Check http://erikdemaine.org/thok/amletter.html for instructions on how to get an A-sized paper from letter paper, and http://erikdemaine.org/thok/squareto.html for square to A-sized paper.

This is my second fold of the model. I decided to use slightly thicker paper for the 24 modules, and thinner paper for the 8 hinges. The first time I folded it I have to admit I though "Never again!", because while assembling the model, a bit here or there kept falling apart. But then again, it unnerves me if something doesn't quite work. So after a couple of hours break I cut some more paper and gave it another try. My second fold is much more stable than the first one, so using thicker paper did help. And I think I was a bit more patient the second time round.

In the video, the modules used were folded from 52.5mm by 74.5mm sheets of paper. The resulting model has a diameter of approximately 13cm.

folded from 24 sheets of A9 paper (37.25mm by 52.5mm)
Finished model: approximately 9cm diameter