Catalan Solids

The Catalan solids are the duals of the Archimedean solids. They are named after the Belgian mathematician Eugene Catalan (1814-1894) who first described the complete set in 1865. The Rhombic Dodecahedron and Rhombic Triacontahedron were described in 1611 by Johannes Kepler [1]. Each Catalan solid has one type of face and a constant dihedral angle, and it possesses the same symmetry as its Archimedean dual.

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Triakis Tetrahedron

Rhombic Dodecahedron

Tetrakis Hexahedron

Triakis Octahedron

Deltoidal Icositetrahedron

Pentagonal Icositetrahedron (dextro)

Pentagonal Icositetrahedron (laevo)

Rhombic Triacontahedron

Disdyakis Dodecahedron

Pentakis Dodecahedron

Triakis Icosahedron

Deltoidal Hexecontahedron

Pentagonal Hexecontahedron (dextro)

Pentagonal Hexecontahedron (laevo)

Disdyakis Triacontahedron

References:[1]Johannes Kepler, Strena Seu de Nive Sexangula [A New Year's Gift of Hexagonal Snow] (1611).
[2]Johannes Kepler, translated by Colin Hardie, The Six-Cornered Snowflake. Oxford: Clarendon Press (1966).
[3]Eugène Catalan, Mémoire sur la Théorie des Polyèdres, Journal de l'École polytechnique 41 (1865), 1-71, +7 plates.