00-31

On the chiral Archimedean solids

by Weißbach, B.; Martini, H.

 

Preprint series: 00-31, Preprints

MSC:
52B99 None of the above but in this section

 

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 Dodecahedron simum (the snub dodecahedron) can be characterized by the following property: it is impossible to construct an edge from the given diameter by ruler and compass.

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


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