Metro, the subway system serving Washington, D.C., has a distinctive look. Underground stations resemble immense, minimalist concrete bunkers. The tiles covering the floors are six-sided—large, terra cotta hexagons. Now, the board in charge of Metro is debating whether to switch to square tiles, like those typically found in most other subway systems around the world.
From a mathematical perspective, both square and hexagonal tiles do the job of tiling the plane. As do tiles of many, many other geometric shapes. And the choices get even wider when you consider using several different tile shapes together. My own bathroom, for example, is tiled with octagons and squares.