# icosahedron

An icosahedron is 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 5^{1/4} φ^{1/2} *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. B_{12}H_{12}^{2–}.