Nonlinear Curvature-Free Periodic Folding in Origami via Symmetry Classification of Linear Modes
Abstract
Broadly studied origami crease patterns such as the Miura-ori are capable of rigid folding that maintains their spatial periodicity. However, periodic crease patterns generically require additional creases and fold into quasi-cylindrical shapes. Here, using group theory, we show that the folding properties of such sheets are largely determined by their spatial symmetries, known as layer groups. Within each symmetry class, the allowed linear shape-periodic modes of sheets are constrained and classified by the irreducible representation they belong to. Such classification further gives a sufficient condition, containing a symmetry constraint and a topological constraint, for the existence of a nonlinear strain mode. In this way, familiar special cases are placed within a unified framework that connects symmetry, network topology, and deployability. Finally, we turn our classification results into a predictive design principle that enables the rapid design of novel sheets with prescribed properties.
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BibTeX
@misc{cheng2026nonlinear,
title = {{Nonlinear Curvature-Free Periodic Folding in Origami via Symmetry Classification of Linear Modes}},
author = {Nan Cheng and Leon M Kamp and Yanxin Feng and Wenqian Sun and Katia Bertoldi and D Zeb Rocklin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08635},
eprint = {2610.08635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08635},
}
RIS
TY - UNPB
TI - Nonlinear Curvature-Free Periodic Folding in Origami via Symmetry Classification of Linear Modes
AU - Nan Cheng
AU - Leon M Kamp
AU - Yanxin Feng
AU - Wenqian Sun
AU - Katia Bertoldi
AU - D Zeb Rocklin
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08635
UR - https://arxiv.org/abs/2610.08635
AB - Broadly studied origami crease patterns such as the Miura-ori are capable of rigid folding that maintains their spatial periodicity. However, periodic crease patterns generically require additional creases and fold into quasi-cylindrical shapes. Here, using group theory, we show that the folding properties of such sheets are largely determined by their spatial symmetries, known as layer groups. Within each symmetry class, the allowed linear shape-periodic modes of sheets are constrained and classified by the irreducible representation they belong to. Such classification further gives a sufficient condition, containing a symmetry constraint and a topological constraint, for the existence of a nonlinear strain mode. In this way, familiar special cases are placed within a unified framework that connects symmetry, network topology, and deployability. Finally, we turn our classification results into a predictive design principle that enables the rapid design of novel sheets with prescribed properties.
ER -