Catalan Solids
A Catalan solid, also known as an Archimedean dual, refers to a polyhedron that serves as the dual counterpart to an Archimedean solid. There exist 13 distinct Catalan solids, named after the Belgian mathematician Eugène Catalan, who initially described them in 1865.
The Catalan solids possess a convex shape and are considered to be face-transitive, although they are not vertex-transitive. This distinction arises because the dual Archimedean solids exhibit vertex-transitivity while lacking face-transitivity. Notably, unlike the Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and these solids maintain constant dihedral angles. Due to their face-transitivity, Catalan solids are categorized as isohedra.
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