The self-assembly of shape-anisotropic nanocrystals into
large-scale
structures is a versatile and scalable approach to creating multifunctional
materials. The tetrahedral geometry is ubiquitous in natural and manmade
materials, yet regular tetrahedra present a formidable challenge in
understanding their self-assembly behavior as they do not tile space.
Here, we report diverse supracrystals from gold nanotetrahedra including
the quasicrystal (QC) and the dimer packing predicted more than a
decade ago and hitherto unknown phases. We solve the complex three-dimensional
(3D) structure of the QC by a combination of electron microscopy,
tomography, and synchrotron X-ray scattering. Nanotetrahedron vertex
sharpness, surface ligands, and assembly conditions work in concert
to regulate supracrystal structure. We also discover that the surface
curvature of supracrystals can induce structural changes of the QC
tiling and eventually, for small supracrystals with high curvature,
stabilize a hexagonal approximant. Our findings bridge the gap between
computational design and experimental realization of soft matter assemblies
and demonstrate the importance of accurate control over nanocrystal
attributes and the assembly conditions to realize increasingly complex
nanopolyhedron supracrystals.