Build table of cylinders that rotate about center of sphere?

c = Cylinder[{{0, 0, 0}, {0, 0, .95}}, 1/8];
b = Ball[{0, 0, 1}, 1];
Show [
Graphics3D[
{Opacity[0.5], c, b}
], Axes → True
]

Hi I’m new to Mathematica so pardon the newb questions.
I am unsure how to build a table of cylinders that rotate about the center of the sphere?
The object of this will ultimately be saved as an stl file for 3D printing.

The cylinder in Mathematica seem to have a cap, is there an option to turn that cap off or are the ends rendered?

You can use Table and Rotate:

c = Cylinder[{{0, 0, 0}, {0, 0, .95}}, 1/8];
b = Ball[{0, 0, 1}, 1];
Show[Graphics3D[{Opacity[0.5], b, 
   Table[Rotate[c, angle, {1, 0, 0}, {0, 0, 1}], {angle, 0, 2 Pi, 
     Pi/3}]}], Axes -> True]

To remove the caps you can parameterize the cylinder:

c = With[{r = 1/8}, 
    ParametricPlot3D[{r*Cos[t], r*Sin[t], z}, {t, 0, 2 Pi}, {z, 
      0, .95}, PlotPoints -> {20, 2}, Mesh -> None]][[1]];
b = Ball[{0, 0, 1}, 1];
Show[Graphics3D[{Opacity[0.5], b, 
   Table[Rotate[c, angle, {1, 0, 0}, {0, 0, 1}], {angle, 0, 2 Pi, 
     Pi/3}]}], Axes -> True]

Thank you so much… Very elegant.

I took the output from Show and Passed it to export…
output = show[…]
Export(“MyFile.stl”, output]
However only the cylinders appear.. the ball seems to have vanished.

I’m curious if i was supposed to have unified this into a single object somehow before exporting to stl?

I have no experience of stl export. Try Sphere instead of Ball.