The Simplex K with 4 Vertices in Dimension 3 is a Tetrahedron and :
K = determinant((x2-x1) , (x3-x2) , (x4-x3) ; (y2-y1) , (y3-y2) , (y4-y3) ; (z2-z1) , (z3-z2) , (z4-z3))
The Volume of this element is :
V(K) = abs(K) / 3!
If V(K) ~= 0 then K is Nearly Degenerated
Moussaoui