John Pickering has been described as a modern-day alchemist who hews his sculptures from pure mathematical principles. His technique is to conjugate a numerical sequence and to cast its form in space. As the form unfolds, it invites us to explore surfaces as sculpture, and to interpret volumes and spaces as architecture. Because of the mathematical rigour that underpins the form, it is already potent, engineered, rational and ultimately, buildable. The Inversion Principle conveys, through photographs, the full impact of Pickering’s sculptures. But equally it describes the meticulous process of making them. It defines the inspirations behind the works (which include Naum Gabo, space probes, satellites and Stockhausen). It dicusses their engineering implications. Finally, it places them within the architectural tradition of the visionary form.