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:
- by definition, the five Platonic solids
- all thirteen Archimedean solids
- the Stella octangula and the star polyhedrons of Kepler
- Kepler's 12 and 30-sided rhombohedron
- all crystal lattices
- all space structures (Bell, Wachsmann, Le Ricolais, Makowski and Fuller) with their different positions
- many symbols and emblems such as the cross, pentagon, pentagram, Star of David, Cross of Saint Andrew and so on
- prisms and anti-prisms
- spiral surfaces
- helix and double helix, cylinder, sphere and cone
- the possible surface tilings by Kepler
- the golden section
- the golden rectangle and the golden triangle
- the golden series and the Modulor by Le Corbusier
- the Ö2-spiral and the harmonious f-spiral, spira mirabilis,
- quasicrystals as non-periodic packing of 30-sided triacontahedrons
- Penrose tiling as non-periodic, two-dimensional projection of quasicristals
- geodesics by Fuller as the central projection of polyhedrons on a circumscribed sphere, and their frequencies
- the fullerenes and the Buckminster fullerene
- Fuller's Dymaxion Map as a projection of the global surface on the icosahedron or other polyhedrons
- The positions and their different symmetries
- Symmetric operations such as translation, reflection, rotation and so on
- Chirality (handedness or right/left-phenomenon)
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.