Robbins constant

In geometry, 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

$0.66170718226717623515583.$