Catalan solids

A Catalan solid is the dual of an Archimedean solid.

The non-regular faces of these Catalan solids are all congruent to each other. At the vertices, however, different numbers of faces meet. In the case of the Archimedean solids, it is the other way round: the number of faces coming together at a vertex is always the same, but the faces are different types of regular polygons.

In the list below the number of faces, edges and vertices are listed as (F, E, V).



F, E, V

Triakis tetrahedron

dual of the
Truncated tetrahedron
12, 18, 8
Rhombic dodecahedron

dual of the
12, 24, 14
Tetrakis hexahedron

dual of the
Truncated octahedron
24, 36, 14
Triakis octahedron

dual of the
Truncated cube
24, 36, 14
Deltoidal icositetrahedron

dual of the
24, 48, 26
Disdyakis dodecahedron

dual of the
Truncated cuboctahedron
48, 72, 26
Rhombic triacontahedron

dual of the
30, 60, 32
Pentakis dodecahedron

dual of the
Truncated icosahedron
60, 90, 32
Triakis icosahedron

dual of the
Truncated dodecahedron
32, 90, 60
Pentagonal icositetrahedron

dual of the
Snub cube
24, 60, 38
Deltoidal hexecontahedron

dual of the
60, 120, 62
Dadakis triacontahedron

dual of the
Truncated icosidodecahedron      
120, 180, 62
Pentagonal hexecontahedron

dual of the
Snub dodecahedron
24, 150, 92
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