By George Hart for the Museum of Mathematics


I believe that in the future, 3D printing machines will commonly be used to make household parts, e.g., when you need to fix a broken appliance knob or handle. I put this into practice recently when I needed a replacement light dimmer knob and decided to make my own. So, I created this knob based on a lovely polyhedron, the rhombic enneacontahedron. It works well and looks like a little geodesic igloo on the wall.

This is a great opportunity to incorporate some mathiness around the house, so I made a second design, based on the (7,6,6) uniform tiling in the hyperbolic plane. Notice there are both 6-sided and 7-sided craters. At each corner, one 7-sided and two 6-sided craters meet.

If you have access to a 3D printer, you can make your own copies of these mathematical dimmer switches using the stl files available here. They fit right on the shafts of standard US dimmer switches.

See all of George Hart’s Math Monday columns