Editing Hard tetrahedron model
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It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as <math>\phi=0.8503</math><ref>[http://dx.doi.org/10.1038/nature08641 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)]</ref> (the [[hard sphere model |hard sphere]] packing fraction is <math>\pi/(3 \sqrt{2}) \approx 74.048%</math> <ref>[http://dx.doi.org/10.1038/26609 Neil J. A. Sloane "Kepler's conjecture confirmed", Nature '''395''' pp. 435-436 (1998)]</ref>). 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"<ref>[http://dx.doi.org/10.1073/pnas.0601389103 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)]</ref>. | It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as <math>\phi=0.8503</math><ref>[http://dx.doi.org/10.1038/nature08641 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)]</ref> (the [[hard sphere model |hard sphere]] packing fraction is <math>\pi/(3 \sqrt{2}) \approx 74.048%</math> <ref>[http://dx.doi.org/10.1038/26609 Neil J. A. Sloane "Kepler's conjecture confirmed", Nature '''395''' pp. 435-436 (1998)]</ref>). 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"<ref>[http://dx.doi.org/10.1073/pnas.0601389103 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)]</ref>. | ||
==Phase diagram== | ==Phase diagram== | ||
<ref>[http:// | <ref>[http://arxiv.org/abs/1106.4765 Amir Haji-Akbari, Michael Engel, Sharon C. Glotzer "Phase Diagram of Hard Tetrahedra", arXiv:1106.4765v2 Sat, 2 Jul (2011)]</ref> | ||
==Truncated tetrahedra== | ==Truncated tetrahedra== | ||
Dimers composed of Archimedean truncated tetrahedra are able to achieve packing fractions as high as <math>\phi= 207/208 \approx 0.9951923</math> | Dimers composed of Archimedean truncated tetrahedra are able to achieve packing fractions as high as <math>\phi= 207/208 \approx 0.9951923</math> | ||