From Trees to Polyhedra

Polyhedra have fascinated mankind since ancient times. Mathematical work about polyhedra has been done in Egypt, Greece, China and India. Typically, it is convex polyhedra that are discussed (3-dimensional surfaces bounded by planes, no notches or tunnels allowed). Historically, it has been the symmetry and metrical properties of convex polyhedra that have gotten a lot of attention. But it turns out that the dots and lines diagrams called graphs (Figure 1) can be used to get surprising rich insights into polyhedra.