The volume of a truncated octahedron can be easily calculated if we know the volume of an octahedron.

The volume of an octahedron of edge length 1 is:

We can calculate the volume of an octahedron of edge length 3:

To calculate the volume of a truncated octahedron we have to remove to an octahedron of edge length 3 six pyramids. These six pyramids make 3 octahedra of edge length 1.

LINKS

	Leonardo da Vinci: Drawing of a truncated octahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the 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.
	Hexagonal section of a cube We can cut in half a cube by a plane and get a section that is a regular hexagon. Using eight of this pieces we can made a truncated octahedron.
	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.
	Leonardo da Vinci: Drawing of a cuboctahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the cuboctahedron.
	Leonardo da Vinci: Drawing of a dodecahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the dodecahedron.
	Leonardo da Vinci:Drawing of an stellated octahedron (stella octangula) made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the stellated octahedron (stella octangula).
	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.