Although, in 1960, I had already exhibited a combinatory model of the five Platonic solids (later called the Metaeder) with van de Loo ; by restricting myself to packable solids at that time, my search for j, i.e. the golden section, the "Divina Proportione", the Fibonacci numbers, the harmonic series, and a pentagonal symmetry, was still in vain. I let the problem lie at the time, although it remained a constant challenge to me throughout the years.
Around 1980, I constructed a man-high Metaeder as an object of meditation and calculation. It consisted of a cube (edge length = 1m) with the tetrahedron and octahedron contained within it as packable regular solids, and the dodecahedron and icosahedron as regular solids circumscribing it.
The cube with the intracubic Platonic solids covered the field of packability, the extracubic solids being non-packable, though determined by the golden section in a wide variety of ways.
The Metaeder contains all basic geometric forms of modern structural architecture:
- the cube with the right angle (or its deformations) stands for Mies van der Rohe ~1950
- the tetrahedron- (semi-)octahedron- packing stands for Wachsmann and his "Hangar" ~1954
- the combination of all packable Platonic solids, the integration of statics and utility, and the rotation of the lattices found in the different positions stands for Schulze-Fielitz 1959.
- in the extracubic field, the truncated icosahedron with 20 hexagons and 12 pentagons as basic shapes in geodesics, as described in the patent of 1954, i.e. the Bucky-ball, one of the 13 Archimedean solids, stands for Buckminster Fuller ~1954
- the diagonal plane in the icosahedron (and in the dodecahedron) are harmonic rectangles intersecting each other vertically, whose subdivision into the golden section produces harmonic series; all of these stand (scaled according to the human proportion) for the Le Corbusier's Modulor of 1951. The basic features of the Modulor are: golden series, rectangularity and human proportion.
Many structural discoveries in architecture were, more or less, made during the 1950's, a decade which we could call the incubation and blossoming period of the second (structural) modern architecture after the 1920's.
It is worthwhile to remember that the double helix (Watson and Crick 1953), quantum chemistry (Pauling) and structural anthropology (Lévi-Strauss 1958) were all discovered during this period.