Catalan solids

Catalan solids

A Catalan solid, also known as a Catalan polyhedron, is a type of polyhedron that is the dual of an Archimedean solid. Unlike Platonic and Archimedean solids, the faces of Catalan solids are not regular polygons. They are named after the Belgian mathematician Eugène Catalan and include shapes such as the deltoidal icositetrahedron.From: Divided Spheres [2019], Arrangements of three to six cubes with maximum disorientation angles [2020], st Century Nanoscience – A Handbook [2020]

Onion-Like Inorganic Fullerenes from a Polyhedral Perspective

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Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020

Ch. Chang, A. B. C. Patzer, D. Sülzle, H. Bauer

The Catalan solids are all convex. They are face-transitive but not vertex-transitive, i.e. all faces are equivalent but the vertex environments are not. This is because the Archimedean solids are vertex-transitive and not face-transitive. 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. Being face-transitive, Catalan solids are isohedral i.e. there is just one kind of face.

Arrangements of three to six cubes with maximum disorientation angles

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Journal Information

Published in Philosophical Magazine, 2020

Susumu Onaka

The shape of the polyhedron in Figure 5(b) is similar to that of a deltoidal icositetrahedron, which is known as one of the Catalan solids [10]. However, the dihedral angles (, or ) of the {100} polyhedron shown in Figure 5(b) are slightly different from that of the deltoidal icositetrahedron ().

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Onion-Like Inorganic Fullerenes from a Polyhedral Perspective

Arrangements of three to six cubes with maximum disorientation angles