Overview
- Group
- SmallGroup(1728,46587)
- Rank
- 4
- Schläfli Type
- {4,4,12}
- Vertices, edges, …
- 18, 36, 108, 12
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,4}6,{4,12|2}}. 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=<(s0*s1)^2> of order 2
12 facets
- 12 of 2-fold non-regular quotient of {4,4}*144
10 vertex figures
- 8 of {4,12}*96a
- 2 of {2,12}*48
P/N, where N=<(s0*s1*s2*s1)^2> of order 3
12 facets
- 12 of 3-fold non-regular quotient of {4,4}*144
6 vertex figures
- 6 of {4,12}*96a
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2> of order 6
12 facets
- 12 of 6-fold non-regular quotient of {4,4}*144
4 vertex figures
- 2 of {4,12}*96a
- 2 of {2,12}*48
Representations
Permutation Representation (GAP)
s0 := ( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)( 48, 51)( 49, 52)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)( 67, 70)( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)( 93, 96)( 94, 97)(101,107)(102,105)(103,106);; s1 := ( 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);; s2 := ( 1, 5)( 2, 7)( 4, 8)( 10, 23)( 11, 25)( 12, 21)( 13, 26)( 14, 19)( 15, 24)( 16, 20)( 17, 22)( 18, 27)( 28, 32)( 29, 34)( 31, 35)( 37, 50)( 38, 52)( 39, 48)( 40, 53)( 41, 46)( 42, 51)( 43, 47)( 44, 49)( 45, 54)( 55, 86)( 56, 88)( 57, 84)( 58, 89)( 59, 82)( 60, 87)( 61, 83)( 62, 85)( 63, 90)( 64,104)( 65,106)( 66,102)( 67,107)( 68,100)( 69,105)( 70,101)( 71,103)( 72,108)( 73, 95)( 74, 97)( 75, 93)( 76, 98)( 77, 91)( 78, 96)( 79, 92)( 80, 94)( 81, 99);; s3 := ( 1, 64)( 2, 65)( 3, 66)( 4, 67)( 5, 68)( 6, 69)( 7, 70)( 8, 71)( 9, 72)( 10, 55)( 11, 56)( 12, 57)( 13, 58)( 14, 59)( 15, 60)( 16, 61)( 17, 62)( 18, 63)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 91)( 29, 92)( 30, 93)( 31, 94)( 32, 95)( 33, 96)( 34, 97)( 35, 98)( 36, 99)( 37, 82)( 38, 83)( 39, 84)( 40, 85)( 41, 86)( 42, 87)( 43, 88)( 44, 89)( 45, 90)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108);; 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*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)( 48, 51)( 49, 52)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)( 67, 70)( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)( 93, 96)( 94, 97)(101,107)(102,105)(103,106); s1 := 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); s2 := Sym(108)!( 1, 5)( 2, 7)( 4, 8)( 10, 23)( 11, 25)( 12, 21)( 13, 26)( 14, 19)( 15, 24)( 16, 20)( 17, 22)( 18, 27)( 28, 32)( 29, 34)( 31, 35)( 37, 50)( 38, 52)( 39, 48)( 40, 53)( 41, 46)( 42, 51)( 43, 47)( 44, 49)( 45, 54)( 55, 86)( 56, 88)( 57, 84)( 58, 89)( 59, 82)( 60, 87)( 61, 83)( 62, 85)( 63, 90)( 64,104)( 65,106)( 66,102)( 67,107)( 68,100)( 69,105)( 70,101)( 71,103)( 72,108)( 73, 95)( 74, 97)( 75, 93)( 76, 98)( 77, 91)( 78, 96)( 79, 92)( 80, 94)( 81, 99); s3 := Sym(108)!( 1, 64)( 2, 65)( 3, 66)( 4, 67)( 5, 68)( 6, 69)( 7, 70)( 8, 71)( 9, 72)( 10, 55)( 11, 56)( 12, 57)( 13, 58)( 14, 59)( 15, 60)( 16, 61)( 17, 62)( 18, 63)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 91)( 29, 92)( 30, 93)( 31, 94)( 32, 95)( 33, 96)( 34, 97)( 35, 98)( 36, 99)( 37, 82)( 38, 83)( 39, 84)( 40, 85)( 41, 86)( 42, 87)( 43, 88)( 44, 89)( 45, 90)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108); 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*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.