The canonical form of a polyhedron (when it exists) can be used to generate the polyhedron's dual using an algorithm like the following:

1. Translate the polyhedron if necessary so that its canonical center (the center of its edge-tangent sphere) is at the origin.
2. Compute the polyhedron's edge tangency radius (the radius of the edge-tangent sphere).
3. For each face of the polyhedron, create a vertex of the dual polyhedron using the following steps:
   • For each edge of the face, compute its closest point to the origin.
   • Compute the circumcenter of all such closest points (easy because all points will lie on a circle).
   • Project this circumcenter away from the origin to a distance equal to the edge tangency radius squared divided by the face's origin distance.
4. Create edges of the dual polyhedron in a one-to-one correspondence with the edges of the original polyhedron: Each edge of the original polyhedron separates two faces. Take the vertices of the dual polyhedron created from those two faces and connect them with an edge of the dual polyhedron.

When this algorithm is applied to a chiral self-dual polyhedron, there are two possibilities: Either the resulting dual polyhedron is an identical copy of the original polyhedron (only rotated), or it is an opposite-handed version of the original polyhedron. In most cases, the dual is identical to the original. In a small percentage of the cases, however, the dual is the opposite-handed version. An appropriate name for these opposite-hand-pairing chiral self-dual polyhedra is "improper" because of the similarity to improper rotations: The opposite-handed dual cannot be brought into identity alignment with the original using rotations alone. A reflection is necessary.

The following table shows the counts of all chiral self-dual polyhedra with up to 16 faces, cross tabulated by number of faces and symmetry type. Each count is shown as a fraction, where the numerator represents the number of improper self duals, and the denominator represents the number of chiral self duals. Many of the counts can be clicked to show representative polyhedra.