Overview
- Group
- SmallGroup(432,741)
- Rank
- 4
- Schläfli Type
- {4,6,3}
- Vertices, edges, …
- 12, 36, 27, 3
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
9-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := (4,7)(5,8)(6,9);; s1 := ( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18);; s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,16)(11,18)(12,17)(14,15);; s3 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18);; 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*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(18)!(4,7)(5,8)(6,9); s1 := Sym(18)!( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18); s2 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,16)(11,18)(12,17)(14,15); s3 := Sym(18)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18); poly := sub<Sym(18)|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*s3, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.