February 10th, 2013

lego me

Where Math Meets Illegal Toys: Archimedan Solids with Magnetballs

All the fun toys get banned. Jarts? Awesome. Battlestar Galactica Missile Launcher (1979)? How else am I supposed to attack my brother? The latest nanny-state awesomeness casualty is magnetballs, which do bad things to your intestines if you swallow them. But if you have a functioning brainstem and don't eat the shiny neodymium magnets, you can build beautiful structures. I set myself the task of constructing all 13 of the Archimedan solids, which required a diverse variety of techniques to complete. Check it out:

01. Cuboctahedron02. Great Rhombicosidodecahedron03. Great Rhombicuboctahedron04. icosidodecahedron
05. Small Rhombicosidodecahedron06. Small Rhombicuboctahedron07. Snub Cube08. Snub Dodecahedron
09. Truncated Cube10. Truncated Dodecahedron11. Truncated Icosahedron12. Truncated Octahedron
13. Truncated Tetrahedron

Archimedan solids generally start as a convex regular polyhedron, then get truncated at each vertex. They are symmetric (the same in all orientations) but not regular (faces are not identical). Two are even chiral, with a left-handed and right-handed twisting version that are mirror images of each other. Line drawings shown here for comparison:

What should I do next?