Given two regular tetrahedrons with edges of length $\sqrt2$, transforming into one another with central symmetry. Let $\Phi$ be the set the midpoints of segments whose ends belong to different tetrahedrons. Find the volume of the figure $\Phi$.
Problem
Source: - All-Russian MO 1998 Regional (R4) 11.7
Tags: geometry, 3D geometry, tetrahedron, Volume