Duals of Platonic Solids

The dual

D

of a polyhedron

P

can be constructed in several different ways. One way is to take the centers of the faces of

P

as the vertices of

D

. Two vertices

u

and

v

of

D

are joined by an edge if the original faces

U

and

V

of

P

had an edge in common. The faces of

P

that met at a vertex

W

become the vertices of the polygon forming a face

w

in

D

. 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.