---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21006'
abstract:
- lang: eng
  text: Modern experimental methods in programmable self-assembly make it possible
    to precisely design particle concentrations, shapes and interactions. However,
    more physical insight is needed before we can take full advantage of this vast
    design space to assemble nanostructures with complex form and function. Here we
    show how a substantial part of this design space can be quickly and comprehensively
    understood by identifying a class of thermodynamic constraints that act on it.
    These thermodynamic constraints form a high-dimensional convex polyhedron that
    determines which nanostructures can be assembled at high equilibrium yield and
    reveals limitations that govern the coexistence of structures. We validate our
    predictions through detailed, quantitative assembly experiments of nanoscale particles
    synthesized using DNA origami. Our results uncover physical relationships underpinning
    many-component programmable self-assembly in equilibrium and form the basis for
    robust inverse design, applicable to various systems from biological protein complexes
    to synthetic nanomachines.
acknowledgement: We thank B. Isaac and A. Tiano for their technical support with the
  electron microscopy and S. Waitukaitis for helpful comments on the manuscript. The
  TEM images were prepared and imaged at the Brandeis Electron Microscopy facility.
  This work was supported by the Gesellschaft für Forschungsförderung Niederösterreich
  under project FTI23-G-011 (M.C.H. and C.P.G.), the Brandeis University Materials
  Research Science and Engineering Center (MRSEC) under grant number NSF DMR-2011846
  (T.E.V., D.H. and W.B.R.) and the Smith Family Foundation (W.B.R.). Open access
  funding provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Maximilian
  full_name: Hübl, Maximilian
  id: 5eb8629e-15b2-11ec-abd3-e6f3e5e01f32
  last_name: Hübl
- first_name: Thomas E.
  full_name: Videbæk, Thomas E.
  last_name: Videbæk
- first_name: Daichi
  full_name: Hayakawa, Daichi
  last_name: Hayakawa
- first_name: W. Benjamin
  full_name: Rogers, W. Benjamin
  last_name: Rogers
- first_name: Carl Peter
  full_name: Goodrich, Carl Peter
  id: EB352CD2-F68A-11E9-89C5-A432E6697425
  last_name: Goodrich
  orcid: 0000-0002-1307-5074
citation:
  ama: Hübl M, Videbæk TE, Hayakawa D, Rogers WB, Goodrich CP. A polyhedral structure
    controls programmable self-assembly. <i>Nature Physics</i>. 2026. doi:<a href="https://doi.org/10.1038/s41567-025-03120-3">10.1038/s41567-025-03120-3</a>
  apa: Hübl, M., Videbæk, T. E., Hayakawa, D., Rogers, W. B., &#38; Goodrich, C. P.
    (2026). A polyhedral structure controls programmable self-assembly. <i>Nature
    Physics</i>. Springer Nature. <a href="https://doi.org/10.1038/s41567-025-03120-3">https://doi.org/10.1038/s41567-025-03120-3</a>
  chicago: Hübl, Maximilian, Thomas E. Videbæk, Daichi Hayakawa, W. Benjamin Rogers,
    and Carl Peter Goodrich. “A Polyhedral Structure Controls Programmable Self-Assembly.”
    <i>Nature Physics</i>. Springer Nature, 2026. <a href="https://doi.org/10.1038/s41567-025-03120-3">https://doi.org/10.1038/s41567-025-03120-3</a>.
  ieee: M. Hübl, T. E. Videbæk, D. Hayakawa, W. B. Rogers, and C. P. Goodrich, “A
    polyhedral structure controls programmable self-assembly,” <i>Nature Physics</i>.
    Springer Nature, 2026.
  ista: Hübl M, Videbæk TE, Hayakawa D, Rogers WB, Goodrich CP. 2026. A polyhedral
    structure controls programmable self-assembly. Nature Physics.
  mla: Hübl, Maximilian, et al. “A Polyhedral Structure Controls Programmable Self-Assembly.”
    <i>Nature Physics</i>, Springer Nature, 2026, doi:<a href="https://doi.org/10.1038/s41567-025-03120-3">10.1038/s41567-025-03120-3</a>.
  short: M. Hübl, T.E. Videbæk, D. Hayakawa, W.B. Rogers, C.P. Goodrich, Nature Physics
    (2026).
corr_author: '1'
date_created: 2026-01-20T10:02:19Z
date_published: 2026-01-08T00:00:00Z
date_updated: 2026-04-28T11:56:45Z
day: '08'
ddc:
- '570'
- '540'
department:
- _id: CaGo
- _id: GradSch
doi: 10.1038/s41567-025-03120-3
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1038/s41567-025-03120-3
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 8dd93da8-16d5-11f0-9cad-d2c70200d9a5
  grant_number: FTI23-G-011
  name: Dynamically reconfigurable self-assembly with triangular DNA-origami bricks
publication: Nature Physics
publication_identifier:
  eissn:
  - 1745-2481
  issn:
  - 1745-2473
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
  link:
  - description: News on ISTA website
    relation: press_release
    url: https://ista.ac.at/en/news/behind-natures-blueprints/
scopus_import: '1'
status: public
title: A polyhedral structure controls programmable self-assembly
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2026'
...