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.

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 |