Octahedron in a Cube / Hexahedron

thingiverse

Each cube can be considered as the dual of a particular octahedron, with the faces and vertices switching places between the two polyhedrons. Very few polyhedrons have a reciprocal that can be easily shown physically by fitting one into the other, but the cube appears to be an exception. A cube is essentially the dual of an octahedron, and vice versa. In this particular design, we have a large octahedron with edges measuring 42.4mm in length that can be slid into a larger cube with edges measuring 60mm in length. This unique model can serve as a desktop puzzle, especially when using the two halves of the octahedron, or a math model for various educational purposes. Among the files included are: 1. Two versions of a cube-shaped box. 2. A Platonic octahedron with all its vertices and edges intact. 3. A Platonic octahedron that has been cut in half, providing two identical pieces that can be used to create a complete octahedron. References for this model include: 1. http://mathworld.wolfram.com/DualPolyhedron.html 2. https://en.wikipedia.org/wiki/Platonic_solid