Investigators find new ways to fill space -- without cubes!
New Ways to Fill Space with Tetrahedra and Octahedra
•Filling space with polyhedra is a problem dating
back to at least to the ancient Greeks. Such space-filling structures (also
called “tilings”) have an intimate
relationship to the spatial arrangement of crystals, quasicrystals, and DNA, and have
important applications in communications, cryptography, information theory and
in the search for gravitational waves.
• It was long believed
that tilings associated with the fcc crystal and its
close relatives (called the “octet truss” by Buckminster Fuller) were the only tilings composed of regular tetrahedra and octahedra. In this work, we
have identified and analyzed a new family of a infinite number of periodic tilings of 3D space with
regular tetrahedra and octahedra. The periodic repeat
unit of the tilings contains an
octahedron contacting six smaller tetrahedra, which makes the tilings distinctly different and combinatorically richer than the fcc tiling.
• The repeat units of
our tilings resemble molecular
clusters with various symmetries.
How these clusters self-assemble determines their fundamental material
properties. These new tilings could be used to
model complex multi- component molecular and nano-particle systems under high pressure and enable one to
design unique building blocks for targeted self-assembly.
•J. Conway, Y. Jiao, and MRSEC Investigator, Sal Torquato PNAS 2011, in
press.
Updated on 11/02/2011