The Platonic and Archimedean solids are a well-known vehicle to describe certain phenomena of our surrounding world. It can be stated that they define natural equilibria of forces, which can be clarified particularly through the packing of spheres. [1][2] To solve the problem of the densest packing, both geometrical and mechanical approach can be exploited. The mechanical approach works on the principle of minimal potential energy whereas the geometrical approach searches for the minimal distances of centers of mass. The vertices of the solids are given by the centers of the spheres.
If we expand this idea by a contrary force, which pushes outwards, we obtain the principle of tensegrity. We can show that we can build up regular and half-regular polyhedra by the interaction of physical forces. Every platonic and Archimedean solid can be converted into a tensegrity structure. Following this, a vast variety of shapes defined by multiple solids can also be obtained.