Generation of forms between two dual tetrahedrons, to link morphology and structural properties of polyhedral surfaces
Résumé
At conferences in Beijing (Monnot, 2018) and Barcelona (Monnot, 2019), the confrontation of Platonic solids with Chinese Elements allowed the hypothesis of their correspondence, morphological and structural. That of Beijing proposed a spatialized "geometrical organon" (Serres, 1969, p.175) for architectural purposes.
This understanding, "facing each other", "one through the other", continues to reveal "unthoughts" - following the methodology of F.Jullien (2019). The research developed in this article will exploit another configuration for an unexplored "vis-à-vis", between Platonic solids and Lai Taiji Diagram (來 氏 太極 圖)
The selection of a particular sequence - nested storing - of the polyhedra according to wuxing - makes it possible to imagine a minimal 2D geometrical representation which clarifies the cosmogenesis related by Plato (Timée, 53c).
This minimal figure justifies the hypothesis that this morphogenesis of regular polyhedra builds / fits between two external formal boundaries, two dual tetrahedrons - the other polyhedra deploying in the space between.
This figure / diagram also reveals structural properties that make it possible to link geometric shapes to their constructive potentialities - thus reconsidering the notion of "form" in an open sense of the "Life of forms" (Focillon, 1934), by connecting their different dimensions ("structurales" and "structurelles" in French –Rénier, 1992).
Finally, this new research allows to extend the work of T.Wester on the structures of polyhedral surfaces (1997). This knowledge, which links geometry, morphology, structure and construction, opens up new perspectives for the design work and architectural education.