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Geometry

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 …

Shad Valley 2016

In 1989 I attended Shad Valley, a one-month Canadian summer program for high school students. I spent a month living on the UBC campus. Basically it was Nerd Camp, though perhaps with a more diverse range of interests and talents than you might expect from the nerd stereotype, and with …

Woven book polyhedra

Earlier this year, at a local coffee shop, I noticed a flyer on the wall with a call for artist submissions for an upcoming show in Halton Hills. The topic of the show was Altered Books. I had never experimented with the artform of altered books before, though I had …

Hypocycloid juggling patterns

I’ve been having fun experimenting with interesting visual patterns that emerge when multiple points are moved around hypocycloids. I ended up writing a Bridges conference paper on the topic, but the animated quality of the results is so crucial that it seemed absolutely necessary to create a web page to …

A new near miss

The photo above is a paper model of a polyhedron that I just assembled. The model consists of four dodecagons (12-sided regular polygons) and 12 decagons (10-sided regular polygons). The holes are 28 equilateral triangles that in theory could be filled with more paper. This polyhedron has a few symmetries, …