Icosahedron which has 20 triangles, 12 vertices and 30 edges. The triangle subdivision of the icosahedron increases the number of triangles by a factor of 4. At each subdivision, the vertices are projected onto the sphere. At the subsequent level of refinement, we have (42, 80), (162, 320), (642, 1280), (2562, 5120), (10242, 20480), (40962, 81920) faces and vertices.
Credit: Moo K. Chung and Seong Ho Seo
Source: Heat Kernel Smoothing via Laplace-Beltrami Eigenfunctions, Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin–Madison