Overview
- Group
- SmallGroup(1728,47234)
- Rank
- 4
- Schläfli Type
- {2,12,12}
- Vertices, edges, …
- 2, 36, 216, 36
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 24)( 7, 26)( 8, 25)( 9, 18)( 10, 20)( 11, 19)( 12, 21)( 13, 23)( 14, 22)( 16, 17)( 28, 29)( 31, 32)( 33, 51)( 34, 53)( 35, 52)( 36, 45)( 37, 47)( 38, 46)( 39, 48)( 40, 50)( 41, 49)( 43, 44)( 55, 56)( 58, 59)( 60, 78)( 61, 80)( 62, 79)( 63, 72)( 64, 74)( 65, 73)( 66, 75)( 67, 77)( 68, 76)( 70, 71)( 82, 83)( 85, 86)( 87,105)( 88,107)( 89,106)( 90, 99)( 91,101)( 92,100)( 93,102)( 94,104)( 95,103)( 97, 98)(109,110);; s2 := ( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 16)( 13, 15)( 14, 17)( 18, 19)( 21, 28)( 22, 27)( 23, 29)( 24, 25)( 30, 31)( 33, 37)( 34, 36)( 35, 38)( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 55)( 49, 54)( 50, 56)( 51, 52)( 57, 85)( 58, 84)( 59, 86)( 60, 91)( 61, 90)( 62, 92)( 63, 88)( 64, 87)( 65, 89)( 66, 97)( 67, 96)( 68, 98)( 69, 94)( 70, 93)( 71, 95)( 72,100)( 73, 99)( 74,101)( 75,109)( 76,108)( 77,110)( 78,106)( 79,105)( 80,107)( 81,103)( 82,102)( 83,104);; s3 := ( 3, 69)( 4, 70)( 5, 71)( 6, 66)( 7, 67)( 8, 68)( 9, 72)( 10, 73)( 11, 74)( 12, 60)( 13, 61)( 14, 62)( 15, 57)( 16, 58)( 17, 59)( 18, 63)( 19, 64)( 20, 65)( 21, 78)( 22, 79)( 23, 80)( 24, 75)( 25, 76)( 26, 77)( 27, 81)( 28, 82)( 29, 83)( 30, 96)( 31, 97)( 32, 98)( 33, 93)( 34, 94)( 35, 95)( 36, 99)( 37,100)( 38,101)( 39, 87)( 40, 88)( 41, 89)( 42, 84)( 43, 85)( 44, 86)( 45, 90)( 46, 91)( 47, 92)( 48,105)( 49,106)( 50,107)( 51,102)( 52,103)( 53,104)( 54,108)( 55,109)( 56,110);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(110)!(1,2); s1 := Sym(110)!( 4, 5)( 6, 24)( 7, 26)( 8, 25)( 9, 18)( 10, 20)( 11, 19)( 12, 21)( 13, 23)( 14, 22)( 16, 17)( 28, 29)( 31, 32)( 33, 51)( 34, 53)( 35, 52)( 36, 45)( 37, 47)( 38, 46)( 39, 48)( 40, 50)( 41, 49)( 43, 44)( 55, 56)( 58, 59)( 60, 78)( 61, 80)( 62, 79)( 63, 72)( 64, 74)( 65, 73)( 66, 75)( 67, 77)( 68, 76)( 70, 71)( 82, 83)( 85, 86)( 87,105)( 88,107)( 89,106)( 90, 99)( 91,101)( 92,100)( 93,102)( 94,104)( 95,103)( 97, 98)(109,110); s2 := Sym(110)!( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 16)( 13, 15)( 14, 17)( 18, 19)( 21, 28)( 22, 27)( 23, 29)( 24, 25)( 30, 31)( 33, 37)( 34, 36)( 35, 38)( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 55)( 49, 54)( 50, 56)( 51, 52)( 57, 85)( 58, 84)( 59, 86)( 60, 91)( 61, 90)( 62, 92)( 63, 88)( 64, 87)( 65, 89)( 66, 97)( 67, 96)( 68, 98)( 69, 94)( 70, 93)( 71, 95)( 72,100)( 73, 99)( 74,101)( 75,109)( 76,108)( 77,110)( 78,106)( 79,105)( 80,107)( 81,103)( 82,102)( 83,104); s3 := Sym(110)!( 3, 69)( 4, 70)( 5, 71)( 6, 66)( 7, 67)( 8, 68)( 9, 72)( 10, 73)( 11, 74)( 12, 60)( 13, 61)( 14, 62)( 15, 57)( 16, 58)( 17, 59)( 18, 63)( 19, 64)( 20, 65)( 21, 78)( 22, 79)( 23, 80)( 24, 75)( 25, 76)( 26, 77)( 27, 81)( 28, 82)( 29, 83)( 30, 96)( 31, 97)( 32, 98)( 33, 93)( 34, 94)( 35, 95)( 36, 99)( 37,100)( 38,101)( 39, 87)( 40, 88)( 41, 89)( 42, 84)( 43, 85)( 44, 86)( 45, 90)( 46, 91)( 47, 92)( 48,105)( 49,106)( 50,107)( 51,102)( 52,103)( 53,104)( 54,108)( 55,109)( 56,110); poly := sub<Sym(110)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;