The boundary characteristic and Pick's theorem in the Archimedean planar tilings
Pick's theorem, giving the area of a lattice polygon by the number of lattice points on its boundary and in its interior, is generalized to certain polygons whose vertices are among the vertices of one of the 11 Archimedean tilings of the plane. For this purpose two combinatorial characteristics of the polygon are introduced in addition to its Pick number, its boundary and adjacency characteristic. The proofs mainly work by shelling appropriate dissections of the polygon.
scientific article; zbMATH DE number 4032506
scientific article