# Packingof Spheres in 3D

I am looking to find out the size of the largest sphere , that can fit in the voids created by packing spheres ( hcp) of radius R.

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This question is not specifically related to Mathematica. Do you have some code that you have already begun working on? –  Hector Sep 18 at 16:34
Are you speaking of regular lattice sphere packings (and if so, which)? Especially if so, this is more a question about maths than use of Mathematica. –  kirma Sep 18 at 16:38
hcp == Hexagonal Close Packing .... –  george Sep 19 at 12:26
In Wikipedia under Positioning and Spacing it says there are two kinds of gaps. One is tetrahedral with a distance from the center of the gap to the center of the sphere $\sqrt {\frac 32}$ for unit spheres, so a sphere of radius $\sqrt {\frac 32}-1$ would fit. The other is octahedral, and will take a sphere of radius $\sqrt 2 -1$