The peculiarities of crystal growth on a Nafion polymeric substrate from supersaturated aqueous solutions of initial substances were studied. The solutions were prepared based on deionized natural water and deuterium-depleted water. As was found earlier, in natural water (deuterium content 157 ± 1 ppm) polymer fibers are capable of unwinding towards the bulk of the liquid, while in deuterium-depleted water (deuterium content ≤ 3 ppm) there is no such effect. Since the distance between the unwound fibers falls in a nanometer range (which is close to the size of the unit cell of the crystal lattice), and these fibers are directed normally to the polymeric substrate, the unwinding can affect crystal growth on the polymer substrate. As was obtained in experiments with X-ray diffractometry, the unwound polymer fibers predetermine syngony of crystals, for which the unit cell is either a rectangular parallelepiped (monoclinic system) or an oblique parallelepiped (triclinic system). A quantitative theoretical model that describes the local interaction of the polymer substrate with the crystalline complexes is presented. Within this model, the polymer substrate can be considered as a flexible matrix for growing crystals.