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A dihedral angle is the angle between two intersecting planes or half-planes. It is a plane angle formed on a third plane, perpendicular to the line of intersection between the two planes or the common edge between the two half-planes. In higher dimensions, a dihedral angle represents the angle between two hyperplanes.
In geometry, dihedral angle is the angle between two planes. Aviation usage differs slightly from usage in geometry. In aviation, the usage " di hedral" evolved to mean the positive, up angle between the left and right wings, while usage with the prefix "an-" (as in " an hedral") evolved to mean the negative, down angle between the wings.
The dihedral angles for the edge-transitive polyhedra are: Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle
This fact can be used to calculate the dihedral angles themselves for a regular or edge-symmetric ideal polyhedron (in which all these angles are equal), by counting how many edges meet at each vertex: an ideal regular tetrahedron, cube or dodecahedron, with three edges per vertex, has dihedral angles = / = (), an ideal regular octahedron or ...
The concept of angles between lines (in the plane or in space), between two planes (dihedral angle) or between a line and a plane can be generalized to arbitrary dimensions. This generalization was first discussed by Camille Jordan . [ 1 ]
The solid angle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by Ω = q θ − ( q − 2 ) π . {\displaystyle \Omega =q\theta -(q-2)\pi .\,} This follows from the spherical excess formula for a spherical polygon and the fact that the vertex figure of the polyhedron { p , q } is a regular q -gon.
Dihedral angle, the angle between two mathematical planes; Dihedral (aeronautics), the upward angle of a fixed-wing aircraft's wings where they meet at the fuselage, dihedral effect of an aircraft, longitudinal dihedral angle of a fixed-wing aircraft; Dihedral group, the group of symmetries of the n-sided polygon in abstract algebra
The property of having a similar arrangement of faces around each vertex can be replaced by any of the following equivalent conditions in the definition: The vertices of a convex regular polyhedron all lie on a sphere. All the dihedral angles of the polyhedron are equal; All the vertex figures of the polyhedron are regular polygons.
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