A solid water phase commonly known as "cubic ice" or "ice I(c)" is frequently encountered in various transitions between the solid, liquid, and gaseous phases of the water substance. It may form, e.g., by water freezing or vapor deposition in the Earth's atmosphere or in extraterrestrial environments, and plays a central role in various cryopreservation techniques; its formation is observed over a wide temperature range from about 120 K up to the melting point of ice. There was multiple and compelling evidence in the past that this phase is not truly cubic but composed of disordered cubic and hexagonal stacking sequences. The complexity of the stacking disorder, however, appears to have been largely overlooked in most of the literature. By analyzing neutron diffraction data with our stacking-disorder model, we show that correlations between next-nearest layers are clearly developed, leading to marked deviations from a simple random stacking in almost all investigated cases. We follow the evolution of the stacking disorder as a function of time and temperature at conditions relevant to atmospheric processes; a continuous transformation toward normal hexagonal ice is observed. We establish a quantitative link between the crystallite size established by diffraction and electron microscopic images of the material; the crystallite size evolves from several nanometers into the micrometer range with progressive annealing. The crystallites are isometric with markedly rough surfaces parallel to the stacking direction, which has implications for atmospheric sciences.