Octahedron in a Cube / Hexahedron

cults3d

The Dual Partnership: Octahedron in a Cube / Hexahedron Each polyhedron has a dual counterpart, where faces and vertices swap places. Only a handful can be easily demonstrated physically by fitting one into the other. The cube appears to be an exceptional case. A hexahedron (aka cube) is the dual of an octahedron, and vice versa. In this design, we have an octahedron (edge length = 42.4mm) that can slide into a cube (edge length = 60mm). It could serve as a desktop puzzle, especially when using the octahedron halves, or a math model for various purposes. Among the Files Two versions of the cube box are provided. A Platonic octahedron is included. A Platonic octahedron half, two of which form an octahedron. References http://mathworld.wolfram.com/DualPolyhedron.html https://en.wikipedia.org/wiki/Platonic_solid