Abstract
The local structure of the derived tilings $$ \mathcal{T} $$ 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 $$ \mathcal{T} $$ contain stars of seven different types, and all the types are represented by stars with interior vertices from the crown Cr of the tiling $$ \mathcal{T} $$ . Also the maximum principle is established, based on which the layer-by-bayer growth algorithm for the derived tilings $$ \mathcal{T} $$ is constructed.
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