Catalan solids are a concept from geometry: For each Archimedean solid there is a Catalan solid that is its duality (mathematics. In total, there are thirteen Catalan solids (as there are thirtin Archimedean solids). They are named after the Belgian mathematician Eugène Charles Catalan of the 19th centurty. Each Catalan solid is a convex polyhedron. Like with Archimewdean solids, each surface is made of the same shape.