Problem

Source: 1976 USAMO Problem 4

Tags: geometry, 3D geometry, tetrahedron, Pythagorean Theorem



If the sum of the lengths of the six edges of a trirectangular tetrahedron $ PABC$ (i.e., $ \angle APB = \angle BPC = \angle CPA = 90^\circ$) is $ S$, determine its maximum volume.