Polyominoes and Polyiamonds as Fundamental Domains for Isohedral Tilings of Crystal Class D2

Abstract

We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have pmm, pmg, pgg or cmm symmetry [1]. These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups [2]. We display the algorithms’ output and give enumeration tables for small values of n. This work is a continuation of our earlier works for the symmetry groups p3, p31m, p3m1, p4, p4g, p4m, p6, and p6m [3–5].

Keywords

• polyominoes
• polyiamonds
• isohedral tilings
• two-dimensional symmetry groups
• fundamental domains