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.
2026-03-27 07:13:34.1774595614
Packingof Spheres in 3D
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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 $\sqrt 2 -1$