Planar tilings by polyominoes, polyhexes, and polyiamonds

摘要

Using computer programs, we enumerate and classify the tiling behavior of small polyominoes (n⩽9), polyhexes (n⩽7), and polyiamonds (n⩽10). For tiles that tile the Euclidean plane, we give diagrams illustrating how they tile. We also show several larger tiles whose minimal fundamental domain in any admitted (periodic) tiling is significantly larger than for any previously known tile.