The rhombic dodecahedron
is a convex polyhedron composed by 12 rhombuses (where the long diagonal is √2 times the short one). It is a Catalan solid dual to the cuboctahedron
. Many of them can come together to form a honeycomb as shown here
(see also this web
of Angel Requena). One can put one ball inside each cell to produce the face-centered cubic packing, the best one as states the famous Kepler conjecture
You can also form a honeycomb with soap bubbles:
But perhaps you might like to discover the symmetries of the rhombic dodecahedron in a funny way. Making this figure with felt allows to put vertices and edges inward, getting the symmetries of the tethrahedron, the cube or the octahedron surprisely clear!
|Folded to a "tetrahedron"|
|Folded to a "cube"|
|Folded to an "octahedron"|
[Added on February 27, 2014:] You can read this interesting article on the Rhombic dodecahedron
by Raul Ibañez.