The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to compute the mean tetrahedron volume in closed form for tetrahedron picking for some simple shapes. shape | V^_ ball tetrahedron picking | (12π)/715 cube tetrahedron picking | 3799/216000 - π^2/2160 octahedron tetrahedron picking | ≈0.01368 sphere tetrahedron picking | (4π)/105 tetrahedron tetrahedron picking | 13/720 - π^2/15015

mean line segment length | mean triangle area | tetrahedron picking