  This paper considers Platonic solids/polytopes in the real Euclidean space
R^n of dimension 3 <= n < infinity. The Platonic solids/polytopes are described
together with their faces of dimensions 0 <= d <= n-1. Dual pairs of Platonic
polytopes are considered in parallel. The underlying finite Coxeter groups are
those of simple Lie algebras of types An, Bn, Cn, F4 and of
non-crystallographic Coxeter groups H3, H4. Our method consists in recursively
decorating the appropriate Coxeter-Dynkin diagram. Each recursion step provides
the essential information about faces of a specific dimension. If, at each
recursion step, all of the faces are in the same Coxeter group orbit, i.e. are
identical, the solid is called Platonic.
