Where does dihedral collide?

In geometry, a dihedral angle is the angle between two intersecting planes, or two half-planes sharing an edge, measured in the plane perpendicular to their line of intersection. It is the three-dimensional analogue of the ordinary angle between two lines and is fundamental to describing polyhedra, crystal faces, and molecular conformations. Coxeter's Introduction to geometry develops dihedral angles among the basics of solid geometry. The referent is the opening between two planes, and it is unrelated to a wing's upward set or an algebraic symmetry group apart from the shared term.[1]

Unit

The angle between two planes measured perpendicular to their common edge (degrees or radians)

Recovery means

Not applicable

Measured by

Computed from the planes' normal vectors or from the edge geometry

In aeronautics, dihedral is the upward angle of an aircraft's wings relative to the horizontal, seen from the front. It is a design choice that gives lateral, or roll, stability: when a wing dips and the aircraft sideslips, the lower wing meets the airflow at a greater effective angle of attack and generates more lift, rolling the aircraft back toward level. Etkin and Reid's Dynamics of flight: Stability and control treats the dihedral effect in lateral stability. The referent is a wing-setting angle that shapes handling, and it is a different construct from the angle between two geometric planes or a group of polygon symmetries, sharing only the word.[2]

Unit

The upward angle of the wing from the horizontal (degrees)

Recovery means

Not applicable

Measured by

Set as a geometric wing angle; its handling effect appears as the roll-due-to-sideslip derivative in stability analysis

In abstract algebra, the dihedral group is the group of symmetries of a regular polygon: its rotations together with its reflections. The dihedral group of the n-gon has 2n elements and is one of the first non-abelian groups a student meets, a standard example of how rotations and reflections compose. Dummit and Foote's Abstract algebra introduces the dihedral groups early as a running example. The referent is an algebraic symmetry group, and it shares only the word dihedral with a wing angle or the angle between two planes.[3]

Unit

The group of 2n symmetries (rotations and reflections) of a regular n-gon

Recovery means

Not applicable

Measured by

Not applicable; characterised by its order (2n) and its generators and relations