Sezaro's formula and polar-zonohedral
Abstract
In the issue of the journal "The Mineralogical Magazine" (No. 81, September 1915), a note by G. Césaro is published, in which the author derives a formula concerning the numerical property of the set of axes of symmetry located in the planes of symmetry of a polyhedron. From the very title of the article, it is evident that the author was interested not in the application of the formula for determining planes of symmetry—which is quite limited, as it applies only to cases where the planes of symmetry pass through all axes of symmetry (i.e., only to mirror types of symmetry, when symmetric figures can be reproduced in zonohedral mirrors)—but rather in the formula itself with its numerical relationships. However, the author was completely unaware that this very formula had been derived by the author [i.e., the writer of the present text] for a very wide application to zonohedra (and in this sense was called zonohedral) and to paired polyhedra (in which case it is called polar zonohedral).
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