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In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the French mathematician, Eugene Catalan who first described them in 1865.
The Catalan solids are all convex. They are face-uniform but not vertex-uniform. This is because the dual Archimedean solids are vertex-uniform and not face uniform. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Additionally, two of the Catalan solids are edge-uniform: the rhombic dodecahedron and the rhombic triacontahedron. These are the duals of the two quasi-regular Archimedean solids.
Just like their dual Archimedean partners there are two chiral Catalan solids: the pentagonal icositetrahedron and the pentagonal hexecontahedron. These each come in two enantiomorphs. Not counting the enantimorphs there are a total of 13 Catalan solids.
External links
- Catalan Solid (http://mathworld.wolfram.com/CatalanSolid.html) – MathWorld site
- Archimedean duals (http://www.georgehart.com/virtual-polyhedra/archimedean-duals-info.html) – at Virtual Reality Polyhedra
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