Tetrahedral coordinates

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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.


[a1] H.S.M. Coxeter, "Regular polytopes" , Dover, reprint (1973) pp. 183
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Tetrahedral coordinates. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article