Questions about the non-constructable polygon of Leon Battista Alberti

Abstract

The process followed by Alberti when designing the façade of the Santa Maria Novella in Florence is well-known. This façade contains 48 ornamental elements which were created through the construction of regular polygons: 7 elements have a pentagonal base, 3 have an hexagonal base, 36 have an octagonal base, and 2 have an icosikaihexagonal base (26 sides). It's interesting that Alberti, having designed all ornaments on the basis of regular polygons which can be constructed using a straightedge and a compass only, decided to top the lateral scrolls with a circular design arising from a 26-sided regular polygon, since this regular polygon cannot be constructed using only a compass and a straightedge. We use a mathematical approach to theoretically compare several approximate methods for constructing an icosikaihexagon using a compass and a straightedge, in order to ascertain which of these methods best suits the point pattern of this special ornament.

Keywords

• icosaka ihexágono
• polígonos
• santa maria novella
• alberti
• geometría clásica