Isotropic spatial axial radiations and notable polyhedra

Abstract

In this paper, isotropic spatial axial radiations are defined by means of a simple metric property and it is shown that the radial skeletons of the Platonic bodies, Archimedean solids and their polar forms, verify this isotropic property. The radial skeletons of the Platonic bodies are obtained from the fundamental skeleton of the octahedron by means of ‘umbrella type’ manipulations. It also gives a way of extending this isotropic and continuous evolution to all the Archimedean solids and their polar forms.