87)( 28, 88)( 29, 82)( 30, 81)( 31, 83)( 32, 84)( 33, 78)( 34, 77)( 35, 79)( 36, 80)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 70)( 42, 69)( 43, 71)( 44, 72)( 45, 66)( 46, 65)( 47, 67)( 48, 68)( 49, 62)( 50, 61)( 51, 63)( 52, 64)(105,110)(106,109)(107,111)(108,112)(113,154)(114,153)(115,155)(116,156)(117,150)(118,149)(119,151)(120,152)(121,146)(122,145)(123,147)(124,148)(125,142)(126,141)(127,143)(128,144)(129,138)(130,137)(131,139)(132,140)(133,134);; 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*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*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(156)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 59, 60)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 83, 84)( 87, 88)( 91, 92)( 95, 96)( 99,100)(103,104)(107,108)(111,112)(115,116)(119,120)(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(147,148)(151,152)(155,156); s1 := Sym(156)!( 2, 4)( 5, 49)( 6, 52)( 7, 51)( 8, 50)( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 41)( 14, 44)( 15, 43)( 16, 42)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 21, 33)( 22, 36)( 23, 35)( 24, 34)( 25, 29)( 26, 32)( 27, 31)( 28, 30)( 53,105)( 54,108)( 55,107)( 56,106)( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)( 64,150)( 65,145)( 66,148)( 67,147)( 68,146)( 69,141)( 70,144)( 71,143)( 72,142)( 73,137)( 74,140)( 75,139)( 76,138)( 77,133)( 78,136)( 79,135)( 80,134)( 81,129)( 82,132)( 83,131)( 84,130)( 85,125)( 86,128)( 87,127)( 88,126)( 89,121)( 90,124)( 91,123)( 92,122)( 93,117)( 94,120)( 95,119)( 96,118)( 97,113)( 98,116)( 99,115)(100,114)(101,109)(102,112)(103,111)(104,110); s2 := Sym(156)!( 1, 58)( 2, 57)( 3, 59)( 4, 60)( 5, 54)( 6, 53)( 7, 55)( 8, 56)( 9,102)( 10,101)( 11,103)( 12,104)( 13, 98)( 14, 97)( 15, 99)( 16,100)( 17, 94)( 18, 93)( 19, 95)( 20, 96)( 21, 90)( 22, 89)( 23, 91)( 24, 92)( 25, 86)( 26, 85)( 27, 87)( 28, 88)( 29, 82)( 30, 81)( 31, 83)( 32, 84)( 33, 78)( 34, 77)( 35, 79)( 36, 80)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 70)( 42, 69)( 43, 71)( 44, 72)( 45, 66)( 46, 65)( 47, 67)( 48, 68)( 49, 62)( 50, 61)( 51, 63)( 52, 64)(105,110)(106,109)(107,111)(108,112)(113,154)(114,153)(115,155)(116,156)(117,150)(118,149)(119,151)(120,152)(121,146)(122,145)(123,147)(124,148)(125,142)(126,141)(127,143)(128,144)(129,138)(130,137)(131,139)(132,140)(133,134); 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*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*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*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.