ABSTRACT
Mirror inversion is a geometric operation closely related to physical paper folding. A cone can be rolled up from a fan-shaped sheet. The resulting shape, the upper part is mirrored, can also be made with one fan-shaped sheet, meaning that new fold lines are added on the crease pattern. The mirror inversion technique for making new shapes applies not only to cones but also to all kinds of three-dimensional origami. The mirrored half section matches the remaining half with no gap, as in the center illustration. Mirror inversion on a developable surface several times produces a variety of shapes containing curved folding. When a part of a solid is flipped by a mirror plane, the sweep locus is flipped together. If the plane, where the section line rests, and mirror surfaces are placed vertically, the sweep locus keeps traveling horizontally. The mirror plane arrangement determines the course of the sweep locus.
