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.
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| 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!
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| Rhombic dodecahedron |
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| Folded to a "tetrahedron" |
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| Folded to a "cube" |
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| Folded to an "octahedron" |
[Added on February 27, 2014:] You can read this interesting
article on the Rhombic dodecahedron by Raul Ibañez.
