Why do bees build hexagonal honeycombs instead of squares or triangles? This project explores exactly that question by testing which shapes can tile a flat surface without gaps. Using LEGO bricks, pattern blocks, and tagboard, you build pentominoes, heptiamonds, wheelbarrow pairs, and kite-and-dart pairs, then experiment with tiling rectangular grids and planes. Twelve pentominoes tile several rectangular grids, and all but one of the 24 heptiamonds tile a plane on their own. With algebra and geometry, you then prove that hexagons use less wax than squares or triangles to enclose the same area — which is precisely why bees rely on them.