Gathering Folds

The border is not aligned with the repeats of Atolls, but I have a consistent amount of border all the way around the pattern.

Why is that? The repeats don't line up with the tiling breaks, and I've chosen to align my grid to the tiling breaks to get an even border.

This means that I folded a custom-rotated grid specifically suited to folding Atolls, and I figured it out from the crease pattern before this design was ever folded.
Yes, there was math involved, but the hardest part was figuring out how the tiling breaks matched up with the crease pattern.