Overview
- Group
- SmallGroup(192,956)
- Rank
- 3
- Schläfli Type
- {3,6}
- Vertices, edges, …
- 16, 48, 32
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 6
- Also known as
- {3,6}(4,0), {3,6}8. if this polytope has another name.
Special Properties
- Toroidal
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
4-fold
8-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
9-fold
10-fold
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*s2*s1*s0*(s2*s1)^2*s2> of order 4
8 facets
- 8 of {3}*6
4 vertex figures
- 4 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);; s1 := ( 5, 9)( 6,10)( 7,12)( 8,11);; s2 := ( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 1, 9)( 2,10)( 3,11)( 4,12); s1 := Sym(12)!( 5, 9)( 6,10)( 7,12)( 8,11); s2 := Sym(12)!( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6); poly := sub<Sym(12)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.