  Expanding the library of self-assembled superstructures provides insight into
the behavior of atomic crystals and supports the development of materials with
mesoscale order. Here we build upon recent findings of soft matter
quasicrystals and report a quasicrystalline binary nanocrystal superlattice
that exhibits correlations in the form of partial matching rules reducing
tiling disorder. We determine a three-dimensional structure model through
electron tomography and direct imaging of surface topography. The 12-fold
rotational symmetry of the quasicrystal is broken in sub-layers, forming a
random tiling of rectangles, large triangles, and small triangles with 6-fold
symmetry. We analyze the geometry of the experimental tiling and discuss
factors relevant for the stabilization of the quasicrystal. Our joint
experimental-computational study demonstrates the power of nanocrystal
superlattice engineering and further narrows the gap between the richness of
crystal structures found with atoms and in soft matter assemblies.
