Coxeter planes

Here are a few nice Coxeter projections of representations of finite Lie algebras. If you don't know what a Coxeter projection is, or a finite Lie algebra for that matter, have a look at my PhD thesis (from which I took these pictures). Or, visit John Stembridge's website for more information and pictures.

Update: some of these pictures do not show the full representation, but only a subset.

The orbits of the two highest dominant weights of the 1764 representation of A₅.

The orbits of the two highest dominant weights of the 5985 representation of A₁₇.

The orbits of the two highest dominant weights of the 442 representation of B₆.

The adjoint representation of B₁₉.

The adjoint representation of D₁₀.