The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ | = | 13/720 - π^2/15015 | = | 0.017398... (OEIS A093525; Mannion 1994; Schneider 1997, p. 170; Zinani 2003). This provides a disproof of the conjecture that the solution to this problem is a rational number (1/57 had been suggested by Croft et al. 1991, p. 54), and renders obsolete Solomon's statement that "Explicit values for random points in non-spherical regions such as tetrahedrons, parallelepipeds, etc., have apparently not yet been successfully calculated".
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