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Catalan Solids
The Catalan Solids are the duals of the Archimedean Solids. The vertices of the dual of a solid are the midpoints of the faces of the original solid.
Catalan Solids have nothing to do with Calalunya, they are named after their first description by belgian mathematician Eugène Catalan in 1865. The faces of these solids are not regular polygons, but they are all equal.
The following table summarizes their characteristics. It shows each Catalan Solid associated with its dual Archimedean Solid. If you click on any image, you are directed to a 3D model that you can zoom and rotate.
The Catalan Solids and their dual Archimedean Solids |
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TRIAKIS TETRAHEDRON F = 12 V = 8 E = 18 |
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TRUNCATED TETRAHEDRON V = 12 F = 8 (4 Triangles + 4 Hexagons) E = 18 |
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TRIAKIS OCTAHEDRON F = 24 V = 14 E = 38 |
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TRUNCATED CUBE V = 24 F = 14 (8 Triangles + 6 Octagons) E = 38 |
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TETRAKIS HEXAHEDRON F = 24 V = 14 E = 36 |
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TRUNCATED OCTAHEDRON V = 24 F = 14 (8 Hexagons + 6 Squares) E = 36 |
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TRIAKIS ICOSAHEDRON F = 60 V = 32 E = 90 |
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TRUNCATED DODECAHEDRON V = 60 F = 32 (20 Triangles + 12 Decagons) E = 90 |
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PENTAKIS DODECAHEDRON F = 60 V = 32 E = 90 |
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TRUNCATED ICOSAHEDRON V = 60 F = 32 (12 Pentagons + 20 Hexagons) E = 90 |
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RHOMBIC DODECAHEDRON F = 12 V = 14 E = 24 |
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CUBOCTAHEDRON V = 12 F = 14 (8 Triangles + 6 Squares) E = 24 |
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DISDYAKIS DODECAHEDRON F = 48 V = 26 E = 72 |
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TRUNCATED CUBOCTAHEDRON V = 48 F = 26 (8 Hexa. + 12 Squa. + 6 Octa.) E = 72 |
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RHOMBIC TRIACONTAHEDRON F = 30 V = 32 E = 60 |
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ICOSIDODECAHEDRON V = 30 F = 32 (20 Triangles + 12 Pentagons) E = 60 |
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DELTOIDAL ICOSITETRAHEDRON F = 24 V = 26 E = 48 |
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RHOMBICUBOCTAHEDRON V = 24 F = 26 (8 Triangles + 18 Squares) E = 48 |
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PENTAGONAL ICOSITETRAHEDRON F = 24 V = 38 E = 60 |
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SNUB CUBE V = 24 F = 38 (32 Triangles + 6 Squares) E = 60 |
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DELTOIDAL HEXECONTAHEDRON F = 60 V = 62 E = 120 |
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RHOMBICOSIDODECAHEDRON V = 60 F = 62 (20 Tria. + 30 Squa. + 12 Pent.) E = 120 |
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PENTAGONAL HEXECONTAHEDRON F = 60 V = 92 E = 150 |
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SNUB DODECAHEDRON V = 60 F = 92 (80 Triangles + 12 Pentagons) E = 150 |
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DISDYAKIS TRIACONTAHEDRON F = 120 V = 62 E = 180 |
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TRUNCATED ICOSIDODECAHEDRON V = 120 F = 62 (30 Squa. + 20 Hexa. + 12 Deca.) E = 180 |