The following articles are a selection of those recently accepted for publication in Acta Crystallographica Section A: Foundations and Advances.
Faces of root polytopes in all dimensions
A root system of a finite reflection group W is a finite set of vectors of the n-dimensional real Euclidean space . It is invariant with respect to W. As long as the reflection group can be specified by a connected Coxeter–Dynkin diagram, it consists of either one orbit of W [root systems of types An (1 ≤ n < ∞), Dn (4 ≤ n < ∞), E6, E7, E8, H2, H3, H4] or of two orbits of W [root systems of types Bn (3 ≤ n < ∞), Cn (2 ≤ n < ∞), F4, G2]. An individual orbit is viewed as the set of vertices of a polytope generated by its W from any one point of the orbit.