ILL 1985 Problem 28
a) Let be the set of the lengths of the edges of an octahedron whose sides are congruent quadrangles. Prove that has at most three elements.
b) 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.
Dataset text AI-MO AoPS. Quoted with source.
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