The shape of possibility

Access through your institution Buy or subscribe The Japanese began exploring origami around the sixth century, likely evolving alongside earlier paper-folding traditions in China. Only in the past few decades, however, has it become a subject of serious mathematical and engineering study, initially for packing solar-panel arrays into rockets. In recent years, other engineering uses have exploded — in robotics, medicine and beyond. Biologists have also discovered natural origami structures in many settings. The tiny protist Lacrymaria olor, for instance, extends its neck more than 30 times its body length by unfolding an intricate folded structure. A recent review shows how this ancient art form connects deeply with topology and geometry (Nat. Rev. Methods Primers 4, 40; 2024).Children learn to make a simple paper box with a few careful folds from a single square sheet. The result is a useful structure that isn’t ‘flat foldable’: it can’t be flattened into a plane, because of geometric constraints. This is an emergent property, independent of developability, determined by angle constraints and local foldability. A cone, for example, is developable but not flat foldable. This is a preview of subscription content, access via your institution Access options Access through your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any time Learn more Subscribe to this journal Receive 12 print issues and online access $259.00 per year only $21.58 per issue Learn more Buy this articlePurchase on SpringerLinkInstant access to the full article PDF.USD 39.95Prices may be subject to local taxes which are calculated during checkout Author informationAuthors and AffiliationsNature Physics https://www.nature.com/nphys/Mark BuchananAuthorsMark BuchananView author publicationsSearch author on:PubMed Google ScholarCorresponding authorCorrespondence to Mark Buchanan.Rights and permissionsReprints and permissionsAbout this articleCite this articleBuchanan, M. The shape of possibility. Nat. Phys. (2025). https://doi.org/10.1038/s41567-025-03128-9Download citationPublished: 10 December 2025Version of record: 10 December 2025DOI: https://doi.org/10.1038/s41567-025-03128-9Share this articleAnyone you share the following link with will be able to read this content:Get shareable linkSorry, a shareable link is not currently available for this article.Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative