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Part of 2010 Sharygin Geometry Olympiad

Problems(1)

Ratio of the edges of the icosahedrons (25)

Source:

For two different regular icosahedrons it is known that some six of their vertices are vertices of a regular octahedron. Find the ratio of the edges of these icosahedrons.

ratiogeometry3D geometryicosahedronoctahedrongeometry unsolved