Abstract
Let M = M ( Ω ) be any triangle-free tiling of a planar polygonal region Ω with regular polygons. We prove that its face vector f ( M ) = ( f 3 , f 4 , f 5 , …) , its symmetry group S ( M ) and the tiling M itself are uniquely determined by its boundary angles code c a ( M ) = c a ( Ω ) = ( t 1 , …, t r ) , a cyclical sequence of numbers t i describing the shape of Ω .
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