I’ve been rereading R. Buckminster Fuller’s Synergetics thanks to a Christmas gift. Thus primed, I was amused to come across two tetrahedron-related posts on BoingBoing:
Bucky was, of course, fascinated by tetrahedra:
113.00 When we take two triangles and add one to the other to make the tetrahedron, we find that one plus one equals four. This is not just a geometrical trick; it is really the same principle that chemistry is using inasmuch as the tetrahedra represent the way that atoms cohere. Thus we discover synergy to be operative in a very important way in chemistry and in all the composition of the Universe. Universe as a whole is behaving in a way that is completely unpredicted by the behavior of any of its parts. Synergy reveals a grand strategy of dealing with the whole instead of the tactics of our conventional educational system, which starts with parts and elements, adding them together locally without really understanding the whole.
(From the online text of Synergetics.)
For more tetrahedral goodness, check out these instructions for making a model of five interlocking tetrahedra from Thomas Hull. I’ve made several of these, and they’re great fun (on the most recent, the tolerances were a bit off, so it ended up being four interlocking tetrahedra). Here’s a nice image of a completed model.
If you’re not up to modular origami, you can also try this printable PDF papercraft version of five tetrahedra as a compound solid.