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
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Rhombic Dodecahedron
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Tetrakis Hexahedron
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Triakis Octahedron
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Deltoidal Icositetrahedron
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Pentagonal Icositetrahedron (dextro)
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Pentagonal Icositetrahedron (laevo)
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Rhombic Triacontahedron
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Disdyakis Dodecahedron
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Pentakis Dodecahedron
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Triakis Icosahedron
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Deltoidal Hexecontahedron
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Pentagonal Hexecontahedron (dextro)
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Pentagonal Hexecontahedron (laevo)
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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.