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cuboid of volume V contains a convex polyhedron M, projection covers face

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1994 p2

February 20, 2020
cubepolyhedronVolumemax3D geometryprojectiongeometry

Problem Statement

A cuboid of volume VV contains a convex polyhedron MM. The orthogonal projection of MM onto each face of the cuboid covers the entire face. What is the smallest possible volume of polyhedron MM?
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