Having no sub-symmetries in the icosahedron
star, the cosmofield cannot involve other than strong-like interactions.
Let [DELTA] be the regular icosahedron
that is dual to the dodecahedron in Section 7 (see Figure 7).
Ivan Sanderson discovered that there are 12 locations equidistantly apart on Earth where anomalies occur (Bermuda Triangle, Devil's Sea east of Japan, etc.), forming an icosahedron
The Magic 8 Ball's "advice" is generated at random, courtesy of an icosahedron
(a 20-sided die) that floats inside the cylinder of blue liquid.
They are the most symmetric fullerenes, with all of the rotational symmetries of a soccer ball or an icosahedron
The radius of wavefront ball is r, and twelve vertex coordinates of the regular icosahedron
are [P.sub.n]([x.sub.n], [y.sub.n], [z.sub.n]) (n = 1, 2,..., 12).
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).
Based on aforementioned design method, other polyhedrons in geometry, such as octahedron, dodecahedron and icosahedron
, can be adopted to project homogeneous and non-singular cloaks similarly.
Maehara  proved that, for the regular icosahedron
I, r([H.sub.I]) has 2 components, and exhibited a polytope P for which r([H.sub.P]) has 3 components.
From there it's on to the pyramid, diamond, and icosahedron
. The rest is up to you and your imagination.
Take, for example, the Dymaxion Map of Buckminster Fuller, which projects the world onto the surfaces of an icosahedron
(a 20-sided three-dimensional polyhedron) that may be unfolded in many directions.
For example, let [SIGMA] be the the complete 2-dimensional simplicial complex on 6 vertices and let [gamma] be the triangulation of [RP.sup.2] obtained by identifying opposite faces in an icosahedron
. Then [gamma] is a cellular spanning forest of [SIGMA] (and in fact E has twelve spanning forests of this kind).