Abstract

Even though the discovery of the regular polyhedra is attributed to the Pythagoreans, there is some fascinating evidence that they may have been known in prehistoric Scotland. In the Ashmolean Museum at Oxford University there are five rounded stones with regularly spaced bumps. The high points of each bump mark the vertices of each of the regular polyhedra. The stone balls also appear to demonstrate the duals of three of the regular polyhedra. For example, if the six faces of the cube become points, they become the six vertices of the octahedron. If the eight faces of the octahedron become points, they become the eight vertices of a cube. Remarkably, groves in the Ashmolean stones indicate each of the duals, including the fact that the tetrahedron is its own dual. Instead of assuming that these ancient Scots were experts in solid geometry, we have hypothesized that they must have discovered all of this by sphere stacking, which will be demonstrate later in this article