The phase behavior of confined water is a topic of intense and current interest due to its relevance in biology, geology, and materials science. Nevertheless, little is known about the phases that water forms even when confined in the simplest geometries, such as water confined between parallel surfaces. Here we use molecular dynamics simulations to compute the phase diagram of two layers of water confined between parallel non hydrogen bonding walls. This study shows that the water bilayer forms a dodecagonal quasicrystal, as well as two previously unreported bilayer crystals, one tiled exclusively by pentagonal rings. Quasicrystals, structures with long-range order but without periodicity, have never before been reported for water. The dodecagonal quasicrystal is obtained from the bilayer liquid through a reversible first-order phase transition and has diffusivity intermediate between that of the bilayer liquid and ice phases. The water quasicrystal and the ice polymorphs based on pentagons are stabilized by compression of the bilayer and are not templated by the confining surfaces, which are smooth. This demonstrates that these novel phases are intrinsically favored in bilayer water and suggests that these structures could be relevant not only for confined water but also for the wetting and properties of water at interfaces.

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