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MathNet 2016-part-02 — 184 problems (EN–VI) Question 85

Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)

Question 85

a) Prove that there exist two regular tetrahedra such that each edge of one is perpendicular to an edge of the other.

b) For an arbitrary regular tetrahedron, prove that there exists a unique tetrahedron with the above property.