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The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snubdodecahedron) cannot be constructed by ruler and compass. We explain that forgeneral reasons their vertices can be constructed via paper folding on thefaces of a cube, respectively dodecahedron, and we present explicit foldingconstructions. The construction of the Cubus simus is particularly elegant. Wealso review and prove the construction rules of the other Archimedean solids.

Constructing the Cubus simus and the Dodecaedron simum via paper folding