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1 Details on the nanoparticle synthesis. Fe 2 O 3 nanoparticles (γ-phase, maghemite) were synthesized by methods adapted from Hyeon et al. [28] 0.2 ml iron pentacarbonyl was injected into 10mL trioctylamine in the presence of 0.65g oleic acid at 250 o C. After being heated at 320 o C for 1 hour, the reaction mixture was cooled to room temperature and 0.17g trimethylamine N-oxide was added. Then the reaction mixture was heated to 120 o C for 1 hour to oxidize the iron nanoparticles to the γ-fe 2 O 3 phase. Fe 3 O 4 nanoparticles (magnetite phase) were synthesized using the method of Park et al [30]. Briefly, the iron-oleate precursor is prepared by reaction of 10.8 g iron(iii) chloride and 36.5 g sodium oleate at 60 C for 4 hours. For the 12.6 nm Fe 3 O 4 nanoparticle synthesis, 3.6 g ironoleate and 1.28 ml oleic acid are dissolved in 20 ml 1-octadecene, which is then heated to 320 C at a rate of 3 C/min and kept at 320 C for 30 minutes. 1

2 a b c d Supplementary Figure 1. (a) TEM image of (3 2,4,3,4) Archimedean tiling assembled from 12.6-nm Fe 3 O 4 and 4.7-nm Au nanocrystals. Inset is the corresponding electron diffraction pattern. (b) and (c) Higher magnification TEM images of (3 2,4,3,4) Archimedean tiling. The red dashed square represents the unit cell of P 4gm plane group. 2

3 Supplementary Figure 2. Selected area electron diffraction patterns with non-crystallographic 12-fold rotational symmetry measured from different samples of dodecagonal quasicrystalline phase self-assembled from 13.4-nm Fe 2 O 3 and 5-nm Au nanocrystals. Different thickness of DDQC domains introduced small differences in the relative intensities of the diffraction spots, but the packing symmetry remained the same for all studied samples. The electron diffraction patterns were measured from 6 µm 2 area. 3

4 Supplementary Figure 3. (a,b) Mapping a DDQC nanoparticle assembly onto square-triangular tiling. (c) An example of a local defect in DDQC lattice formed around several disclination points. The disclination strengths (n), shown as encircled numbers, can be calculated as n = 12( n 4 + n 6 ), where n sq and n tr are the numbers of squares and trangles which share sq tr 1 a common vertex. See Leung, P. W., Henley, C. L. & Chester, G. V. Phys. Rev. B 39, (1989) for more details on topological defects typical for DDQC phase. 4

5 doi: /nature08439 Supplementary Figure 4. Transition from single layer DDQC lattice to a multilayer structure. In multilayer domains the nanocrystals and (Au)6 clusters followed one-on-one packing seen as the contrast differences and moiré fringes (parallel stripes with period much larger than atomic lattice spacing). The moiré fringes originate from diffraction of electrons in a column of nanocrystals with mutually rotated atomic lattice planes. The structure self-assembled from 13.4nm Fe2O3 and 5-nm Au nanocrystals. 5

6 Supplementary Figure 5. In three dimensions the DDQC lattice can be described as a periodic stack of quasiperiodic layers. The superstructure in the right-bottom corner resembles a side view of such stacked quasiperiodic layers. The structure self-assembled from 13.4-nm Fe 2 O 3 and 5-nm Au nanocrystals. 6

7 Aperiodic Periodic 50 nm Supplementary Figure 6. TEM image of a DDQC superlattice projection viewed normal to the twelvefold symmetry axis. Inset shows the FFT pattern confirming co-existence of periodic and aperiodic crystallographic directions, orthogonal to each other. The structure self-assembled from 13.4-nm Fe 2 O 3 and 5-nm Au nanocrystals. 7

8 Supplementary Figure 7. TEM image of 12-fold quasicrystalline superstructure assembled from 12.6-nm Fe 3 O 4 and 4.7-nm Au nanocrystals. Inset is the corresponding electron diffraction pattern. Four types of Archimedean tiling elements are indicated: 3 6, 4 4, (3 2,4,3,4) and (3 3, 4 2 ). A minor distortion from perfect 12-fold symmetry seen in the electron diffraction pattern could originate from a finite size dispersion of nanoparticles or from local defects. 8

9 Supplementary Figure 8. Examples of small domains of DDQC lattice self-assembled from 13.4-nm Fe 2 O 3 and 5-nm Au nanocrystals. 9

10 doi: /nature08439 Supplementary Figure 8 (continued). An example of a large DDQC domain assembled from 13.4-nm Fe2O3 and 5-nm Au nanocrystals showing a transition from two-dimensional to threedimensional quasicrystalline nanocrystal packings. 10

11 Electrophoretic mobility of Au and iron oxide nanocrystals in TCE nm iron oxide nanocrystals 5 nm Au nanocrystals Intensity, (norm.) Mobility, m 2 /Vs 10-8 Supplementary Figure 9. Distribution of the electrophoretic mobilities in colloidal solutions of 10-nm Fe 2 O 3 and 5-nm Au nanocrystals in tetrachloroethylene. Electrophoretic mobility measurements were performed by optical interferometry using Zetasizer Nano ZS Series (Marvern) allowing measurements in non-polar organic solvents. The concentrations of additives (oleic acid) were similar to those used for self-assembly experiments. After preparation the colloidal solutions were left in dark for several hours to allow the systems to equilibrate before each measurement. 11