tetrahedral faces OAB, OAC, OBC and ABC.

A useful formula for calculating the solid angle of the tetrahedron at the origin O that is purely a function of the vertex angles , , is given by L'Huilier's theorem as

where

Another interesting formula involves expressing the vertices as vectors in 3 dimensional space. Let be the vector positions of the vertices A, B and C, and let , , and be the magnitude of each vector (the origin-point distance). The solid angle subtended

1.Previous
3.Next