Improving the precision and function of encapsulating three-dimensional (3D) DNA nanostructures via curved geometries could have transformative impacts on areas such as molecular transport, drug delivery, and nanofabrication. However, the addition of non-rasterized curvature escalates design complexity without algorithmic regularity, and these challenges have limited the ad hoc development and usage of previously unknown shapes. In this work, we develop and automate the application of a set of previously unknown design principles that now includes a multilayer design for closed and curved DNA nanostructures to resolve past obstacles in shape selection, yield, mechanical rigidity, and accessibility. We design, analyze, and experimentally demonstrate a set of diverse 3D curved nanoarchitectures, showing planar asymmetry and examining partial multilayer designs. Our automated design tool implements a combined algorithmic and numerical approximation strategy for scaffold routing and crossover placement, which may enable wider applications of general DNA nanostructure design for nonregular or oblique shapes.

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