Under ambient conditions, Zn is a hexagonal metal with a large c/a ratio of 1.856. Plastic deformation is predominantly accommodated by basal ⟨a⟩ slip and compression twins on the {10-12} planes. Increasing hydrostatic pressure drastically reduces the c/a ratio of Zn and, when a critical threshold of c/a=√3 at about 10 GPa is crossed, the {10-12} twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when c/a=√3, remains unknown. Here, we strain-cycle a textured polycrystalline sample of pure Zn at uniform hydrostatic pressures ranging between 2 and 17 GPa, over which the c/a ratio crosses the c/a=√3 compressive-tensile transition for {10-12} twins. During deformation, the state of the sample is monitored through x-ray diffraction to extract texture and internal strain evolution. By comparing the experimental results with the predictions of an elastoviscoplastic polycrystal simulation, we confirm the androgynous nature of {10-12} twin response at low and high pressures. When c/a=3, polycrystalline Zn does not display any evidence of twinning and its plastic behavior is controlled by mostly basal and pyramidal ⟨c+a⟩ slip activity, with a very small contribution of prismatic ⟨a⟩ slip. Evidence for the activity of other {10-1n} twinning modes, which have been suggested for Zn under high pressure, are not observed.