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 x or y y with x > y x>y
  • In each vertex you can find 3 3 or 6 6 edges
  • All dihedral angles are equal

Find x y \cfrac{x}{y}

Give your answer to 3 decimal places.


The answer is 1.666.

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