Hard polyhedra model
The hard polyhedra model is an approximation to describe the behavior of anisotropic colloidal particles with screened interaction.
It was first pointed out by Agarwal and Escobedo  the possibility that measures of shape could lead to a roadmap of the structures to be self-assembled: very anisotropic particles would lead to the formation of liquid crystals while very spherical ones would form plastic crystals at intermediate packing fractions.
Later, Damasceno, Engel and Glotzer . showed that, in addition to the sphericity of the particle (measured by calculating its isoperimetric quotient), by knowing the types of "bonds" that a given polyhedron is able to make already in the dense liquid the class of crystalline structure could be predicted. That was made possible due to the observation that facetted particles tend to maximize their face-to-face contacts at intermediate packing fractions. .
- Sharon C. Glotzer and Michael Solomon "Anisotropy of building blocks and their assembly into complex structures", Nature Materials 6 pp. 557 - 562 (2007)
- Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials 10 pp. 230–235 (2011)
- Pablo F. Damasceno, Michael Engel and Sharon C. Glotzer "Predictive Self-Assembly of Polyhedra into Complex Structures", Science 337 pp. 453-457 (2012)
- 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)
- de Graaf and Manna "A Roadmap for the Assembly of Polyhedral Particles", Science 337 pp. 417-418 (2012)
- Elizabeth R. Chen, Daphne Klotsa, Michael Engel, Pablo F. Damasceno, and Sharon C. Glotzer "Complexity in Surfaces of Densest Packings for Families of Polyhedra", Physical Review X 4 011024 (2014)