Final stellation of the icosahedron 180 triangular faces, which are the outermost triangular regions in the stellation diagram. These join along 270 edges, which in turn meet at 92 vertices, with an Euler characteristic of 2. The 92 vertices lie on the surfaces of three concentric spheres. The innermost group of 20 vertices form the vertices of a regular dodecahedron; the next layer of 12 form the vertices of a regular icosahedron; and the outer layer of 60 form the vertices of a nonuniform truncated icosahedron. The radii of these spheres are in the ratio When regarded as a three-dimensional solid object with edge lengths
12 (number) is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number. If an odd perfect number is of the form 12"k" + 1, it has at least twelve distinct prime factors. A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for "any" arrangement of spheres (the Kepler