# 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 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 shell & sufficiently large having 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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