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.

How to give a sense to senseless vectors in plane

“…However, a projection of senseless vectors over a plane can be defined, and a theorem about isotropic radiation of senseless vectors [6] (no matter whether they are defined in two or three dimensions) can be proved. But these topics are to be dealt with in a future paper.…”

The construction of stellated regular polyhedra from constant width strips

“…Recently, our group has paid attention to the study of some questions related to polyhedra topics [1,6]. We have solved the five Platonic bodies construction problem starting from constant width continuous strips (see [1]), without performing measurement or using geometric instruments.…”