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IMO 1985 — Shortlist Question 2

IMO Shortlist · IMO 1985 — Shortlist

Question 2

(BRA 3) A polyhedron has 12 faces and is such that:
(i) all faces are isosceles triangles,
(ii) all edges have length either $x$ or $y$,
(iii) at each vertex either 3 or 6 edges meet, and
(iv) all dihedral angles are equal.
Find the ratio $x/y$.