A polyhedron with 20 faces. A regular
icosahedron has faces that are all equilateral triangles,
and is one of the five Platonic solids.
The length from vertex to opposing vertex
of a regular icosahedron is 51/4 φ1/2 d
where φ (phi) is the golden ratio
and d is the length of the side of one of the triangular faces. Chopping
off each vertex (corner) of a regular icosahedron reveals the 12 pentagonal
and 20 hexagonal faces of the truncated icosahedron, which
is one of the 13 Archimedean solids
(shapes made from truncating Platonic solids in certain ways).
In chemistry, icosahedral units are found in many boron
derivatives, e.g. B12H122-.