Duals of Platonic Solids
The dual of a polyhedron can be constructed in several different ways. One way is to take the centers of the faces of as the vertices of . Two vertices and of are joined by an edge if the original faces and of had an edge in common. The faces of that met at a vertex become the vertices of the polygon forming a face in . Other ways to construct a dual are to rotate the original polyhedron's sides by 90°, to truncate its vertices or edges, or to stellate it.