Polar tetrahedral angle

A polar tetrahedral angle is a special kind of solid angle formed at a vertex of a regular tetrahedron. It is the angle at the vertex where three plane angles (the faces of the tetrahedron meeting at that vertex) come together. The 'polar' refers to the fact that this angle is measured at the 'pole' or vertex, and is often considered in relation to the geometry of the tetrahedron.

Important properties

• A polar tetrahedral angle is the solid angle at a vertex of a regular tetrahedron.

• It is formed by three plane angles (the faces) meeting at a point.

• The measure of a polar tetrahedral angle is less than $2\pi$ steradians.

• All four vertices of a regular tetrahedron have congruent polar tetrahedral angles.