The Gr\"unbaum--Dress Polyhedra

Regular polyhedra have been investigated since antiquity. In ordinary euclidean 3-space, the class of regular polyhedra has been considerably extended to what are now called the Gr\"unbaum--Dress polyhedra. The talk presents a new approach to these polyhedra, which also leads to a quicker proof of the completeness of the enumeration than that found by Dress. Presentations of their symmetry groups will also be discussed. This is joint work with Peter McMullen.