7 equdistant scenarios for closed ball locations

After this loads up (about 30 seconds)

to ZOOM in or out...
while holding down the SHIFT button
left click ( with the cursor over any of the 8 graphics displayed below ) and drag.

The grey dots above represent the 7 scenarios for the symmetrically determined locations for a closed ball.
The grey dots are shown as progressively larger...showing the two 3 spheres attached together.

The intervals given below are based upon spheres in a ccp, having a diameter of the square root of 2.
This results in, the ccp spheres all having integer only (x, y, z ) coordinates for their centers.

center of a sphere [1]
intervals at [Sqrt of (2n) ]
touch point [2]
intervals at [Sqrt of (2 + 4n)]
3 spheres [3]
intervals at [Sqrt of (6n) )] / 3
rotated 3 spheres [3]
intervals at [Sqrt of (1 + 6n)] / 3

tetrahedron of spheres [4]
intervals at [Sqrt of (3 +8 n) )] / 2
1/2 octahedron cluster [5]
intervals at [Sqrt of (1 + 4n)] / 2
octahedron cluster [6]
intervals at [Sqrt of (1 + 2n)]
These graphics were made in collaboration with Maurice Starck.
Several of the intervals calibrations were done by Mark Newbold