The dihedral angle is the angle between two planes. The dihedral
angle between the planes
which have normal vectors and is simply given via the dot
product of the normals,
The dihedral angle is therefore trivial to compute via equation (3) if the two planes are specified in Hessian
normal form
|
(5)
|
for planes
(Gellert et al. 1989, p. 541).
The dihedral angle between planes in a general tetrahedron is closely connected with the face areas via a generalization of the law
of cosines.
See also
Angle,
Contact Angle,
Hessian Normal Form,
Line-Line
Angle,
Plane,
Plane-Plane
Intersection,
Tetrahedron,
Trihedron,
Vertex Angle
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References
Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR
Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold,
1989.Kern, W. F. and Bland, J. R. Solid
Mensuration with Proofs, 2nd ed. New York: Wiley, p. 15, 1948.Referenced
on Wolfram|Alpha
Dihedral Angle
Cite this as:
Weisstein, Eric W. "Dihedral Angle." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DihedralAngle.html
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