Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 43 (2002), No. 1, 121-133. On the Chiral Archimedean Solids Dedicated to Prof. Dr.

Abstract. We discuss a unified way to derive the convex semiregular polyhedra from the Platonic solids. Based on this we prove that, among the Archimedean solids, Cubus simus (i.e., the snub cube) and Dodecaedron simum (the snub dodecahedron) can be characterized by the following property: it is impossible to construct an edge from the given diameter of the circumsphere by ruler and compass