Doesn't look like there's going to be an easy way to do this.

One thing which you can benefit from is that the pattern is symmetrical with
6 sides, like a cube. The corners of that cube are marked on the ball by
where 3 seams come together (in the image you provided, in the upper left,
upper right, lower left, and lower right, and there are four more we can't
see). So it may be possible to "cut" the sphere into 6 parts by using
gradient patterns with normals like <1,0,1>, and then make a single, square
image map which, when overlaid on top of these parts properly, creates the
seams in the right places.

 - Slime
 [ http://www.slimeland.com/ ]

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