Science Fair Project Encyclopedia
All 28 Andreini tessellations are found in crystal arrangements.
(There are also a few other quasicrystal arrangements that are not Andreini tessellations. ).
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)    . Octet trusses are now one of the most common type of truss used in construction.
Some important examples are:
- The tiling of cubes
- The tiling of octahedra and cuboctahedra
- The tiling of truncated octahedra
- The tiling of octahedra and tetrahedra
- The tiling of tetrahedra and truncated tetrahedra
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