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Heesch Numbers, Part 2: Polyforms

In the first post in this series, I introduced the concept of a shape’s Heesch number. In brief, if a shape doesn’t tile the plane, its Heesch number is a measure of the maximum number of times you can surround the shape with layers of copies of itself. (Shapes that do …

Heesch numbers, Part 1

I love tiling theory. It’s a branch of mathematics that brings together many beautiful ideas, and that offers a lot of open questions for exploration. And of course, it gives us tools to apply mathematics in the world of art and design. Normally, in my research as a computer scientist …