Regular polygonal systems - Kovič, Jurij (Ars mathematica contemporanea, 2019)
Let ?$M = M(Ω)$? be any triangle-free tiling of a planar polygonal region 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 ?$c_{a}(M) = c_{a}(Ω) = (t_{1},t_{2},…, t_{r}$?, a cyclical sequence of numbers ?$t_{i}$?, describing the shape of ?$ (Ω)$?.
Keywords: boundary code; face vector; pravilni večkotniški sistem; reconstructibility from the boundary; regular polygonal system; rekonstruktibilnost iz roba; robna koda; simetrijska grupa; symmetry group; vektor lic