The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces.

It is a space-filling polyhedron. These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.

Steinhaus, in his book 'Mathematical Snapshots' wrote:[The truncated octahedron] "fills the whole space in such a way that only 4 solids meet in each vertex; it is semiregular -which means that its faces are regular polygons. There is no other solid having these properties and thus it gives the simplest decomposition of space in congruent parts." (pag. 188)

LINKS

	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.
	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 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.
	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.
	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).