# Hard tetrahedron model

The **hard tetrahedron model** is a subset of hard polyhedra model that has been put forward as a potential model for water^{[1]}.

## Maximum packing fraction[edit]

It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as ^{[2]} (the hard sphere packing fraction is ^{[3]}). 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"^{[4]}.

## Phase diagram[edit]

^{[5]}

## Truncated tetrahedra[edit]

Dimers composed of Archimedean truncated tetrahedra are able to achieve packing fractions as high as
^{[6]}^{[7]} while a non-regular truncated tetrahedra can completely tile space ^{[8]}.

## Virial coefficients[edit]

Virial coefficients ^{[9]}.

## References[edit]

- ↑ Jiri Kolafa and Ivo Nezbeda "The hard tetrahedron fluid: a model for the structure of water?", Molecular Physics
**84**pp. 421-434 (1995) - ↑ Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray and Sharon C. Glotzer "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature
**462**pp. 773-777 (2009) - ↑ Neil J. A. Sloane "Kepler's conjecture confirmed", Nature
**395**pp. 435-436 (1998) - ↑ J. H. Conway and S. Torquato "Packing, tiling, and covering with tetrahedra", Proceedings of the National Academy of Sciences of the United States of America
**103**10612-10617 (2006) - ↑ Amir Haji-Akbari, Michael Engel, and Sharon C. Glotzer "Phase diagram of hard tetrahedra", Journal of Chemical Physics
**135**194101 (2011) - ↑ Joost de Graaf, René van Roij, and Marjolein Dijkstra "Dense Regular Packings of Irregular Nonconvex Particles", Physical Review Letters
**107**155501 (2011) - ↑ Yang Jiao and Salvatore Torquato "A packing of truncated tetrahedra that nearly fills all of space and its melting properties", Journal of Chemical Physics
**135**151101 (2011) - ↑ Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces", ACS Nano
**6**pp. 609-614 (2012) - ↑ Jiří Kolafa and Stanislav Labík "Virial coefficients and the equation of state of the hard tetrahedron fluid", Molecular Physics
**113**pp. 1119-1123 (2015)

**Related reading**