NANOARCHITECTURE IN THE METAEDER

In the following scale of sizes, the dimensions for building and city construction are between 10-³ and 10³ meters, in other words between millimeters and kilometers. The cell, building block for all living organisms, is situated in the micrometer (:) range, i.e. millionths of a meter, the molecule as element in structural chemistry in the nanometer range, i.e. thousand billionths of a meter, the atom is in the picometer range, i.e. trillionths of a meter, and elementary particles are in the femtometer range (quadrillionths of a meter). In spite of its different binding forces, spatial structure, in its basic elementary form between decimeter and dekameter is - cum grano salis - a more or less perfect image of what we call the nano range in structural chemistry, i.e. its enlargement by the factor of a billion.

In 1912, Max von Laue used natural crystals as a diffraction grid for X-rays. This demonstrated experimentally for the first time the correctness of the crystal structure theory, according to which the crystal is a three-dimensionally periodic discontinuation of elementary particles as well as atoms.

If, for example, X-rays are passed through an object in different directions, such as in this case through the same zink blende (sphalerite) crystal, different patterns of interference are obtained, these being both parallel to the edge of a cube having a four fold symmetry (a- position) and parallel to the spatial diagonal of the same cube having a three fold symmetry (b- position).

This proved:

that the structure of crystalline material is built up on the lines of polyhedron packing, and

that molecules are not spatially symmetric (as in the sphere), but show different geometrical projection patterns in different directions.

This is an analogy to my discovery in 1959 concerning the positions in spatial structures, which recognized all configurations of flat grids published or constructed at that time as constituting an order of the same spatial lattice, which I defined via the cube as being the only Platonic solid packable within itself in a gapless manner and the only prism among the Platonic solids having the positions:

a- standing on one of its faces

b- standing on one of its vertices

g- standing on one of its edges,

which I call "face down"(a) , "vertex down"(b) and "edge down"(g) .

Position is particularly important for a macrostructure within a field of gravity, as its static behaviour and usability differ between those useable areas which are, as a rule, horizontal, and those requiring a vertical partition of space according to the direction of gravity in relation to the structure.