Overview
- Group
- SmallGroup(1728,30413)
- Rank
- 4
- Schläfli Type
- {12,12,2}
- Vertices, edges, …
- 36, 216, 36, 2
- Order of s0s1s2s3
- 4
- 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
12-fold
27-fold
54-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106);; s1 := ( 1, 2)( 4, 19)( 5, 21)( 6, 20)( 7, 12)( 8, 11)( 9, 10)( 13, 27)( 14, 26)( 15, 25)( 16, 18)( 22, 23)( 28, 29)( 31, 46)( 32, 48)( 33, 47)( 34, 39)( 35, 38)( 36, 37)( 40, 54)( 41, 53)( 42, 52)( 43, 45)( 49, 50)( 55, 83)( 56, 82)( 57, 84)( 58,100)( 59,102)( 60,101)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67,108)( 68,107)( 69,106)( 70, 99)( 71, 98)( 72, 97)( 73, 85)( 74, 87)( 75, 86)( 76,104)( 77,103)( 78,105)( 79, 96)( 80, 95)( 81, 94);; s2 := ( 1, 62)( 2, 63)( 3, 61)( 4, 58)( 5, 59)( 6, 60)( 7, 57)( 8, 55)( 9, 56)( 10, 80)( 11, 81)( 12, 79)( 13, 76)( 14, 77)( 15, 78)( 16, 75)( 17, 73)( 18, 74)( 19, 71)( 20, 72)( 21, 70)( 22, 67)( 23, 68)( 24, 69)( 25, 66)( 26, 64)( 27, 65)( 28, 89)( 29, 90)( 30, 88)( 31, 85)( 32, 86)( 33, 87)( 34, 84)( 35, 82)( 36, 83)( 37,107)( 38,108)( 39,106)( 40,103)( 41,104)( 42,105)( 43,102)( 44,100)( 45,101)( 46, 98)( 47, 99)( 48, 97)( 49, 94)( 50, 95)( 51, 96)( 52, 93)( 53, 91)( 54, 92);; s3 := (109,110);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(110)!( 2, 3)( 4, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106); s1 := Sym(110)!( 1, 2)( 4, 19)( 5, 21)( 6, 20)( 7, 12)( 8, 11)( 9, 10)( 13, 27)( 14, 26)( 15, 25)( 16, 18)( 22, 23)( 28, 29)( 31, 46)( 32, 48)( 33, 47)( 34, 39)( 35, 38)( 36, 37)( 40, 54)( 41, 53)( 42, 52)( 43, 45)( 49, 50)( 55, 83)( 56, 82)( 57, 84)( 58,100)( 59,102)( 60,101)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67,108)( 68,107)( 69,106)( 70, 99)( 71, 98)( 72, 97)( 73, 85)( 74, 87)( 75, 86)( 76,104)( 77,103)( 78,105)( 79, 96)( 80, 95)( 81, 94); s2 := Sym(110)!( 1, 62)( 2, 63)( 3, 61)( 4, 58)( 5, 59)( 6, 60)( 7, 57)( 8, 55)( 9, 56)( 10, 80)( 11, 81)( 12, 79)( 13, 76)( 14, 77)( 15, 78)( 16, 75)( 17, 73)( 18, 74)( 19, 71)( 20, 72)( 21, 70)( 22, 67)( 23, 68)( 24, 69)( 25, 66)( 26, 64)( 27, 65)( 28, 89)( 29, 90)( 30, 88)( 31, 85)( 32, 86)( 33, 87)( 34, 84)( 35, 82)( 36, 83)( 37,107)( 38,108)( 39,106)( 40,103)( 41,104)( 42,105)( 43,102)( 44,100)( 45,101)( 46, 98)( 47, 99)( 48, 97)( 49, 94)( 50, 95)( 51, 96)( 52, 93)( 53, 91)( 54, 92); s3 := Sym(110)!(109,110); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;