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Proc Natl Acad Sci U S A. 2011 Dec 13;108(50):19885-90. doi: 10.1073/pnas.1110857108. Epub 2011 Dec 2.

Algorithmic design of self-folding polyhedra.

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Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA.


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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