Hard tetrahedron model

The hard tetrahedron model. Such a structure has been put forward as a potential model for water.

Maximum packing fraction

It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as $\phi =0.8503$ (the hard sphere packing fraction is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi/(3 \sqrt{2}) \approx 74.048%} ). This is in stark contrast to work as recent as in 2006, where it was suggested that the "...regular tetrahedron might even be the convex body having the smallest possible packing density".

Truncated tetrahedra

Dimers composed of truncated tetrahedra are able to achieve packing fractions as high as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi= 207/208 \approx 0.9951923}

References

Related reading

• Daan Frenkel "The tetrahedral dice are cast … and pack densely", Physics 3 37 (2010)