# Polyhedral angle

From Encyclopedia of Mathematics

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