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 $\{$${10\overline{1}2}$$\}$ 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 $\{$${10\overline{1}2}$$\}$ twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when $c/a=\sqrt{3}$, 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 $\{$${10\overline{1}2}$$\}$ twins. During deformation, the state of the sample is monitored in situ 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 $\{$${10\overline{1}2}$$\}$ twin response at low and high pressures. When $c/a=\sqrt{3}$, 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 $\{$${10\overline{1}n}$$\}$ twinning modes, which have been suggested for Zn under high pressure, are not observed.