Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 121-133 (2002)

On the Chiral Archimedean Solids

Bernulf Weissbach, Horst Martini

Institut für Algebra und Geometrie, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg; Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz

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.

Keywords: Archimedean solids, enantiomorphism, Platonic solids, regular polyhedra, ruler-and-compass constructions, semiregular polyhedra, snub cube, snub dodecahedron

Classification (MSC2000): 52B10

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