Overview
- Group
- SmallGroup(576,8355)
- Rank
- 3
- Schläfli Type
- {6,12}
- Vertices, edges, …
- 24, 144, 48
- Order of s0s1s2
- 12
- 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
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
2-fold
3-fold
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*s2*s1*s0*(s2*s1)^2*s2> of order 2
24 facets
- 24 of {6}*12
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^3> of order 2
24 facets
- 24 of {6}*12
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^3*s1> of order 2
24 facets
- 24 of {6}*12
12 vertex figures
- 12 of {12}*24
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, s0*(s1*s2)^3*s1*s0*s1*s2*s1> of order 4
12 facets
- 12 of {6}*12
6 vertex figures
- 6 of {12}*24
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2> of order 4
12 facets
- 12 of {6}*12
6 vertex figures
- 6 of {12}*24
P/N, where N=<s0*(s2*s1)^2*s0*s1*s2*s1> of order 4
12 facets
- 12 of {6}*12
6 vertex figures
- 6 of {12}*24
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)(132,140);; s1 := ( 1, 89)( 2, 90)( 3, 92)( 4, 91)( 5, 85)( 6, 86)( 7, 88)( 8, 87)( 9, 93)( 10, 94)( 11, 96)( 12, 95)( 13, 77)( 14, 78)( 15, 80)( 16, 79)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 81)( 22, 82)( 23, 84)( 24, 83)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33,105)( 34,106)( 35,108)( 36,107)( 37,125)( 38,126)( 39,128)( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)( 48,131)( 49,113)( 50,114)( 51,116)( 52,115)( 53,109)( 54,110)( 55,112)( 56,111)( 57,117)( 58,118)( 59,120)( 60,119)( 61,137)( 62,138)( 63,140)( 64,139)( 65,133)( 66,134)( 67,136)( 68,135)( 69,141)( 70,142)( 71,144)( 72,143);; s2 := ( 1, 4)( 5, 8)( 9, 12)( 13, 28)( 14, 26)( 15, 27)( 16, 25)( 17, 32)( 18, 30)( 19, 31)( 20, 29)( 21, 36)( 22, 34)( 23, 35)( 24, 33)( 37, 40)( 41, 44)( 45, 48)( 49, 64)( 50, 62)( 51, 63)( 52, 61)( 53, 68)( 54, 66)( 55, 67)( 56, 65)( 57, 72)( 58, 70)( 59, 71)( 60, 69)( 73,112)( 74,110)( 75,111)( 76,109)( 77,116)( 78,114)( 79,115)( 80,113)( 81,120)( 82,118)( 83,119)( 84,117)( 85,136)( 86,134)( 87,135)( 88,133)( 89,140)( 90,138)( 91,139)( 92,137)( 93,144)( 94,142)( 95,143)( 96,141)( 97,124)( 98,122)( 99,123)(100,121)(101,128)(102,126)(103,127)(104,125)(105,132)(106,130)(107,131)(108,129);; 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,
s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0,
s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)(132,140); s1 := Sym(144)!( 1, 89)( 2, 90)( 3, 92)( 4, 91)( 5, 85)( 6, 86)( 7, 88)( 8, 87)( 9, 93)( 10, 94)( 11, 96)( 12, 95)( 13, 77)( 14, 78)( 15, 80)( 16, 79)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 81)( 22, 82)( 23, 84)( 24, 83)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33,105)( 34,106)( 35,108)( 36,107)( 37,125)( 38,126)( 39,128)( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)( 48,131)( 49,113)( 50,114)( 51,116)( 52,115)( 53,109)( 54,110)( 55,112)( 56,111)( 57,117)( 58,118)( 59,120)( 60,119)( 61,137)( 62,138)( 63,140)( 64,139)( 65,133)( 66,134)( 67,136)( 68,135)( 69,141)( 70,142)( 71,144)( 72,143); s2 := Sym(144)!( 1, 4)( 5, 8)( 9, 12)( 13, 28)( 14, 26)( 15, 27)( 16, 25)( 17, 32)( 18, 30)( 19, 31)( 20, 29)( 21, 36)( 22, 34)( 23, 35)( 24, 33)( 37, 40)( 41, 44)( 45, 48)( 49, 64)( 50, 62)( 51, 63)( 52, 61)( 53, 68)( 54, 66)( 55, 67)( 56, 65)( 57, 72)( 58, 70)( 59, 71)( 60, 69)( 73,112)( 74,110)( 75,111)( 76,109)( 77,116)( 78,114)( 79,115)( 80,113)( 81,120)( 82,118)( 83,119)( 84,117)( 85,136)( 86,134)( 87,135)( 88,133)( 89,140)( 90,138)( 91,139)( 92,137)( 93,144)( 94,142)( 95,143)( 96,141)( 97,124)( 98,122)( 99,123)(100,121)(101,128)(102,126)(103,127)(104,125)(105,132)(106,130)(107,131)(108,129); poly := sub<Sym(144)|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, s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0, s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.