Robbins constant

In geometry, the Robbins constant, named after David P. Robbins, is the average distance between two points selected at random within a unit cube. Robbins constant can be expressed as

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

Its numerical value is approximately

$0.66170718226717623515582.$