Pick four points at random on the surface of a unit Sphere. Find the distribution of possible volumes of
(nonregular) Tetrahedra. Without loss of generality, the first point can be chosen as (1, 0, 0).
Designate the other points , , and . Then the distances from the first Vertex are
See also Point-Point Distance--1-D, Triangle Inscribing in a Circle, Triangle Inscribing in an Ellipse
Buchta, C. ``A Note on the Volume of a Random Polytope in a Tetrahedron.'' Ill. J. Math. 30, 653-659, 1986.