We describe a representation for periodic tilings of the plane by regular polygons. Our
approach is to represent explicitly a small subset of seed vertices from which we systematically generate all elements of the tiling by translations. We represent a tiling concretely
by a (2+n)×4 integer matrix containing lattice coordinates for two translation vectors
and n seed vertices. We discuss several properties of this representation and describe
how to exploit the representation elegantly and efficiently for reconstruction, rendering,
and automatic crystallographic classification by symmetry detection
