Combinatorial Aperiodicity of Polyhedral Prototiles∗
نویسنده
چکیده
The paper studies combinatorial prototiles of locally finite face-to-face tilings of euclidean d-space Ed by convex d-polytopes. A finite set P of prototiles is called combinatorially aperiodic if P admits a locally finite face-to-face tiling by combinatorially equivalent copies of the prototiles in P, but no such tiling with a combinatorial automorphism of infinite order. The paper describes some properties of combinatorially aperiodic protosets and their tilings, and also discusses some open problems and conjectures.
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