Catalan solid

The Archimedean solids are thirteen highly-symmetric polyhedra with regular faces and symmetric vertices.

Their dual, the Archimedean solids, are vertex-transitive but not face-transitive.

[1] Additionally, two Catalan solids, the rhombic dodecahedron and rhombic triacontahedron, are edge-transitive, meaning their edges are symmetric to each other.

[citation needed] Some Catalan solids were discovered by Johannes Kepler during his study of zonohedra, and Eugene Catalan completed the list of the thirteen solids in 1865.

[4] Two Catalan solids, the pentagonal icositetrahedron and the pentagonal hexecontahedron, are chiral, meaning that these two solids are not their own mirror images.

Set of Catalan solids
The rhombic dodecahedron 's construction, the dual polyhedron of a cuboctahedron , by Dorman Luke construction