The task to reduce the material consumption in the building industry is urgent. Conserving concrete saves nature and money. To reduce the consumption of concrete in buildings we design hollow bodies in ceiling structures. In a free geometrical optimization process we restrict to those forms which can be fabricated in half shells. Our main goal is the best concrete saving ratio with respect to the restrictions of the building process. We show some possible forms and focus later on the better possibilities, the crossing channels. A smoothing step to avoid edges that cause stress peaks will raise the concrete saving even higher. We evaluate the use in technical applications under some questions like the concrete ventilation or the problem-free traversing in the fabrication process.

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.