Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but
the mean tetrahedron volume is numerically
approximately equal to 
.
Octahedron Tetrahedron Picking
See also
Ball Tetrahedron Picking, Cube Tetrahedron Picking, Octahedron, Point Picking, Sphere Tetrahedron Picking, Tetrahedron, Tetrahedron Tetrahedron PickingExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Octahedron Tetrahedron PickingCite this as:
Weisstein, Eric W. "Octahedron Tetrahedron Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OctahedronTetrahedronPicking.html