An Octahedron
is a polyhedron with eight faces. For example, a cube with two of
its corners cut off is an octahedron.

A regular octahedron has eight
identical equilateral triangle faces, meeting four at each of its
vertices. Picture it as two square based pyramids with their bases
stuck together.

The crystals of some chemical compounds occur naturally
as regular octahedral, for example, alum.