Synthetic Methods for Constructing Polyhedra

In this paper, we propose an explanation and application of the synthetic method to the representation of the Platonic and Archimedean Solids (PS and AS). The intention is to illustrate the potential of this method in a historical and theoretical context. The study of regular and semiregular polyhedra in this sense is an ideal theme to illustrate the heuristic potential of drawing. Therefore, some synthetic constructions of PS and AS are proposed, defining the constructive algorithms of these figures. The working environment used is the mathematical representation method; for some constructions, parametric and physical simulating tools were used. Particular attention is dedicated to two different synthetic methods: the first, is the construction of the snub cube through paper folding and the second, is a more general method that exploits a physical simulator engine.