ABSTRACT
Geometric construction using folding methods proposed by Humiaki Huzita is based on marking figures using the tools of origami. Instead of a ruler and a compass, “creases” are used as tools to shape figures; i.e., a crease given by folding can simultaneously bring about coincidences of points and segments via reflection across the fold line. Huzita referred to these basic folding steps as “axioms” and defined seven such origami axioms [Huzita 91]. In this paper, I call them (origami) operations. There are eight operations for folding in the Euclidean plane; the eighth operation was added by Jacques Justin [Justin 91] and Koshiro Hatori. (See [Alperin and Lang 09] for details.)
In this paper, we try to create operations for spherical origami construction in order to know the essence of origami construction. We reformulate operations of planar origami construction into operations that act within spherical origami, with the condition that each point and its antipodal point on the sphere are to be set in our study. Considering the correspondence between two poles and the equator (a great circle) of the sphere, we clarify the essence of origami construction. Finally, we reduce the operations to four spherical origami operations.
