hexagonon

Greek hex meant six and gōnia meant angle. A hexagonon was a six-angled figure. The regular hexagon is unique among regular polygons: it tiles the plane perfectly without gaps or overlaps, using less material per unit area than any other shape to enclose equal spaces. Bees discovered this optimization independently of mathematicians — honeycomb cells are regular hexagons.

Pappus of Alexandria demonstrated in the 4th century CE that the honeycomb conjecture was true: the regular hexagon is the most efficient way to tile a plane with cells of equal area. He proved it geometrically, but rigorous mathematical proof of the general case waited until Thomas Hales's 1999 proof using computer-assisted calculation.

Carbon atoms arrange in hexagonal patterns in several configurations. Graphite — the 'lead' in pencils — consists of hexagonal sheets of carbon stacked loosely. Graphene — a single hexagonal carbon sheet — was isolated by Andre Geim and Konstantin Novoselov in Manchester in 2004, winning them the 2010 Nobel Prize in Physics. Graphene is the strongest material ever tested, 200 times stronger than steel at one atom thick.

Snowflakes are hexagonal because water molecules form hexagonal hydrogen-bonded rings when they crystallize. No two snowflakes are identical not because of some mystical principle but because the probability of two ice crystals following the same growth path through identical atmospheric conditions is essentially zero. The hexagonal structure is determined; the specific shape is not.