Catalan solids

Not counting the enantiomorphs there are a total of 13 Catalan solids.

Below is a set of polyhedra that can be generated from the Catalan solids.

The Catalan solids, the bipyramids and the trapezohedra are all isohedral.

However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles.

The Catalan solids are all convex.

Catalan solids - duals of the Archimedean solids.

Catalan solids:

The above operations allow all of the semiregular polyhedrons and Catalan solids to be generated from regular polyhedrons.

His descriptive operators can generate all the Archimedean solids and Catalan solids from regular seeds.

Additionally, two of the Catalan solids are edge-transitive: the rhombic dodecahedron and the rhombic triacontahedron.

In addition, certain Catalan solids (duals of Archimedean solids) are again zonohedra:

It is also topologically related as a part of sequence of Catalan solids with face configuration Vn.6.6, and also continuing into the hyperbolic plane.

It also has the most faces among the Archimedean and Catalan solids, with the snub dodecahedron, with 92 faces, in second place.

The Catalan solids are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865.

Both geodesic and non-geodesic structures can be derived similarly from the Archimedean solids and Catalan solids.

These duals include the Catalan solids, the convex dipyramids and antidipyramids or trapezohedra, and their nonconvex analogues.

These duals are transitive on their edges and faces (but not on their vertices); they are the edge-transitive Catalan solids.

Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are 'not' regular polygons.

The first row generates the Archimedean solids and the second row the Catalan solids, the second row forms being duals of the first.

Two of the Catalan solids are chiral: the pentagonal icositetrahedron and the pentagonal hexecontahedron, dual to the chiral snub cube and snub dodecahedron.