A challenging problem of platonic solid by HCR

Geometry Level 5

A tiny sphere with radius 5 mm is resting in one of 12 vertices (corners) of a sufficiently large icosahedron (hollow thin shell type). Find out the minimum gap (in mm) between sphere & one of the five edges meeting at that vertex (corner).

Details and Assumptions:

  • Icosahedron is hollow thin shell & sufficiently large having a tiny sphere resting in one of its 12 vertices.

  • Sphere touches all five equilateral triangular faces meeting at that vertex.

  • Sphere doesn't touch any of five edges meeting at that vertex (corner) of icosahedron.


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