  A shape's Heesch number is the number of layers of copies of the shape that
can be placed around it without gaps or overlaps. Experimentation and
exhaustive searching have turned up examples of shapes with finite Heesch
numbers up to six, but nothing higher. The computational problem of classifying
simple families of shapes by Heesch number can provide more experimental data
to fuel our understanding of this topic. I present a technique for computing
Heesch numbers of non-tiling polyforms using a SAT solver, and the results of
exhaustive computation of Heesch numbers up to 19-ominoes, 17-hexes, and
24-iamonds.
