Polyhedra and Art

Through history, polyhedra have been closely associated with the world of art. The peak of this relationship was certainly in the Renaissance. For some Renaissance artists, polyhedra simply provided challenging models to demonstrate their mastery of perspective.  For others, polyhedra were symbolic of deep religious or philosophical truths.  For example, Plato's association in the Timaeus between the Platonic solids and the elements of fire, earth, air, and water (and the universe) was of great import in the Renaissance.  This was tied to the mastery of geometry necessary for perspective, and suggested a mathematical foundation for rationalizing artistry and understanding sight, just as renaissance science explored mathematical and visual foundations for understanding the physical world, astronomy, and anatomy.  For other artists, polyhedra simply provide inspiration and a storehouse of forms with various symmetries from which to draw on.  This is especially so in twentieth century sculpture, free of the material and representational constraints of earlier conceptions of sculpture.