Abusing symmetry: Realizing complex 2D and 3D nanostructures with pluripotent DNA origami colloids*

The explosion in the diversity and complexity of nanoparticles that can be synthesized in recent years empowers programmable self-assembly of more and more complex nanostructures. However, the inverse design of different structures, even simple geometries like 2D planar crystals, is difficult. Here, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of 2D tilings of equilateral triangles. We also show that the application of our symmetry-based approach is not limited to two-dimensional tilings. By considering the angles between two neighboring triangles as an additional degree of freedom, we show how various 2D tilings can be wrapped onto different three-dimensional objects, including polyhedra, tubules, and toroids. To demonstrate the utility of our design approach, we synthesize DNA origami triangles that can bind edge-to-edge through DNA hybridization. By encoding the interaction specificity and the dihedral angles for each triangle, we assemble 2D tilings with various symmetries, as well as polyhedra and tubules using multiple species of triangles. Going forward, this work opens up pathways towards designing and assembling nanostructures with ever increasing complexity.