Symmetries and color symmetries of a family of tilings with a singular point

Abstract

Abstract. We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on colorings of regular tilings arising from sublattice colorings of the centers of its tiles. In addition, we determine conditions so that the coloring of a tiling with singularity that is obtained in this manner is perfect.

Tilings with Singularity and Spiral Tilings Obtained from Archimedean Tilings

“…A singular point of a plane tiling is a point in the plane where every circular disk about meets infinitely many tiles of the tiling. Tilings with a singular point were obtained in [1] by applying the conformal map…”