Hexagons are awesome: there one of only 3 regular polygons that tessellate (the others are triangle and squares). What makes them unique and awesome is that there are no diagonal neighbours. For example, each square has 8 neighbours: the 4 that share an edge and the 4 that share a corner. What makes the diagonals difficult is that there not the same distance away as the edge neighbours. If you’re trying to move around a square grid then you need to have rules that deal with diagonal movement and that’s messy. However for hexagons there’s no such issue: each hexagon is adjacent to 6 others and there are no diagonals.

That alone is enough to make hexagons awesome (and is why they are used in most wargames and has lead to the term hex and counter wargames to describe the paper based hobby. One other perk to hexagons is that they go together neatly: they lock each other in and can be put together to make much more satisfying shapes than squares. 3 hexagons make quite a pleasing little blob, but 3 squares makes a rather unsatisfying “L”. Triangles are too awkward and small to even bring up at this points.

However, one area where hexagons struggle is when buildings and cities are involved. In our cities (particularly modern ones) the 90′ angle reigns supreme: rectangles and squares are everywhere. Sure there are exceptions and there are triangular, octagonal, circular and even pentagonal buildings. However, the vast majority of our cities are made up of buildings that from above look like squares and rectangles. For a hexagon the natural angle is 60′ and some have tried to have city grids on this scale. However, the results just look wrong:

However, such a grid is easy to design and there is an evenness to moving along either set of roads. If we break this grid down: it’s a grid of parallelograms with a 60′ angle between the roads.

If we look at the tiles then we can make this with a single tile that doesn’t even need to be rotated:

So while this type of layout is possible, and actually pretty simple, it is awful aesthetically. On every street corner there is a copy of the Flat Iron Buiding. Which, while a spectacular building is a one of a kind for a reason.

Now you can put a rectangular grid onto a hexagon. One way is to basically cut each hexagon into quarters like this:

Now this gives you a pretty decent grid: not quite a square, but close enough. However, you need two different types of tiles and you have an ugly crack running down half your roads. You can see the two different tiles required below.

One thing you can do is merge these two tiles together:

Once you’ve done this you now only need one type of tile, but your grid is now much more rectangular, which depending on the type of developed area you are modelling, might be good. However, it still doesn’t site well with the majority of developed areas (humans love squares). You also still have cracks running down the centre of your roads.

So what to do with such a quandary. Well, all the designs you see just the hexagon symmetrically – what if we took our squarish grid and offset it a little:

Now this looks pretty good, and if you blow it up – you can see it’s actually all made from one tile that just needs to be rotated:

So, now that this is all said and done – maybe you’ve joined me for this theory maybe not. However, the perfect tile to build a nice urban area is the following:

By dropping some roads, adding some thin lanes (with similar geometry) we can put together some nice hexagonal developed sectors that can still be joined together, but will look nice and not be based around a crazy triangular geometry.