Could spacetime have crystalline properties? Space-time is currently modeled as a continuous manifold. However, space-time shares many features in general relativity that mimic a fluid-like thing. Fluids are certain states of matter and under certain circumstances they can turn into solids and form lattice-like crystalline structures. Thus, does general relativity and/or analogue models for space-time have some predictions for space-time crystalline-like lattice properties?
 A: I am going to make this brief. As pointed out space has a crystalline structure in LQG. This has some odd problems in that it violates Lorentz invariance on scales close to the scale length of the crystal. It also has to be remembered that spacetime is transformed by Lorentz boosts, so a crystalline structure in one frame involves a different spatial surface from the spatial frame and its crystalline structure in another. One can connect different spatial surfaces with null rays, which are invariant, and make transformations. However, this is computationally complicated.
With spacetime these null rays or segments can form polytopes with spatial elements. Whether these actually exist is dubious, for it seems unlikely there would be Lorentz violations on scales approaching quantum gravity. This is not to say one can't do numerics this way. With numerical relativity adaptive gridding has generally won the day. Regge calculus and discrete polytope structures are less common.
A: I don't know much about GR, but I'd be surprised if there was any reason to believe spacetime could have crystalline properties. I think there is a flaw in your logic in extrapolating the observation that 'spacetime shares some features with fluids' to indicate possible crystalline behaviour. For example, the Navier-Stokes equations that govern classical Fluid Dynamics don't in themselves account for any crystalline behaviour - formation of crystals is usually a feature of a phase change, which is modeled by other physical/thermodynamic equations.
So, I wouldn't think a comparison with 'fluid behaviour' would necessarily lead to the possibility of phase changes and formation of crystals. Perhaps it would be better to ask whether there is any indication that spacetime could undergo a phase change and solidify? What would that even mean, for spacetime to solidify?
