Overview
- Group
- SmallGroup(192,956)
- Rank
- 3
- Schläfli Type
- {6,3}
- Vertices, edges, …
- 32, 48, 16
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 6
- Also known as
- {6,3}(4,0), {6,3}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)^2*s1*s2*s1*s0*s1> of order 2
8 facets
- 8 of {6}*12
16 vertex figures
- 16 of {3}*6
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);; s1 := ( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12);; 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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 1, 9)( 2,10)( 3,11)( 4,12); s1 := Sym(12)!( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12); 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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.