PUB - Publikationen an der Universität Bielefeld

Consider the d-dimensional euclidean space E-d. Two main results are pre sented: First, for any N is an element of N, the number of types of periodic equivariant tilings (T, Gamma) that have precisely N orbits of (2, 4, 6,...)-flags with respect to the symmetry group Gamma, is finite. Second, for any N is an element of N, the number of types of convex, periodic equivariant tilings (T, Gamma) that have precisely N orbits of tiles with respect to the symmetry group Gamma, is finite. The former result (and some generalizations) is proved combinatorially, using Delaney symbols, whereas the proof of the latter result is based on both geometric arguments and Delaney symbols.