Dual uniform polyhedron

The face-transitive polyhedra comprise a set of 9 regular polyhedra, two finite sets comprising 66 non-regular polyhedra, and two infinite sets: The full set are described by Wenninger, together with instructions for constructing models, in his book Dual Models.

[2] Dorman Luke's construction proceeds as follows: The line segments EF, FG, GH, HE are already drawn, as parts of the tangent lines.

The polygon EFGH is the face of the dual polyhedron that corresponds to the original vertex V. In this example, the size of the vertex figure was chosen so that its circumcircle lies on the intersphere of the cuboctahedron, which also becomes the intersphere of the dual rhombic dodecahedron.

Dorman Luke's construction can only be used when a polyhedron has such an intersphere so that the vertex figure has a circumcircle.

For instance, it can be applied to the uniform polyhedra.