Hexagons Win Every Time

Squares and equilateral triangles also tile perfectly, but they waste material. A square has a perimeter-to-area ratio worse than a hexagon. Triangles are even worse. The hexagon hits the sweet spot — closest to a circle (the most efficient single shape) while still tiling without gaps.

Circles are the ultimate enclosers of area, but they leave gaps when packed together. Hexagons are nature's compromise: nearly circular efficiency with perfect tessellation. This is why hexagonal patterns appear in basalt columns, turtle shells, and bubble rafts — physics naturally optimizes.