2017/09/11 by Hull, Thomas C., Tachi, Tomohiro
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1709.03210
In this paper, we will show methods to interpret some rigid origami with higher degree vertices as the limit case of structures with degree-4 supplementary angle vertices. The interpretation is based on separating each crease into two parallel creases, or double lines, connected by additional structures at the vertex. We show that double-lined versions of degree-4 flat-foldable vertices possess a rigid folding motion, as do symmetric degree-2n vertices. The latter gives us a symbolic analysis of the original vertex, showing that the tangent of the quarter fold angles are proportional to each other. The double line method is also a potentially useful in giving thickness to rigid origami mechanisms. By making single crease into two creases, the fold angles can be distributed to avoid 180^∘ folds, when panels can easily collide with each other. This can be understood as an extension of the crease offset method of thick rigid origami with an additional guarantee of rigid-foldability.