Catalan Solid

The Dual Polyhedra of the Archimedean Solids, given in the following table.

Archimedean Solid	Dual
Great Rhombicuboctahedron	Disdyakis Dodecahedron
Rhombicosidodecahedron	Deltoidal Hexecontahedron
Small Rhombicuboctahedron	Deltoidal Icositetrahedron
Great Rhombicosidodecahedron	Disdyakis Triacontahedron
Snub Dodecahedron (laevo)	Pentagonal Hexecontahedron (dextro)
Snub Cube (laevo)	Pentagonal Icositetrahedron (dextro)
Truncated Icosahedron	Pentakis Dodecahedron
Cuboctahedron	Rhombic Dodecahedron
Icosidodecahedron	Rhombic Triacontahedron
Truncated Octahedron	Tetrakis Hexahedron
Truncated Dodecahedron	Triakis Icosahedron
Truncated Cube	Triakis Octahedron
Truncated Tetrahedron	Triakis Tetrahedron

Here are the Archimedean Duals (Holden 1971, Pearce 1978) displayed in alphabetical order (left to right, then continuing to the next row).

Here are the Archimedean solids paired with the corresponding Catalan solids.

$\begin{figure}\begin{center}\BoxedEPSF{DualsArchimedeanSolids1.epsf}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{DualsArchimedeanSolids2.epsf}\end{center}\end{figure}$

References

Catalan, E. ``Mémoire sur la Théorie des Polyèdres.'' J. l'École Polytechnique (Paris) 41, 1-71, 1865.

Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991.