One of my favorite doodle games

involves drawing a polyhedron, and then progressively truncating it, taking it’s dual, or performing some other simple operation to come up with other polyhedra.


In the image sequence below, I started by drawing an icosahedron. By finding the midpoints of each edge segment, I was able to truncate it and create an icosidodecahedron.* I performed the same operation again to form the next shape in the sequence. The shape after that was formed by taking the dual of the previous shape. You can easily draw the dual polyhedron by finding the middle of the faces of your previous polyhedron, and using those points as the vertices of your new polyhedron.
If you have paper with pretty good translucency, you can create each new polyhedron on a new sheet. Of course, you can also overlay them on a single image.
You can use this strategy to create a flipbook that starts with a cube and slowly truncates it and morphs it into an octahedron.
*This is a full truncation. It is, of course, possible, to divide the edges up differently to partially truncate your shape.

Chopstick wrappers

Seem to exist just to give you something convenient to fold while waiting for your meal. Here are some of my recent chopstick wrapper folds – a heptagon, a trihexaflexagon, an octahedron, and the “hand holding chopsticks”.


The Gathering for Gardner 10

was held at the end of March 2012. I had a really great time there, and, in addition to meeting lots of amazing people, learning a bunch of cool things, and seeing some astounding close up magic, also had the opportunity to put together a bunch of fun sculptures. Here are the three biggest projects that I contributed to.

This slide-together is my own design, based off of a pentagonal hexecontahedron. Zachary Abel and Brett Wines helped with construction.
Gathering For Gardner - 01
This pen and rubber band structure, dubbed the “Ritz Icosidodecarlton” was a joint project with Zachary Abel, Lucas Garron, Brett Wines, Alex Fink, and Sai. Vi Hart also supplied some artistic input.
2012-03-30 16.00.22
Finally, this giant rubber band structure with the balloons (based off of a snub cube with “tendrils”) was designed by Zachary Abel and put together by a large group people (I didn’t all the names).