New light on the rediscovery of the Archimedean solids during the Renaissance

Abstract

It is customarily asserted that the Archimedean solids were rediscovered by Renaissance artists such as Piero della Francesca (ca. 1412-1492), Albrecht Durer (1471-1528), and Daniele Barbaro (1513-1570) step by step without knowledge of the ancient prehistory, which is only reported by Pappos in book V of his collectio (about 320 A.D.) and afterwards led to the modern name Archimedean solids. This story is well told in a fundamental paper (Field 1997). Let us summarize what has been said and generally accepted until now: 1 . Renaissance people were not, or at least not seriously, interested in the "combinatorial regularity"1 of these solids but merely in their ball-like shape, i.e. in the existence of a circumscribed sphere. In particular Durer in his Underweysung['525] pointed repeatedly to the fact that the solids treated by him riiren in einer holen kugel mit all iren ecken cm(touch a hollow sphere with all their vertices). Consequently alongside some Archimedean solids they also designed and studied some nonArchimedean solids. For example, Pacioli and Durer designed a "polyhedronal approximation" of the sphere with piecewise linear meridians and parallel circles, and the famous polyhedron in Durer's MELENCOLIA I has a circumscribed sphere (Schreiber 1999).