Overview
- Group
- SmallGroup(1728,46587)
- Rank
- 4
- Schläfli Type
- {12,4,4}
- Vertices, edges, …
- 12, 108, 36, 18
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{12,4|2},{4,4}6}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
12-fold
18-fold
36-fold
54-fold
72-fold
108-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*s2)^2> of order 2
10 facets
- 2 of {12,2}*48
- 8 of {12,4}*96a
12 vertex figures
- 12 of 2-fold non-regular quotient of {4,4}*144
P/N, where N=<(s1*s2*s3*s2)^2> of order 3
6 facets
- 6 of {12,4}*96a
12 vertex figures
- 12 of 3-fold non-regular quotient of {4,4}*144
P/N, where N=<(s1*s2)^2, (s1*s2*s3*s2)^2> of order 6
4 facets
- 2 of {12,2}*48
- 2 of {12,4}*96a
12 vertex figures
- 12 of 6-fold non-regular quotient of {4,4}*144
Representations
Permutation Representation (GAP)
s0 := ( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64,100)( 65,101)( 66,102)( 67,103)( 68,104)( 69,105)( 70,106)( 71,107)( 72,108)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99);; s1 := ( 1, 64)( 2, 71)( 3, 69)( 4, 70)( 5, 68)( 6, 66)( 7, 67)( 8, 65)( 9, 72)( 10, 55)( 11, 62)( 12, 60)( 13, 61)( 14, 59)( 15, 57)( 16, 58)( 17, 56)( 18, 63)( 19, 73)( 20, 80)( 21, 78)( 22, 79)( 23, 77)( 24, 75)( 25, 76)( 26, 74)( 27, 81)( 28, 91)( 29, 98)( 30, 96)( 31, 97)( 32, 95)( 33, 93)( 34, 94)( 35, 92)( 36, 99)( 37, 82)( 38, 89)( 39, 87)( 40, 88)( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46,100)( 47,107)( 48,105)( 49,106)( 50,104)( 51,102)( 52,103)( 53,101)( 54,108);; s2 := ( 4, 9)( 5, 7)( 6, 8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 40, 45)( 41, 43)( 42, 44)( 49, 54)( 50, 52)( 51, 53)( 58, 63)( 59, 61)( 60, 62)( 67, 72)( 68, 70)( 69, 71)( 76, 81)( 77, 79)( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)(103,108)(104,106)(105,107);; s3 := ( 1, 5)( 2, 7)( 4, 8)( 10, 14)( 11, 16)( 13, 17)( 19, 23)( 20, 25)( 22, 26)( 28, 32)( 29, 34)( 31, 35)( 37, 41)( 38, 43)( 40, 44)( 46, 50)( 47, 52)( 49, 53)( 55, 59)( 56, 61)( 58, 62)( 64, 68)( 65, 70)( 67, 71)( 73, 77)( 74, 79)( 76, 80)( 82, 86)( 83, 88)( 85, 89)( 91, 95)( 92, 97)( 94, 98)(100,104)(101,106)(103,107);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
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(108)!( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64,100)( 65,101)( 66,102)( 67,103)( 68,104)( 69,105)( 70,106)( 71,107)( 72,108)( 73, 91)( 74, 92)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99); s1 := Sym(108)!( 1, 64)( 2, 71)( 3, 69)( 4, 70)( 5, 68)( 6, 66)( 7, 67)( 8, 65)( 9, 72)( 10, 55)( 11, 62)( 12, 60)( 13, 61)( 14, 59)( 15, 57)( 16, 58)( 17, 56)( 18, 63)( 19, 73)( 20, 80)( 21, 78)( 22, 79)( 23, 77)( 24, 75)( 25, 76)( 26, 74)( 27, 81)( 28, 91)( 29, 98)( 30, 96)( 31, 97)( 32, 95)( 33, 93)( 34, 94)( 35, 92)( 36, 99)( 37, 82)( 38, 89)( 39, 87)( 40, 88)( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46,100)( 47,107)( 48,105)( 49,106)( 50,104)( 51,102)( 52,103)( 53,101)( 54,108); s2 := Sym(108)!( 4, 9)( 5, 7)( 6, 8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 40, 45)( 41, 43)( 42, 44)( 49, 54)( 50, 52)( 51, 53)( 58, 63)( 59, 61)( 60, 62)( 67, 72)( 68, 70)( 69, 71)( 76, 81)( 77, 79)( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)(103,108)(104,106)(105,107); s3 := Sym(108)!( 1, 5)( 2, 7)( 4, 8)( 10, 14)( 11, 16)( 13, 17)( 19, 23)( 20, 25)( 22, 26)( 28, 32)( 29, 34)( 31, 35)( 37, 41)( 38, 43)( 40, 44)( 46, 50)( 47, 52)( 49, 53)( 55, 59)( 56, 61)( 58, 62)( 64, 68)( 65, 70)( 67, 71)( 73, 77)( 74, 79)( 76, 80)( 82, 86)( 83, 88)( 85, 89)( 91, 95)( 92, 97)( 94, 98)(100,104)(101,106)(103,107); poly := sub<Sym(108)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 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.