Zsolt Lángi:
Characterization of affinely regular polygons

Coxeter proved in 1943 that if p_1, p_2, ... p_n are vertices of a
convex polygon, and there is a real number t>1 such that p_{j+2}-p_{j-1}= t
(p_{j+1}-p_j) for every value of the index j, then the polygon is affinely
regular. In this talk we prove a generalization of this statement. We apply
our method to characterize symmetric realizations of polytopes of certain
combinatorial types.