A Local Algorithm for Constructing Derived Tilings of the Two-Dimensional Torus.

The local structure of the derived tilings T of the two-dimensional torus 𝕋2 is studied. The polygonal types of stars in these tilings are classified. It is proved that in the nondegenerate case, the tilings T contain stars of seven different types, and all the types are represented by stars with interior vertices from the crown Cr of the tiling T . Also the maximum principle is established, based on which the layer-by-bayer growth algorithm for the derived tilings T is constructed. [ABSTRACT FROM AUTHOR]