efficiency of 3d solids

I spent the weekend sketching, most times beginning with 7 straight lines that resemble a cube in perspective. The question of how closely I should adhere to my premise that a cube is the "best" shape kept coming to mind. I had based this premise on a general understanding, but I now needed to run the mathematics to give me a scale on how advantageous the house geometry really is.

This chart shows the surface areas of various shapes, each containing 1000 cubic units of volume. I mentioned in my last post several of the benefits to reducing surface area, and these results give me a sense of the factor of those benefits. (the "house" shape is a square house with a gable roof & in most cases the proportion of dimensions affects these figures.)

A relevant consideration is the fact that roofs & foundations are often much more expensive than walls, and they transmit heat in different ways, so the idea of minimizing footprint should be factored in with other decisions as well.

I was directed toward some great examples and discussion of cube houses by the folks at designcommunity.com. Here are a few inspirational pics: