Anyone following the hexagonal news of late has no doubt noticed a flurry of stories related to the upcoming release of Civilization V, and in particular its new hexagonal tile system. In this blog's opinion, the adoption of hexagonal tiles by the Civ franchise is a long overdue development, and frankly one that should've been incorporated into at least the last two Civ releases. Indeed, many DOS-based strategy games have used hexagonal tiles going back to the late '80s, and one has to wonder why Civilization ever used square tiles. (I remember playing the original Civilization in the early '90s, well before the advent of my own hexagonal illumination, and thinking that, in fact, it would be better with a hexagonal grid. I can only imagine part of the media excitement here—aside from just the general awesomeness of hexagons—is due to the fact that many, many other people have had the exact same thought over the past twenty years.)
The following is a brief survey of some elemental properties of hexagons, and why they might be useful. It is not intended to be a comprehensive treatment of the subject. My specific concern here is with the mathematical properties of hexagons, and, to an extent, their role in the natural world. I have avoided discussing hexagons as they pertain to human culture, religion, history, and other "local" concerns, though there are many fascinating instances of hexagonality and sixness in these areas, and they will no doubt be treated more fully elsewhere at another time.