Compounding octahedron-hexahedron
Hexahedron and its pyramids
For a hexahedron, students found two possibilties:
1. You mirror the midpoint of the hexahedron an all its faces, then you get a star with fourteen vertices.
2. You spin this pyramids by 45° at the perpendicular line on the faces. mutual interpenetration
By cutting off the pyramids, you get the body as a core of this star, which is called a cuboctahedron, and that is an Archimedean solid, an its name is obviously based on its arising.