Form Generation Of Polyhedric Building Shapes

Abstract

The Platonic - or regular - and the Archimedean - or semi-regular - polyhedra can be considered as portions of space that are completely surrounded by one or more kinds of regular polygons. The numbers and positions in space of these polygons are strictly ruled by universal criteria. It is therefore possible to form these polyhedra by placing polygons around the centre of the coordinate system in distinct numbers, at certain distances and under certain angles in accordance with these rules. This is called here ‘rotation’ and the forelying paper describes a method where this is done for the regular and semi-regular polyhedra and for related figures that are found by derivation from these polyhedra. The figures that are rotated have not necessarily to be regular polygons, nor do have to be strictly planar. This method thus allows the rotation of arbitrary figures – also spatial ones – and the rotation procedure can even be used repeatedly, so that very complex configurations can be described.