A cube intersected by a plane perpendicular to its diagonal can be cut in half. We get a section that is a regular hexagon.

Using eight of these half cubes we can build a truncated octahedron. This relation between the cube and the truncated octahedron can help us to understand that the truncated octahedron is a space-filling polyhedron.

The volume of this half cube is:

LINKS

	A truncated octahedron made by eight half cubes Using eight half cubes we can make a truncated octahedron. The cube tesselate the space an so do the truncated octahedron. We can calculate the volume of a truncated octahedron.
	The truncated octahedron is a space-filling polyhedron These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.
	The volume of a truncated octahedron The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces. Its volume can be calculated knowing the volume of an octahedron.
	Volume of an octahedron The volume of an octahedron is four times the volume of a tetrahedron. It is easy to calculate and then we can get the volume of a tetrahedron.
	The volume of the tetrahedron The volume of a tetrahedron is one third of the prism that contains it.
	Regular dodecahedron One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.