A new method to obtain and define regular polyhedra (Q1771162)

The authors propose a new way of constructing regular polyhedra, namely by opening a given spatial direction (like an umbrella) such that a regular polygon is obtained which lies in a plane orthogonal to that direction. In addition, the obtained configuration of regular polygons has to satisfy certain metrical conditions such that the boundary of the polyhedron is obtained. So the authors get a way to construct so-called ``isotropic polyhedra'', a class containing also the regular and the Archimedean solids.