Download Wolfram Notebook

A Catalan solid, also called an Archimedean dual, is one of the 13 dual polyhedra of the 13 Archimedean solids. They are named for E. Catalan, who studied them in his memoir (Catalan 1865).

The following table pairs each Archimedean solid with its corresponding Catalan solid and includes one net for each dual. Each drawing shows one representative. The snub cube and snub dodecahedron, as well as their duals, each have two enantiomorphs.

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

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

See also

Archimedean Solid, Dual Polyhedron, Semiregular Polyhedron

Explore with Wolfram|Alpha

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, 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.Pedagoguery Software. Poly. http://www.peda.com/poly/.Webb, R. "Archimedean Solids and Catalan Solids." https://www.software3d.com/Archimedean.php.Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, 1983.

Referenced on Wolfram|Alpha

Catalan Solid

Cite this as:

Weisstein, Eric W. "Catalan Solid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CatalanSolid.html

Subject classifications