Regular polygonal systems

Jurij Kovič

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) = (f3, f4, f5, …), its symmetry group S(M) and the tiling M itself are uniquely determined by its boundary angles code ca(M) = ca(Ω) = (t1, …, tr), a cyclical sequence of numbers ti describing the shape of Ω.


Keywords


Regular polygonal system, boundary code, face vector, symmetry group, reconstructibility from the boundary

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DOI: https://doi.org/10.26493/1855-3974.997.7ef

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications