Success! After posting to the blog last night that I had failed at figuring out this vase pattern, I sat back down in my chair, took one last look at the piece, and suddenly knew what I was supposed to do. A few folds later, and I had a completed vase.
Pattern is from "Amazing Origami" by Kunihiko Kasahara. It starts with a square piece of paper which is folded to create 6 60-degree angles, then cut to create a hexagon. This hexagon is then manipulated to become this lovely little vase.
And some bonus coverage of yesterday's project (which was finished late last evening and photographed under artificial light):
I think you can see the shape of it much better here.