Jack Love
The Platonic solids have been the inspiration for the pieces I have created thus far. My work explores the structure of these objects and their relationships to one another, and attempts to express this structure in a way that is aesthetically appealing.
Since these objects are naturally beautiful, my job is pretty easy. The real challenge is going from the idealized mathematical world to the real world of physical materials and construction strategies. I use Google SketchUp to design the pieces, and an automated CNC router called a ShopBot to cut out the parts.
Take either the icosahedron or dodecahedron and center it at the origin. Project its vertices outward from the origin onto the surface of a sphere surrounding it, giving a collection of points on a sphere. Draw a great circle through two points if they are images of two adjacent vertices in the original polytope. Each of these great circles is partitioned into arcs by its intersection with the other great circles thus produced. The arcs come in three lengths and are projections of the edges of, respectively, an icosahedron, a dodecahedron, and a third polytope whose facets are rhombic.
This model exhibits this construction. The convex arcs correspond to the icosa, the concave to the dodeca, and the straight to the rhombic.