Figure 1.
The structure of the C60 molecule.
(a) The polytope is formed by 60 vertices equidistant from its center. Its surface consists of 12 regular pentagons and 20 regular hexagons. All 90 edges are of the same length. (b) The
polytope viewed in the direction almost parallel to the plane spanned by
and
, which makes the
orbits (pentagons and decagons) easy to identify. (c) The
polytope viewed in the direction parallel to the
plane spanned by
and
. Surface edges of
are omitted in (b) and (c). Horizontal segments are projections of the
orbits. The number in a row shows the
coordinate of the
orbit. The vertical direction is that of
.
Figure 2.
The structure of the C70 molecule.
(a) The polytope has 105 edges and 12 pentagonal and 25 hexagonal faces. (b)
viewed from a direction almost parallel to the plane of
and
. (c) The
structure of
viewed from a direction parallel to the plane of
and
. The column of numbers shows the
-coordinate of the
orbits of vertices of
. The inserted decagon has the
-coordinate equal to 0. Surface edges are omitted in (b) and (c).
Figure 3.
The 12 pentagons of the surface of
are shown without the hexagons. The 60 dots are the vertices of
. The polytope is oriented as in Fig. 1.
Figure 4.
A ring of hexagons from the middle of the surface of
and
unwrapped into the plane. Horizontal lines indicate positions of the four
decagons in
and five
decagons in
. The dominant points identify the
decagons relative to the basis
. Dashed lines are the boundaries of the ring of five inserted hexagons.