As much as I would like to take credit for the octagon shape instead of the more conventional rectangle for our house, we can't;  The structure was already there, built around 1983.  We decided to keep it that way, mostly to save by rebuilding over the existing foundations, and also by reducing the amount of red tape.

As I learned later, it turns out building an octagon is one of the most efficient shape for several good reasons, all listed below:

The Geometry of Green

Keep it simple. That is the advice from most green building gurus, especially regarding a home's footprint.  The fewer corners in a structure, the fewer materials and labor required to build it.  Unfortunately, few green advocates actually stick to that logic, building complex designs and shapes that erode resource efficiency.  But the funny thing is, according to simple physics (surface area to volume enclosed), a simple square or rectangle is actually not the most efficient shape after all.  - So, what is then?

A book that was once a best seller 150 years ago reveals in a logical and simple way what shapes the most efficient building are made of.  The program director of for Sustainable Conservation in San Francisco, Allen Dusault, a well known, published author and proponent of sustainable architecture, science and technology, explain his findings and its significant implications.  More

Advantages of the octagon plan

Compared with a square, an octagon encloses approximately 20% additional space with the same perimeter!

According to Fowler, who built his own octagon house right here in Fishkill, NY, an octagon house was cheaper to build, allowed for additional living space, received more natural light, was easier to heat, and remained cooler in the summer. These benefits all derive from the geometry of an octagon: the shape encloses space efficiently, minimizing external surface area and consequently heat loss / heat gain, building costs etc. A circle is the most efficient shape, but difficult to build and awkward to furnish, so an octagon is a sensible approximation.  Much more at Wikipedia