Archimedean Dual

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below (cf. Pearce 1978, Holden 1991).

The rhombic dodecahedron and rhombic triacontahedron are the only two Archimedean duals that are equilateral and the disdyakis dodecahedron and disdyakis triacontahedron are the only two Archimedean duals that have three distinct edge lengths. The remaining 9 Archimedean duals have two distinct edge lengths.


Hume (1986) gives exact solutions for the side lengths, angles, and dihedral angles of the Archimedean duals.


Nets for the Archimedean duals are illustrated above.

The figure below illustrates the Archimedean solids paired vertically with their duals.


See also

Archimedean Solid, Catalan Solid

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Holden, A. Shapes, Space, and Symmetry. New York: Dover, p. 54, 1991.Hume, A. "Exact Descriptions of Regular and Semi-Regular Polyhedra and Their Duals." Computing Science Tech. Rep., No. 130. Murray Hill, NJ: AT&T Bell Laboratories, 1986.Pearce, P. Structure in Nature Is a Strategy for Design. Cambridge, MA: MIT Press, pp. 34-35, 1978.Webb, R. "Archimedean Solids and Catalan Solids."

Referenced on Wolfram|Alpha

Archimedean Dual

Cite this as:

Weisstein, Eric W. "Archimedean Dual." From MathWorld--A Wolfram Web Resource.

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