Domes and polyhedron shaped buildings and designs are seen all around the world. Old and ancient examples are mostly churches, minarets, the arctic igloo. Today we have high-tech examples of geodesics from added super-domes in different sizes and materials, to simplified and nature orientated and sustainable buildings.
The structural behavior of Platonic polyhedra - from first experiments and full scale buildings made by Buckminster Fuller, architect and engineer, to other experiments showing the fact, that plate structures are not a type of lattice structure, but a independent type of structure with dual properties to the lattice structures. This was confirmed when the basic equation of stability for plate structures was found.
Plates and lattices are duals like axial and shear forces, like the closed and the open, and in the same way as yin and yang are incompatible, but yet form some interesting combinations.
Conditions of stability to convex singular coherent polyhedra, as combinations of these form the basis for nearly all buildings considered with characteristics of pi-free three dimensional geometry. Topology, stability and geometry are similar seen in quite different levels: The carbon molecule structure with 60 atoms on each vertice - similar to the geometry of the truncated icosahedron. Resent NASA´s Spitzer Space Telescope discovered small "buckeyballs" in space 6.500 light-years away stacked together in enormous structures hundred of millions of miles wide. In the biological world Radiolaria and Foramifera as high frequency plate polyhedra. The structural concept of honeycomb, and maybe a good example of pure plate structure, the sea Urchin.
This page will highlight news and developments from around the world - in light of polyhedra to sinus related trans-formations - updated to new concepts, ideas as full scale examples.
Carbon molecule Radiolaria Radiolaria Polycystinea Echinus Esculentus
Bee honey comb Radiolaria bracelets Buckeyballs in space, NASA 2010