Abstract |
k-Uniform tilings by regular polygons are tilings with k equivalence classes of vertices with respect to the symmetries of the tiling. The enumeration of all k-uniform tilings for specific values of k is a far from trivial problem. In the seminar, I will review the most important steps in the investigation of k-uniform tilings: Kepler's enumeration of the 1-uniform tilings in 1619, the rediscovery of the 1-uniform tilings by Sommerville in 1905, the complete enumeration of the k-homogeneous tilings (a set of tilings which includes the 1-uniform and 2-uniform tilings) by Krötenheerdt in 1969-1970, Chavey's enumeration of the 3-uniform tilings in 1984, and Galebach's enumeration of the 4-uniform, 5-uniform and 6-uniform tilings in 2002-2003. I will also discuss some approaches that might be used in future work on k-uniform tilings. |