Robert J Lang has something similar to your crane tessellation. His is unofficially called "crane on a plane"
It's essentially four 5-unit long center flaps (one for a head, 2 wings, and a tail) with a bird base in the middle. I couldn't find any pictures online but the crease pattern is in his second edition of Origami Design secrets on page 495 as an example of box pleating, if you have the book.