Platonic Solids

Architecture has traditionally been an additive process. Idealized components are combined, arranged, and re-configured to generate a building. The components that constitute the building are mostly conceived a priori. As a result, buildings can be described by breaking them down into smaller and smaller modules, until one arrives at geometric primitives - volumes such as cylinders, cubes, prisms, and platonic solids. Not only can buildings be described in this reductionist manner, but large parts of the generative processes involved in their production can be understood. These processes are linear and have traditionally involved operations such as translating, rotating, and scaling of components. In the past decades they have been expanded to incorporate various types of deformation. Yet the combinatorial logic has remained largely on the level of the geometric components themselves, and not on the level of operations.

Given the computational power at our disposal today, the question arises as to what extent a purely operations-based geometric process can generate form. Rather than studying the possibilities in combining numerous primitives, the question is what potential is inherent in a single primitive given an appropriate process. 

The Platonic Solids project aims to explore this approach. It takes the most primitive forms, the platonic solids, and repeatedly employs one single operation – the division of a form’s face into smaller faces – until a new form is produced. The recursively applied process remains entirely constant, only the variables that control its division operation are permitted to change. This single process affects the form's topography and topology, and influences attributes such as the degree of branching, porosity, and fractalization - just to name a few. The resulting forms display a novel aesthetic and an astounding complexity that largely defies attempts at reductionism.

Subdivision algorithms in this project are based on the work of Daniel Doo & Malcolm Sabin, Edwin Catmull & Jim Clark, Jörg Peters & Ulrich Reif, and Charles Loop. Forms are generated in processing and exported as dxf files. Each form consists of 200,000 to 16 million faces. Images shown have an original resolution of 8000 x 8000 pixels.
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