For the second edition, he has added a section devoted to phi math itself, and, in response to many requests, has added a new polyhedron: the

truncated icosahedron, or Bucky Ball.

Since Plato's work, two other classes of equilateral convex polyhedra, as the collective of these shapes are called Archimedean solids (including

truncated icosahedron) and Kepler solids (including rhombic polyhedra).Equilateral convex polyhedra need to have certain characteristics.

The geometrical structure of [C.sub.60] is a

truncated icosahedron with a carbon atom at the corners of each hexagon and a bond along each edge (Figure 1).

Munari and his work served as a filter through which to (re) discover the performative furniture of artist and designer Martino Gamper (based in turn on works by Gila Ponti); the wall drawings, as beautiful as Japanese wallpaper, by Bruno Persat, which result from a series of arbitrated penalties (in which the ball, replaced by a

truncated icosahedron, is projected onto a wall covered in charcoal); or a fragment of Mark Geffriaud's imaginary house, for which he produces one of the architectural elements at each of his exhibitions (here, a stone step).

We use the fact that a football is a spherical version of the

truncated icosahedron, in which an icosahedron with 20 triangular faces has its 12 vertices cut off (truncated) to create the pentagonal faces.

The problem with this shape, compared with the

truncated icosahedron, is that its edges will be much more pointed.

For example, the

truncated icosahedron, which is the polyhedron giving the structure of the soccer ball, has two hexagons and a pentagon meeting at each vertex.

One example is the

truncated icosahedron, familiar as the pattern on a soccer ball, which consists of 12 pentagons and 20 hexagons.

In 1985, researchers in England and Houston suggested that vaporized carbon atoms from laser-blasted graphite might rearrange into exceptionally stable cage structures -- most notably a 20-sided

truncated icosahedron composed of exactly 60 carbon atoms (SN: 1/28/89, p.56).

Since then, the proposed structure for C.sub.60., officially called a

truncated icosahedron, has been joined by proposed structures for a slew of fullerenes with different numbers of carbon atoms.