Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 108, Issue 50, Pages 19885-19890Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1110857108
Keywords
microfabrication; origami; programmable matter; viral capsid
Categories
Funding
- National Science Foundation Grants Division of Mathematical Sciences [0748482]
- Emerging Frontiers in Research and Innovation (EFRI) [1022638, 1022730]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0748482] Funding Source: National Science Foundation
- Emerging Frontiers & Multidisciplinary Activities
- Directorate For Engineering [1022638, 1022730] Funding Source: National Science Foundation
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Self-assembly has emerged as a paradigm for highly parallel fabrication of complex three-dimensional structures. However, there are few principles that guide a priori design, yield, and defect tolerance of self-assembling structures. We examine with experiment and theory the geometric principles that underlie self-folding of submillimeter-scale higher polyhedra from two-dimensional nets. In particular, we computationally search for nets within a large set of possibilities and then test these nets experimentally. Our main findings are that (i) compactness is a simple and effective design principle for maximizing the yield of self-folding polyhedra; and (ii) shortest paths from 2D nets to 3D polyhedra in the configuration space are important for rationalizing experimentally observed folding pathways. Our work provides a model problem amenable to experimental and theoretical analysis of design principles and pathways in self-assembly.
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