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 $x/y.$
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Tags: geometry, 3D geometry, polyhedron, angles, Euler s Theorem, IMO Shortlist
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 $x/y.$