# Platonic Solids

39 38 a cunnIng twISt and a structural wonder Picture a cuboctahedron made of rigid struts joined at flexible vertices. This structure was named the jitterbug by R. Buckminster Fuller 18951983, and is shown opposite with the rigid triangular faces filled in for clarity. The jitterbug can be slowly collapsed in on itself in two ways so that the square holes become distorted. When the distance between the closing corners equals the edge length of the triangles, an icosahedron is defined. Continue collapsing the structure and it becomes an octahedron. If the top triangle is then given a twist the structure flattens to form four triangles which close up to give the tetrahedron. Geodesic domes are another of Buckminster Fullers structural discoveries. These are parts of geodesic spheres, which are formed by subdividing the faces of a triangular polyhedron, usually the icosahedron, into smaller triangles, and then projecting the new vertices outward to the same distance from the centre as the original ones below. A distant relative of the geodesic sphere is the popular Renaissance polyhedron of seventytwo sides known as Campanus sphere below right.