Question: Connecting the dots on the surface

I have a number of dots that lie on the sphere. I want to draw a handsome sphere with three axes, put dots on the sphere and connect them. The problem is that some dots are pretty far from the other and so the line connecting them goes under the surface of the sphere and so is not seen. Therefore the question, how the dots can be connected so the line would be seen (or the line would lie on the surface of the sphere)?

Here's the

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