METAEDER

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.