- Because none of the Platonic solids, except for the cube, contains obvious 90° angles, building them is a counterintuitive, mind-bending experience. Before we get to the dodecahedron, let’s warm up with something simpler: an octahedron.
- You can make this in a few minutes using 12 plastic cocktail straws and 6 squares of duct tape, laying them out as in the diagram. Circle the straws around so that point A sticks to point B. The squares of tape should bend like hinges while the straws remain straight.
- Now hinge the vertical straws so that their points C all meet together at point D. Again, keep the straws rigid, and flex the tape. Turn the structure upside down, bring points E to point F, and the result should look like photos 2 and 3. To prevent the straws from coming unstuck, you can bend the tape inward so that it sticks to itself.
- Octahedrons are a common structure on the molecular scale, and because a crystal grows by repeating itself, tiny octahedrons assemble to form big ones. Search for “crystal octahedron” on eBay, and you’ll discover that rockhounds know all about Platonic solids.
- Notice how rigid your drinking-straw octahedron is. In fact, its shape is so efficient that it can support as much as 1,000 times its own weight. This suggests how rocks and metals achieve their strength.

For more fun with Platonic solids, check out our Weekend Project on Picnic Geometry and learn how to make an icosahedron out of paper plates: http://makezine.com/go/picnic_geometry

**This project first appeared in MAKE Volume 11, page 164.**