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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References 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." http://www.software3d.com/Archimedean.html . Referenced
on Wolfram|Alpha Archimedean Dual
Cite this as:
Weisstein, Eric W. "Archimedean Dual."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ArchimedeanDual.html

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