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.