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Find all points X for which Z(X) is minimal - [ILL 1977]

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January 11, 2011
geometry proposedgeometry

Problem Statement

A hexahedron ABCDEABCDE is made of two regular congruent tetrahedra ABCDABCD and ABCE.ABCE. Prove that there exists only one isometry Z\mathbf Z that maps points A,B,C,D,EA, B, C, D, E onto B,C,A,E,D,B, C, A, E, D, respectively. Find all points XX on the surface of hexahedron whose distance from Z(X)\mathbf Z(X) is minimal.
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