Finite Coxeter Groups

sage.categories.finite_coxeter_groups.FiniteCoxeterGroups

The category of finite Coxeter groups.

EXAMPLES:

sage: CoxeterGroups.Finite()
Category of finite coxeter groups
sage: FiniteCoxeterGroups().super_categories()
[Category of finite generalized coxeter groups,
 Category of coxeter groups]

sage: G = CoxeterGroups().Finite().example()
sage: G.cayley_graph(side = "right").plot()
Graphics object consisting of 40 graphics primitives

Here are some further examples:

sage: WeylGroups().Finite().example()
The symmetric group on {0, ..., 3}

sage: WeylGroup(["B", 3])
Weyl Group of type ['B', 3] (as a matrix group acting on the ambient space)

Those other examples will eventually be also in this category:

sage: SymmetricGroup(4)
Symmetric group of order 4! as a permutation group
sage: DihedralGroup(5)
Dihedral group of order 10 as a permutation group