A geodesic dome is constructed by subdividing each triangular face of an icosahedron into ν² smaller triangles, then projecting all vertices onto the circumscribed sphere.
Frequency ν: each edge is divided into ν equal segments. Higher ν → more triangles → more spherical, but more strut types. The ν=3 dome was popularized by Buckminster Fuller for the 1967 Montreal Expo.
Most subdivision methods produce 2 or 3 distinct strut lengths for low ν, rising with ν. The structure distributes loads efficiently — geodesic domes have the highest volume-to-surface-area ratio of any man-made structure.