This is a edpos or equal distant points on a sphere. See the pdf files for the complicated math.
I tried several ways to mount the bottles (aluminum) to the sphere but this is the best.
Use a 2x4 jig to hold the caps at a 90 degree angle to the ball and glue with E6000. See photo of jig
This takes 50 caps
When dry put a drop of oit in the caps to allow the bottles to screw on and be more weather tight.
With the ball outside may fill with water and the bottles WILL fall off and distort the 3d ball.
Drill small pin holes for the water to escape if you want this in the rain.
The hanging wire should be longer than the one shown. Put a washer or ball bearing on the bottom as to support the weight and allow to spin.