Regular polytopes in ordinary space

The three aims of this paper are to obtain the proof by Dress of the completeness of the enumeration of the Grunbaum-Dress polyhedra (that is, the regular apeirohedra, or apeirotopes of rank 3) in ordinary space E-3 in a quicker and more perspicuous way, to give presentations of those of their symmetry groups which are affinely irreducible, and to describe all the discrete regular apeirotopes of rank 4 in E-3. The paper gives a complete classification of the discrete regular polytopes in ordinary space.