ABSTRACT
This project was inspired by the intuition that origami must have some significant mathematical properties. Much of the origami commonly done in the United States folds flat; some origami is then made three-dimensional by manipulating the flat-folded paper to look more lifelike. The most common examples of this phenomenon are the flapping bird and the water bomb. Flat-foldability has been analyzed in [2] and [4]. However, there is nothing either artistically or mathematically which restricts one to folding paper flat. There are origami designs (though comparatively few) which require non-flat folds-creases where the dihedral angle is neither 0 nor 2n-for example, the traditional Masu box.
