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I will describe the packing of hard tetrahedra. Contrary to recent speculations, Monte Carlo simulations show that at finite temperatures this Platonic solid packs with quite high volume fractions and has very complicated, probably quasi-crystalline phases and (likely) a modestly complicated phase diagram. An analytic high pressure equation of state for hard particles that summarizes this data is given and compared to the simulation data. Interestingly, this system is shown robustly to have an only modestly first order transition from an isotropic fluid to a quasi-crystal (or quasi-crystal-like) structure. Contrary to speculations made two decades ago and not yet contradicted clearly in the literature, this suggests that the fluid to quasi-crystal transition can be described by a Landau theory. The likely order-parameter of that theory, and the likely structure of this theory will be discussed briefly.

Collaborators: Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Peter Palffy-Muhoray and Sharon C. Glotzer