# Platonic Solids

1 IntroductIon Imagine a sphere. It is Unitys perfect symbol. Each point on its surface is identical to every other, equidistant from the unique point at its centre. Establishing a single point on the sphere allows others to be defined in relation to it. The simplest and most obvious relationship is with the point directly opposite, found by extending a line through the spheres centre to the other side. Add a third point and space all three as far from each other as possible to define an equilateral triangle. The three points lie on a circle with radius equal to the spheres and sharing its centre, an example of the largest circles possible on a sphere, known as great circles. Point, line and triangle occupy zero, one and two dimensions respectively. It takes a minimum of four points to define an uncurved three dimensional form. This small book charts the unfolding of number in three dimensional space through the most fundamental forms derived from the sphere. A cornerstone of mathematical and artistic inquiry since antiquity, after countless generations these beautiful forms continue to intrigue and inspire. Cairo, 2001