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