Lattice Tilings of a Plane into Polyominoes and Molecular Layers in Crystal Structures: Structural Class cm, Z = 2(m)

Abstract— Lattice tilings of a plane into polyominoes are constructed for N from 3 to 12, where N is the order of the packing space. A total of 5191 symmetrically independent lattice tilings of the plane with one polyomino in a reduced (primitive) cell are obtained, among which 122 variants belong to the structural class (SC) cm, Z = 2(m), with a rectangular conventional (centered) unit cell. Chain tilings of the plane are derived, for which both the SC and structural subclass (SSC) are identified. The results of the analysis of the lattice tilings of a plane into polyominoes are illustrated with examples of real molecular layers in crystal structures.