Most of Leonardo's drawings for Pacioli's book, which was finished in 1498, are variations of the five shapes known as Platonic solids. These are polyhedrons that have the same number of faces meeting at each vertex: pyramids, cubes, octahedrons (eight faces), dodecahedrons (twelve), and icosahedrons (twenty). He also illustrated more complex shapes, such as a rhombicuboctahedron, which has twenty-six facets, eight of them equilateral triangles that are bordered by squares (fig. 58). He pioneered a new method for making such shapes understandable: instead of drawing them as solids, he made them see-through skeletons, as if constructed of wooden beams. His sixty illustrations for Pacioli were the only drawings he published during his lifetime. Fig.