Robbins constant

The average distance between two points selected at random within a unit cube is often referred to as Robbins constant (after David P. Robbins). Robbins constant can be expressed as

$(4+17{\sqrt {2}}-6{\sqrt {3}}-7\pi )/105+1/5\ln(1+{\sqrt {2}})+2/5\ln(2+{\sqrt {3}})$.

Its numerical value is approximately

$0.66170718226717623515583$.