12 Identical Spheres can touch One Other Sphere

Theorem

A total of $12$ identical spheres can touch one other such sphere.

Each of the outer spheres touch the sphere in the center and $3$ other spheres.


Proof


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12$
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