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
truncated octahedron. 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.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Bienenwabe_mit_Eiern_und_Brut_5.jpg/799px-Bienenwabe_mit_Eiern_und_Brut_5.jpg) |
Source: http://en.wikipedia.org/wiki/File:Bienenwabe_mit_Eiern_und_Brut_5.jpg |
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!
![](http://4.bp.blogspot.com/-JwwXS9z1kKc/T9EW32XnCbI/AAAAAAAAD0g/lL_DHkKWfs8/s640/IMG_4631.JPG) |
Rhombic dodecahedron |
![](http://1.bp.blogspot.com/-eBJMMPDyGe4/T9EW269pA9I/AAAAAAAAD0M/U4_UxaeoYJs/s640/IMG_4630.JPG) |
Folded to a "tetrahedron" |
![](http://3.bp.blogspot.com/-ElPNSEJsSB0/T9EW20KLdvI/AAAAAAAAD0E/rNI46f46hSk/s640/IMG_4629.JPG) |
Folded to a "cube" |
![](http://1.bp.blogspot.com/-0H4v0Vd4rxw/T9EW3GUj8DI/AAAAAAAAD0I/31QeBCmut7k/s640/IMG_4628.JPG) |
Folded to an "octahedron" |
[Added on February 27, 2014:] You can read this interesting
article on the Rhombic dodecahedron by Raul Ibañez.