Playing with a strange polyhedron

Geometry Level 3

Suppouse you have the following polyhedron:

  • It has 12 faces
  • All its faces are isosceles triangles
  • All its edges has length \(x\) or \(y\)
  • In each vertex you can find \(3\) or \(6\) edges
  • All dihedral angles are equal

Find \(\cfrac{x}{y}\)

Give your answer to 3 decimal places.


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