Curved foldings with common creases and crease patterns
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara and, Kotaro Yamada

TL;DR
This paper explores the mathematical possibilities of curved foldings in paper origami, revealing that four distinct non-congruent foldings can exist for a given crease and crease pattern, including two previously unknown configurations.
Contribution
It establishes that, generally, four non-congruent curved foldings are possible for a given crease and pattern, introducing two new configurations not previously documented.
Findings
Four non-congruent curved foldings identified
Two new folding configurations discovered
Enhanced understanding of origami crease pattern possibilities
Abstract
Consider a curve in a domain in the plane . Thinking of as a piece of paper, one can make a curved folding in the Euclidean space . The singular set of as a space curve is called the crease of and the initially given plane curve is called the crease pattern of . In this paper, we show that in general there are four distinct non-congruent curved foldings with a given pair consisting of a crease and crease pattern. Two of these possibilities were already known, but it seems that the other two possibilities (i.e. four possibilities in total) are presented here for the first time.
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Taxonomy
TopicsAdvanced Materials and Mechanics · Mathematics and Applications · Computational Geometry and Mesh Generation
