Thursday, June 7, 2012


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
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!

Rhombic dodecahedron

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.