Allegorical Hexagon

As an efficient construction basic unit in nature, hexagons are widespread – the structure of crystals and honey combs are well-known examples. Consequently, the hexagon has become a symbol of efficiency, use of material, space and solidity, and matured in almost all cultures to an allegoric symbol.
The four colour theorem, first presented by the English mathematician F. Guthrie in 1852, states that, put simply, on a surface any map of autonomous regions can be presented by using only four different colours.
It took until 1976 for this theorem was proven by K. Appel and W. Haken. It was, by the way, the first theorem to be proven by using a computer.
Given six equally sided and equally sized triangles, on a plain surface there are 12 different arrangement possible. These 12 “pieces” therefore have the same surface of six triangle-units, but only the hexagon, being the most compact in shape, shows a circumference of six side lengths. All others, more or less odd shaped, show a circumference of eight side lengths.
Despite its complexity, it is possible to fit all 12 different pieces into a surface of a rhomb with six-fold side length. Rotating the rhomb structure around one of its large angle corners generates a regular hexagon again.