andreini tessellation

The Andreini tessellations are tilings of three-dimensional space using Platonic and Archimedean solids such that all vertices are identical. They are special case of uniform tessellation . There are 28 such tessellations. See B. Grnbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56. All 28 Andreini tessellations are found in crystal arrangements. (There are also a few other quasicrystal arrangements that are not Andreini tessellations. http://www.cmp.caltech.edu/~lifshitz/symmetry.html). The tiling of octahedra and tetrahedra is of special importance since its vertices form a cubic close-packing of spheres. The space-filling trusses of packed octahedra and tetrahedra was apparently first discovered by Alexander Graham Bell and independently re-discovered by Buckminster Fuller (who called it the octet truss and patented it in the 1940s) http://tabletoptelephone.com/~hopspage/Fuller.html http://members.cruzio.com/~devarco/energy.htm http://www.n55.dk/MANUALS/DISCUSSIONS/OTHER_TEXTS/CM_TEXT.html http://www.cjfearnley.com/fuller-faq-2.html. Octet trusses are now one of the most common type of truss used in construction. Some important examples are:

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