The Metaeder is a variant of Kepler's combination of the Platonic solids, and is to serve, in our view, as a basic figure in structural architecture - one may name it "radical", i.e. from the roots.
Science has always searched for a finite list of its elements, for classification, for example, five and only five Platonic solids, thirteen and only thirteen Archimedean solids, Kepler's seventeen and only seventeen surface tessellations, the periodic system of the elements, 32 classes of crystals, the ongoing attempt to find a complete sequence of the genome. Structural research has proved its importance in the history of science; thus, Kepler founded his laws on the basis of Tycho Brahe’s observations and data, Buckminster Fuller developed his geodesics, the bucky-ball, as a basic figure of various geodesic domed buildings in macro-architecture, posthumously the Buckminster fullerene and the fullerenes were found in nano-architecture, the basis for a new branch of carbon chemistry.
The Metaeder is a combination of the five Platonic solids. The Metaeder with its crystalline intracubic and quasicrystalline extracubic packings is the attempt to produce a finite list of all possible figurations of an architecture combined from elements. The intracubic polyhedrons, tetrahedron, octahedron and cube fill space, and form an analogy to inorganic matter (crystals); however, the extra-cubic dodecahedron and the icosahedron are non space-filling, and form geometrical series, particularly the golden series, which is often found in organisms, plants and animals.

The Metaeder contains:

The universality of the Metaeder is the theoretical basis of structural architecture, inasmuch as it consists of equal, or similar or different, but coordinated elements. It contains the elementary cells of a structural architecture, it provides the sum of possibilities of regular space divisions.

The Metaeder is an object of meditation, a spatial mandala; its laws, proportions and beauties are revealed only in the spatial model.

In geometry, polyhedrons are solids having plane faces circumscribed by straight lines. The flat areas make up its sides, the straight lines determine its edges, and the crossing points of their edges form its vertices.