Thanks for all of your help. I have been able to obtain an original of this effect, complete with instructions and the prop. After further research, I have discovered that the proper topological name for the prop is a tetratetraflexagon. Mr. Maven's directions to the Japanese site was very helpful in visualizing the sequence and nature of the reveals. Even with the directions, it takes a knack.
I would think that this effect might be very popular in Japan, not only because of the effect itself but also because of the Japanese penchant for things folded. ?
Thanks again to everyone.
Those who don't believe in magic will never find it.