A regular icosahedron has 20 facets, each an equilateral triangle. My "dome" structure is a regular icosahedron; it's just missing the five bottom facets so it rests on a planar surface. The structure has 11 vertices, each connected via a stamped, galvanized steel plate (Star Plate) to which pine 2x2s are fastened with carriage bolts.

From Stromberg's Chicks Gamebirds and Poultry Supplies.