Several physical and mathematical ideas factor into building a geodesic dome. For example, a con-vexly curved surface is stronger than a flat one, most materials are stronger in tension than in compression, and the most rigid structure is a triangle. A hemisphere encloses the most space with the least amount of material while the tetrahedron encloses the least volume with the most surface. These principles make geodesic domes the strongest, lightest, most energy efficient buildings ever devised.
Geodesic domes are efficient structures in several ways. The triangle is a very stable shape; for example, a force applied to the corner of a rectangle can deform it into a parallelogram, but the same force will not deform a triangle. This makes geodesic dome buildings highly resistant to such forces as snow coverings, earthquakes, wind, and even tornadoes. The surface area of a geodesic dome is only 38% of the surface area of a box-shaped building enclosing the same floor space. There is less surface exposed to outdoor temperature fluctuations, making the building cheaper to heat and cool than a rectilinear structure. Geodesic domes can be constructed quickly without heavy equipment. Using prefabricated components, it takes just a few people to erect the dome for a 2,000-sq ft (185-sq m) home in 10 hours or less.
A geometric dome supports itself without needing internal columns or interior load-bearing walls. This property makes such structures appealing for use as churches, sports arenas, and exhibition halls. The aesthetic appeal of lofty ceilings makes them attractive as homes, and full or partial second-story floors are easily suspended halfway up the enclosure without any support other than attachment to the dome itself.