Starting from an icosahedron (20 equilateral triangle faces), each edge subdivision increases the face count by 4×. After frequency k, the sphere has 20·4^k triangular faces, all projected to unit sphere.
An icosahedron has 12 vertices, 30 edges, 20 faces (F=20·4^k). Geodesic frequency k=0 is pure icosahedron. Edge midpoints are normalized to the sphere surface, giving the geodesic approximation. Used in architecture (Buckminster Fuller), virology (capsid geometry), and finite-element meshing.