Morphological evolutions of transpolyhedra. Eloquence of the images to generate tensegrity structures

Abstract

The image, as shown by the artistic research of Lucio Saffaro, can be interpreted as visual repre- sentation of complex concepts, theme clearly useful in the architectural and engineering field. The construction of innovative structural solutions also arises from the graphic evolutions of simple forms. That’s the case of tensegral structures, born from the movement of polyhedral poles. Without the graphic support, it’s difficult to understand what a tensegrity is, definable as «a system in a self–balanced, stable state that includes a series of compressed components inside a continuum of tensed components». Analyzing this concept, one can identify the “com- pressed components” as the poles present inside the system, while the “tensed components” are made up of the net of tie–rods that connect each element, creating said continuum. The construction of said systems is possible through geometric procedures starting from each type of polyhedron, whether it’s regular, semi–regular or Catalan: this geometric procedure is a set of rotations and translations, to which follows the connection between cables and poles in order to provide the correct redistribution of the tensions. The morphological evolution of the polyhedra passes through the intermediate polyhedric configurations, called “transpolyhedra”. The tense- gral structure, according to the geometric procedure previously described, is entirely inscribable inside these solids and between them exist various geometric relations: by decomposing the polyhedron into regular figures is therefore possible to know immediately the number of poles of the tensegral structure, the number of cables, the geometries to the knot and to have a map of the connections between the same. The design of the polyhedron isn’t restricted to the represen- tation of the occupied volumetry, but constitutes a significant number of information regarding the correspondent tensegral structure.