Yet another project from "Amazing Origami" by Kunihiko Kasahara. This one starts with a two-sided regular octagon. Adding a few folds to the octagon creates this great UFO shape.
Here I'll just quote the book: "I would like to introduce you to a different technique here, called iso-area folding. This was invented by Toshikazu Kawasaki, a Japanese mathematician and prominent origami scholar."
Essentially, once this UFO is folded it creates a shape which can be turned (by pushing down on the top until it flips) and still have the same shape.