Planar Drawings of Origami Polyhedra

Abstract

This work studies the structure of origami bases via graph drawings of origami polyhedra. In particular, we propose a new class of polyhedra, called extreme-base polyhedra, that capture the essence of “extreme” origami bases. We develop a linear-time algorithm to find the “natural” straight-line planar drawing of these polyhedra. This algorithm demonstrates a recursive structure in the polyhedra that was not apparent before, and leads to interesting fractals.