IMO 1985 LL FRG28

Let M be the set of the lengths of an octahedron whose sides

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IMO 1985 LL FRG28

Origin: FRG

Problem

Let M be the set of the lengths of an octahedron whose sides are congruent quadrangles. Prove that M has at most three elements. (FRG 1a) Let an octahedron whose sides are congruent quadrangles be given. Prove that each of these quadrangles has two equal sides meeting at a common vertex.