I took and modified these templates so that there would be a complete nesting sequence.įor some reason, my. Materials and Toolsįor the simpler versions of either a octahedron in a cube or a cube in an octahedron use these templates from Gijs Korthals Altes' awesome site. Note from the video: Taping a hinge onto the boxes works really well for the cubes, but not as great for the octahedron since it really doesn't allow the octahedron to open correctly because the motion is impeded by the cube inside. Please enable JavaScript to watch this video. I think one of the easiest ways to really see this is to build a paper model of an octahedron nested in a cube and a cube nested in an octahedron.Īll of these boxes fit "perfectly" into the next larger box as you can see in this video. If you replace the faces of an octahedron by vertices at the center then you end up with a cube. If you replace the faces of a cube by vertices at the center then you end up with a octahedron. The cube and the octahedron are dual polyhedra of each other. If you cut the corners off a cube, you get and octahedron-and vice versa just a bit weird!" ![]() For instance, if you look at some of the drawings of Leonardo da Vinci, you will see that he recognized that the cube and octahedron are kinda opposites. ![]() "There is something cool and special about the platonic solids-there is something so simple, yet so complex about them. ![]() Imaatfal was commenting about how the cube and octahedron are related to each other. These boxes are inspired by a comment from Imaatfal Avidya on a corkboard post on Platonic polyhedra from sonobe units.
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