The traditional Navaho dwelling is the hogan, an octagonal structure made of logs. I would guess that the 8-sided shape is due to the unavailability of logs much longer than 10 feet. Assuming an inside wall length of 8 feet (i.e., 10-foot logs) a rectangular structure would have a floor area of 64 square feet, whereas an octagonal building made from the same logs would have about 309 square feet of interior space.

But not all hogans are made from logs. The stone hogan below lacks the canonical shape, which tends to confirm my theory that the octagonal form is a result of log length.

There are a number of traditional hogans in the Canyon, but most people who stay there for any length of time occupy more conventional frame structures - though they may maintain a nearby hogan for ritual reasons. This pattern is also seen outside the Canyon, where many people live in a frame building (frequently a single-wide trailer) but have an adjacent hogan. Often, the hogans are also frame buildings, retaining only the octangonal shape and running heavily to plywood and tarpaper for building materials.