Tetrahedral coordinates

of a point $P$ in three-dimensional space

Numbers $x_1,x_2,x_3,x_4$ which are proportional (with given coefficient of proportionality) to the distances from $P$ to the faces of a fixed tetrahedron, not necessarily regular. Analogously, one may introduce general normal coordinates for any dimension. The two-dimensional analogues of tetrahedral coordinates are called trilinear coordinates. See also Barycentric coordinates.

References

[a1]	H.S.M. Coxeter, "Regular polytopes" , Dover, reprint (1973) pp. 183