Gatorade Bottle Project: From Octahedron to Cube/Hexahedron or Vice Versa, Platonic Duals
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####Gatorade Bottle Project: From Octahedron to Cube/Hexahedron or Vice Versa, Platonic Duals The Platonic octahedron is the dual of the cube (also known as hexahedron). The other way around, the cube is the dual of the octahedron. The key idea is that each face of one solid becomes a vertex of the other. That is why, in either case, we need 12 rubber bands. With a bit of imagination, the cube and the octahedron alternate going on forever. ####Starting with the Octahedron, Build a Big Cube 1. Eight (8) bottles and 8 bottom adapters 2. Twelve (12) rubber bands. ####Starting with the cube, Build a Big Octahedron 1. Six (6) Bottles and 6 bottom adapters 2. Twelve (12) rubber bands. ####References 1. https://en.wikipedia.org/wiki/Platonic_solid 2. http://demonstrations.wolfram.com/DualsOfPlatonicSolids/
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