This work focuses on the dynamic modeling and observation of polyhedral, growing crystals, emphasizing the importance of shape in particulate materials across various industries. Due to anisotropic molecular structures, crystal growth occurs at varying rates in different directions, leading to non-spherical, polyhedral shapes that can be symmetric under ideal conditions. The study is divided into three main parts. First, a system-theoretic framework is established to describe the evolution of single crystals and crystal populations. The second part discusses how to extract shape information from suspension images, which is then used to determine growth kinetics and model experimental outcomes. It reveals that models for single crystal development show hybrid dynamics when face numbers change. To extend this to the population level, the framework is broadened to include hybrid systems capable of velocity field switches or state space jumps. Morphology cones, representing different crystal shapes in state space, are identified, and it is found that they do not encompass the entire state space, reducing computational time for solving evolution equations. The modeling is complemented by a crystal shape observation scheme, utilizing an image processing routine to extract individual particle projections from 2D grayscale images. This method is validated against synthetic data and successfully applied to observe batch cooling crystal
