Reprinting and adding from 2016 because I’m in a mathy mood.
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Cool people have always admired Bucky Fuller, and academic mathematicians spend lots of time dealing with optimal packings of shapes in space. Mathy packings always have a Bucky flavor. Fancy polyhedra jumbled in fancy ways.
In THEORY a sphere uses less material to surround a given volume. Even in theory the advantage is small. In practice the advantage is the other way around. Raw material isn’t the main expense for a house.
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Just for fun I tried a THEORETICAL comparison. The WPA Teacherage is the closest of my models to a dome-like shape. It’s about 30 wide x 30 long x 10 high without the roof. Including the roof, the volume is about 13k cubic feet, and the surface area of walls and roof is about 2600 square feet.
A hemisphere that nominally encloses the same volume is 36 feet in diameter, needing a slightly wider lot. NOMINALLY is a big word, since real rooms and furniture could only occupy about 2/3 of the hemisphere. Nevertheless, the surface area of this NOMINALLY equal volume is about 2000 square feet vs the 2600 of the rectangular house. Not much gain even THEORETICALLY.
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Aside from fine points of dimensions, the land, zoning permits, taxes, and utility connections will be the same for both. Contractor labor will be MUCH HIGHER for a dome because skills and tools and lumber are standardized for rectangular construction. Everything on a dome needs to be custom-made.
In plain reality, humans already found the optimal packing a long time ago.
Rectangles.
Any departure from a rectangle wastes space. The closer you get to a circle, the more waste.
Recent household appliances are growing more bulgy and circular**, which makes them harder to fit into a shelf. A bulgy box can’t hold more than a rectangular box, and a bulgy box claims more space than it needs.
Why is the rectangle naturally optimal? We don’t think of humans as rectangular, but in fact our boundary is rectangular in nearly all situations.
Standing:
Walking:
Sitting on a chair:
Sitting Korean style:
Laying down:
The ONLY exception is sitting cross-legged, which is not a common activity. In that pose we’re sort of trapezoidal:
But even when trapezoidal we don’t ‘pack’ hexagonally like the mathematicians think. We don’t do this:
We do this:
When we form groups of humans or things that aren’t purely randomish (milling around) we favor rows and columns.
Why? Because we don’t walk in zigzags. An efficient walk is a straight line, so rows of crops or livestock or merchandise or houses are most efficient in a straight line. Later on, the rows were further enforced by pipes and canals and wires and railroads, which are also more efficient when straight.
Our huts and houses can be either round or rectangular. Round houses (tipis, yurts) are favored by nomads who don’t settle in villages and don’t own furniture. The advantage of a tipi is not efficient space usage, it’s minimalist structural stability. A cone of logs is stable when tied with one rope.
When we settle down in permanent villages, with houses packed closely for protection and for convenient walking and utility service, the houses are rectangles.
So why is the Bucky stuff so wonderful? Damned if I know. It’s NOT efficient. It’s just dumb.
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** Bulgy appliances and computers were trendy in 2016. Fortunately the trend didn’t last long.
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Sidenote: There’s a Buckydome in this neighborhood. I sometimes see it on walks, though it’s partly hidden by trees. It’s smaller than the model above, and appears to have a rectangular addition and a basement with a garage. The city’s official plat map shows that it’s actually two domes with a rectangle between them, not quite squared off. Nicely illustrates the difficulty of mixing circles and rectangles.
Polistra's Mill 