Diamond Cubic - Greg Egan

Diamond Cubic

This picture by Greg Egan shows the pattern of carbon atoms in a diamond, called the diamond cubic. Each atom is bonded to four neighbors. This pattern is found not just in carbon but also other elements in the same column of the periodic table: silicon, germanium, and tin.

Heawood Graph - Koko90

Heawood Graph

This is the Heawood graph. This graph can be drawn on a torus with no edges crossing in such a way that it divides the torus into 7 hexagons, each pair of which shares an edge. In 1890, Percy John Heawood proved that for any map drawn on a torus, it takes at most 7 colors to ensure that no two countries sharing a common boundary have the same color. The Heawood graph proves that the number 7 is optimal.