{"knowledge_schema": {"broad_category": "Materials Science \u2192 Crystallography \u2192 Interplanar Spacing", "refinement": "This problem involves calculating the interplanar distance for a specific crystallographic plane in a rhombohedral crystal system.", "specific_scope": "The focus is on the (111) plane of a rhombohedral crystal with given interatomic distances and angles.", "goal": "Calculate the interplanar distance of the (111) plane using the provided parameters."}, "summary": "This problem requires understanding the geometry of a rhombohedral crystal system to calculate the interplanar distance for the (111) plane. Given the interatomic distance and the angles, the task is to apply the appropriate formula for interplanar spacing in a rhombohedral lattice. The goal is to determine the correct interplanar distance from the provided options."}