This book offers a material history of the development of geometry in the sixteenth century, providing an innovative and transformative account of the Platonic solids and their elaboration in late Renaissance culture. The project argues that in the hands of sixteenth-century artisans and architects, the Platonic solids transformed from mere classical philosophical concepts into the premier subjects for the display of virtuosic skill in geometrical drawing and precision measurement. Stripping the solids of their bookish, Neo-Platonic trappings generated a new, and self-consciously “material” approach to geometry and ignited a century of geometrical form-making that pushed the mathematical diagram to the edge of representability, in the process redefining what it meant to practice and study geometry. Beginning with the late fifteenth-century editions of Euclid’s Elements, the first printed book in Europe to include geometrical images, and Albrecht Dürer’s groundbreaking work on geometry, The Polyhedrists traces the lifespan of the Platonic solids from their use as perspectival tools and pedagogical devices in the Renaissance studiolo into princely Kunstkammern and onto the surfaces of domestic spaces and objects, charting a trajectory from the workshop to the court and the early cosmology of Johannes Kepler. Situated at the intersection of the history of art, architecture, and mathematics, the book uncovers the influence of the decorative arts and artisanal experimentation with geometry on the formulation of Renaissance mathematical knowledge and its new engagement with materials and concepts of materiality.

Noam Andrews is a licensed architect in the United Kingdom and Belgium, and research fellow (2018–21) at the University of Ghent, Belgium, in the Faculty of Arts and Philosophy. He has been the recipient of fellowships from the Metropolitan Museum of Art; Villa I Tatti–Harvard University Center for Italian Renaissance Studies; and the Max Planck Institute for the History of Science, and has curated exhibitions at Ghent University (Dürer copyright), The Metropolitan Museum of Art (Picturing Math), and Harvard University (Building Geometry and Images at Work) on the history of visualizing mathematics and mathematical models respectively. Andrews received his doctorate from the department of the history of science, Harvard University. In addition, he earned a master's of research degree in humanities and cultural studies from Birkbeck, University of London, and bachelor's degrees in architecture from Cornell University and the Architectural Association School of Architecture in London, where he taught a Diploma Unit from 2007–10.