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Polyhedral angle

From Encyclopedia of Mathematics
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The infinite convex region in space bounded by a sequence of rays (emanating from one point, the vertex) and the angular regions between adjacent pairs of rays; in other words, a baseless pyramid. The angular regions are called the faces. A polyhedral angle is called regular if all its linear angles are equal and all its dihedral angles are equal. The measure of a polyhedral angle is the area bounded by the spherical polygon (see Fig.) which is obtained by the intersection of the faces of the polyhedral angle with a sphere of unit radius with centre at the vertex of the polyhedral angle.

Figure: p073610a

How to Cite This Entry:
Polyhedral angle. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Polyhedral_angle&oldid=15055