Hi yessirnosir!
I'm sorry that no one has taken up this question. It seems all of the "experts" must be on vacation. I saw your question the other day, but felt that someone else would be sure to help you out.
I'm afraid that i don't have time to go into a lot of detail here, but I'll hit the basics and check back with you.
The first thing that you need to do is turn your basketball texture pattern into a symbol. A symbol is illustrators name for a repeatable object. Since you want to tile the image across the surface of the sphere.
Once that is done, reopen your 3D dialog box and click the button that says "Map Art..." (it is just under the cancel button)
That dialog box will open and let you select your new basketball texture symbol and adjust the size and orientation to suit and give you a preview as well.
Best of luck to you.
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by: yessirnosirPosted on 2009-02-08 at 07:47:23ID: 23584025
continuing to hack around, I managed to cover the basketball surface by using Photoshop to do create a much larger sample of the dimple pattern -- large enough to cover the whole ball in Illustrator. But the end result isn't as smooth as I had hoped, and I've got some strange yellow artifacts in the dimple pattern, and some roughness around the edge of the ball.
So I'm still hoping someone will have some suggestions about how to make this look better. If not, I guess I'll close the question accepting my current output as the answer.
current version of file, with dimples applied to whole ball