How to array sticks on the surface of sphere?

I’m really looking for the method to array sticks on the spherical surface regularly.

Like this figure, I want to array sticks or balls regulary without overlaping. But I can’t help but make sticks overlap around the North/South pole.

Please help! which function should I use?

For anyone else stumbling across this question:
You may use the Array on surface (ArraySrf) command with respect to a sphere.