An integrated geometric-graph-theoretic method for depicting origami structures and the truss frameworks that go with them

Abstract

Numerous intriguing uses for origami have been found in science and engineering. In 
order to create an inventive origami structure with the necessary qualities, appropriate 
representations and assessment of crease patterns are crucial. However, scientists and engineers 
that use origami in a variety of domains often face this difficulty. Graph products are a good option 
for the creation of crease patterns since the majority of useful origami structures have repeating 
unit cells. In order to depict crease patterns and the related truss frameworks of origami structures, 
we will use both directed and undirected graph products. We show that an origami crease pattern 
may be precisely defined by a certain graph product of independent graphs because the pattern can 
be thought of as a collection of directionless crease lines that meet the foldability criterion. It turns 
out that this combined geometric-graph-theoretic approach may be successfully used to the 
creation of various crease patterns and provide appropriate node and element numbering. 
Additionally, the provided technique improves configuration processing for geometric, kinematic, 
or mechanical study on origami structures by helping to create the required matrices and models 
of origami structures.