Overview
- Group
- SmallGroup(1296,3490)
- Rank
- 4
- Schläfli Type
- {4,3,6}
- Vertices, edges, …
- 12, 54, 81, 27
- Order of s0s1s2s3
- 9
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Locally Toroidal
- Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);; s1 := ( 7,10)( 8,11)( 9,12);; s2 := ( 4,10)( 5,12)( 6,11);; s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11);; 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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s0*s2*s3*s2*s3*s2*s1*s0*s1*s2*s3*s2*s3*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12); s1 := Sym(12)!( 7,10)( 8,11)( 9,12); s2 := Sym(12)!( 4,10)( 5,12)( 6,11); s3 := Sym(12)!( 1, 2)( 4, 5)( 7, 8)(10,11); poly := sub<Sym(12)|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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s0*s2*s3*s2*s3*s2*s1*s0*s1*s2*s3*s2*s3*s2*s1*s0 >;
References
None.
to this polytope.