Recognizability of Polyhexes by Tiling and Wang Systems

The polyhexes are the hexagonal polyominoes on the honeycomb lattice. In this paper we define various types of polyhexes and show that various classes of column (row) polyhexes can be naturally represented as two dimensional words of tiling recognizable languages. We prove the recognizability of polyhexes through Wang tiles and obtain the result that the classes of polyhexes recognized by hexagonal tiling and hexagonal Wang tiles are equivalent.