This is easily seen by examining the construction of the dual polyhedron.

This puzzle is the dual polyhedron of the Skewb.

The octahedron is the dual polyhedron to the cube.

The dual polyhedron of the antiprisms are the trapezohedron.

For polyhedra, a birectification creates a dual polyhedron.

Every polyhedron has a dual polyhedron 'with faces and vertices interchanged'.

Its dual polyhedron is the rhombic dodecahedron.

For every polyhedron there exists a dual polyhedron having:

The Hasse diagram of the dual polyhedron is obtained very simply, by turning the original diagram upside-down.

The polygon EFGH is a face of the dual polyhedron.

The dual polyhedron can also be listed by this notation, but prefixed by a V. See face configuration.

One can construct the dual polyhedron by taking the vertices of the dual to be the centers of the faces of the original figure.

A polyhedron which is isohedral has a dual polyhedron that is vertex-transitive (isogonal).

It is dual to the dual polyhedron's stellation diagram, which shows all the possible edges and vertices for some face plane of the original core.

If the original cube has edge length 1, its dual polyhedron (an octahedron) has edge length .

Its dual polyhedron is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids.

In geometry, a 'pentagonal icositetrahedron' is a Catalan solid which is the Dual polyhedron of the snub cube.

The polar body of a polyhedron or polytope is its dual polyhedron or dual polytope.

Every stellation of one polyhedron is dual, or reciprocal, to some facetting of the dual polyhedron.

The octagonal trapezohedron or deltohedron is the sixth in an infinite series of face-uniform polyhedra which are dual polyhedron to the antiprisms.

A commonplace example is found in the reciprocation of a symmetrical polyhedron in a concentric sphere to obtain the dual polyhedron.

In geometry, the tridyakis icosahedron is the dual polyhedron of the nonconvex uniform polyhedron, icositruncated dodecadodecahedron.

It is the largest sphere that is contained wholly within the polyhedron, and is dual to the dual polyhedron's circumsphere.

For every stellation of some polyhedron, there is a dual facetting of the dual polyhedron, and vice versa.

For a uniform polyhedron, the face of the dual polyhedron may be found from the original polyhedron's vertex figure using the 'Dorman Luke' construction.