Twelve identical circles touching one another on a sphere

Geometry Level 5

Twelve identical circles, each having a flat radius r, are touching one another at 30 different points (i.e. each one exactly touches five other circles) on a spherical surface with a radius R. Find out the ratio R/r.

Details: Each of 12 identical circles exactly touches other five circles without overlapping thus they are closely packed & covering up the whole sphere.

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