Ball Tetrahedron Picking

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball.  random tetrahedra can be picked in a unit ball in the Wolfram Language using the function RandomPoint[Ball[], n, 4].

The mean tetrahedron volume of a tetrahedron formed by four random points in a unit ball is

(OEIS A093591; Hostinsky 1925; Solomon 1978, p. 124; Zinani 2003).

REFERENCES:

Groemer, H. "On Some Mean Values Associated with a Randomly Selected Simplex in a Convex Set." Pacific J. Math. 45, 525-533, 1973.

Hostinsky, B. "Sur les probabilités géométriques." Publ. Fac. Sci. Univ. Masaryk, No. 50. Brno, Czechoslovakia, 1925.

Kingman, J. F. C. "Random Secants of a Convex Body." J. Appl. Prob. 6, 660-672, 1969.

Sloane, N. J. A. Sequence A093591 in "The On-Line Encyclopedia of Integer Sequences."

Solomon, H. Geometric Probability. Philadelphia, PA: SIAM, 1978.

Zinani, A. "The Expected Volume of a Tetrahedron Whose Vertices are Chosen at Random in the Interior of a Cube." Monatshefte Math. 139, 341-348, 2003.