Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

Carlos M. Duque, Douglas M. Hall, Botond Tyukodi, Michael F. Hagan, Christian D. Santangelo, Gregory M. Grason

Research output: Contribution to journalArticlepeer-review


We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Original languageEnglish (US)
Pages (from-to)e2315648121
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number18
StatePublished - Apr 30 2024


  • addressable assembly
  • programmable materials
  • self-assembly
  • self-closing assembly
  • triply periodic polyhedra

ASJC Scopus subject areas

  • General


Dive into the research topics of 'Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra'. Together they form a unique fingerprint.

Cite this