HCR's Theorem for dihedral angles in a regular n-gonal right pyramid

In this paper, a theorem is formulated and proved that yields generalized closed-form expressions for the dihedral angle between any two arbitrary lateral faces of a regular n-gonal right pyramid. The dihedral angles are expressed in terms of the apex angle, defined as the angle between two adjacent lateral edges meeting at the apex. The proposed formulation establishes a direct analytical relationship between the edge geometry at the apex and the corresponding dihedral angles of the pyramid. Due to its generality, the theorem applies to all regular and uniform polyhedra whose vertex configuration coincides with that of a right pyramid, as well as to regular n-gonal right prisms with an arbitrary number of sides. The resulting formulas are useful for geometric modeling, construction of physical models, and the development of computational algorithms for the analysis of polyhedral structures and equally inclined sets of concurrent vectors in three-dimensional space.