IMO 1966 LL HUN20

We are given three equal rectangles with the same center in

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IMO 1966 LL HUN20

Origin: HUN

Problem

We are given three equal rectangles with the same center in three mutually perpendicular planes, with the long sides also mutually perpendicular. Consider the polyhedron with vertices at the vertices of these rectangles. (a) Find the volume of this polyhedron; (b) can this polyhedron be regular, and under what conditions?