Folding the Hyperbolic Crane

T he purest form of origami is widely considered to be folding only, from an uncut square. This purity is, of course, a modern innovation, as historical origami included both cuts and odd-sized sheets of paper, and the 20th-century blossoming of origami in Japan and the west used multiple sheets for both composite and modular folding. That diversity of starting material continues today. Composite origami (in which multiple sheets are folded into different parts of a subject and then fitted together) fell out of favor in the 1970s and 1980s, but then came roaring back with the publication of Issei Yoshino’s Super Complex Origami [Yoshino 96] and continues to make regular appearances at origami exhibitions in the form of plants and flowers. Modular origami (in which multiple sheets are folded into one or a few identical units that are then assembled) never really diminished at all; the kusudamas of the past evolved into the extensive collections of modulars described in books by Kasahara [Kasahara 88], Fuse [Fuse 90], Mukerji [Mukerji 07], and more. Even if we stick to uncut single-sheet folding, however, there are still ways we can vary the starting sheet: by shape, for example. There are numerous origami forms from shapes other than square, including rectangles that are golden ð1 : ð ffiffiffi