This afternoon, I stumbled upon this phase diagram of water, showing the different phases of ice. Depending on temperature and pressure, solid water can have a large variety of crystal structures.
I couldn't avoid having a closer look: Ice-Nine exists!
from Landolt-Börnstein: "Physical properties of ice"
(DOI: 10.1007/10201909_90 - free PDF preview)
Fortunately, unlike its mythical cousin, the real Ice-Nine (labelled "IX" in the lower left corner of the diagram) cannot occur at ambient conditions, but exists as a metastable phase only below about -100 centigrade (170 K), and at pressures of a few kbar.
So, no danger that it may accidentally solidify all liquid water...