Dihedralkulmat

Dihedralkulmat is a term used in some geometric discussions to denote a family of formulas that describe how dihedral angles, the angles between adjacent faces of a polyhedron or molecular model, relate to one another within a given structure. The term fuses the English "dihedral" with kulmat, a word meaning angles in several languages; it is not a standard term in formal mathematics.

Definition and scope: A dihedral angle is defined by two intersecting planes along a shared edge. Dihedralkulmat refers to equations that connect these angles across a polyhedron, mesh, or conformational model, incorporating symmetry, curvature constraints, and consistency across the structure. Common patterns include equalities enforced by symmetry and relationships derived from spherical geometry on the dual graph.

Examples: In a regular tetrahedron, all dihedral angles are equal to arccos(1/3) (approximately 70.53 degrees); such uniformity is captured by dihedralkulmat in simplified form. In a cube, every dihedral angle is 90 degrees, another basic relation that dihedralkulmat expresses.

Applications: The concept is used mainly in computer graphics for mesh processing and shading, in molecular modeling to reason about conformations and steric constraints, and in architectural design for evaluating dihedral constraints in polyhedral frameworks.

See also: Dihedral angle, Polyhedron, Spherical geometry. Notes: The term is not universally standardized and may appear primarily in regional or informal writings. Further reading can be found in general discussions of dihedral angles and polyhedral geometry.