Icosahedron subdivided into geodesic polyhedron: triangles = 20·f², vertices = 10·f²+2
Buckminster Fuller's geodesic dome subdivides each icosahedral face at frequency f into f² triangles, giving 20f² total triangles. The Goldberg polyhedron is the dual (faces↔vertices), yielding 12 pentagons + 10(f²−1) hexagons — the same topology as a soccer ball (C₆₀ fullerene at f=1). Euler's formula V−E+F=2 is satisfied at every subdivision level.