THE GENERATION AND CLASSIFICATION OF TILE-K-TRANSITIVE TILINGS OF THE EUCLIDEAN PLANE, THE SPHERE AND THE HYPERBOLIC PLANE

Algorithms based on the theory of Delaney-Dress symbols are discussed that can be used to recursively produce all possible equivariant types of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane, for any (reasonable) k is-an-element-of N. A number of results can be obtained using computer implementations of the algorithms.