Although the properties of inorganic materials depend on their compositions and are so intricate to be simply put, they come from the interactions over local atomic coordinations, their connections, and the global crystal structure. We can see typical patterns of local atomic coordinations, where charged ions orderly fill up the space or electron orbits make bonds with certain symmetries in their environments. Crystal structures can take a variety of symmetries and atom coordinates, but the local environments of atoms, their connections, and the global symmetries often arise harmonically. Grasping these geometric concepts is thus fundamental for understanding and designing crystal structures. In machine learning literature, a method was developed for the geometric attribution of local atomic environments , and the order parameters were defined to systematically describe the coordinations . Our study has benefit from these work via Robocrystallographer , which was also used in recent work showing that graph neural network (GNN)'s performance could be augmented by using space group information , and informing both space groups and local atomic environments to a transformer-based architecture could improve the predictive performance . Another recent study focused on the shapes of motifs in crystals, analyzed the statistics of polyhedra, and developed descriptors for the machine learning of crystals . The concept of motifs was also introduced to improve the prediction performance of a GNN model . A mathematical insight on crystal structures was presented for generating space-filling polyhedra with satisfying some symmetries . We share their motivations but have been independently motivated to develop a way of integrally embedding in our model the foundational concepts of inorganic crystal structure: the local atomic environments, their connections, and the global symmetries.