Noble Polyhedron - Duality of Noble Polyhedra

Duality of Noble Polyhedra

We can distinguish between dual structural forms (topologies) on the one hand, and dual geometrical arrangements when reciprocated about a concentric sphere, on the other. Where the distinction is not made below, the term 'dual' covers both kinds.

The dual of a noble polyhedron is also noble. Many are also self-dual:

• The regular polyhedra form dual pairs, with the tetrahedron being self-dual.
• The disphenoid tetrahedra are all topologically identical. Geometrically they come in dual pairs – one elongated, and one correspondingly squashed.
• A crown polyhedron is topologically self-dual. It does not seem to be known whether any geometrically self-dual examples exist.
• The wreath and V-faced polyhedra are dual to each other.