Supplementary Figures

Supplementary Figures Spatial arrangement Variation in the morphology of central NCs (shape x size) x Variation in the morphology of satellite NCs (shape x size) x Variations in the spatial arrangement = Diverse HMNC architectures Supplementary Figure S1. Schematic illustration of the architectural diversity of heterogeneous metallic nanocrystals (HMNCs). The three axes are the three architecturedetermining elements of a HMNC, namely the shape and size of central and satellite nanocrystals (NCs) and their spatial arrangement. Variations in these architecture-determining elements generate an unprecedented diversity of HMNCs. 1

Satellite NCs Central NCs Supplementary Figure S2. Schematic illustration of the architectural diversity of the HMNCs through the tuning of the shapes of the central (vertical axis) and satellite NCs (horizontal axis). Only the most commonly synthesized shapes (octahedrons, cubes, and their truncated forms with different truncation degrees) are shown. The satellite NCs are all located on the corners of the central NCs. 2

Supplementary Figure S3. SEM (left column) and TEM (right column) images of the corner-satellite Au/AgPd HMNCs with Au central NCs in different polyhedral shapes. The central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. 3

Supplementary Figure S4. Large area SEM images of the corner-satellite Au/AgPd HMNCs with Au central NCs in different polyhedral shapes. The central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. The HMNCs are monodisperse in both size and shape. 4

Supplementary Figure S5. Comparison of (Row 1) the geometric models of central NCs in different polyhedral shapes, with (Row 2) the geometric models and (Row 3) SEM images of the corresponding corner-satellite HMNCs. The central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncation degrees respectively, and (D) cubes. The vertices of the central NCs and geometric centre of each satellite NC in the HMNCs are marked by. The location and number of geometric centres of the satellite NCs agree well with the corresponding vertices of the central NCs. 5

Supplementary Figure S6. Identifying the exposed facets of corner-satellite NCs in Au/AgPd HMNCs. Au central NCs are: (A) octahedrons, truncated octahedrons with (B) small and (C) large truncations, and (D) cubes. Column 1 and 2 are TEM images of the HMNCs viewed from the <100> and <110> directions respectively. The characteristic projection angles of an octahedron (90 in <100> direction; 109.5 and 70.5 in <110> direction) are marked. The insets are the corresponding (bottom left) geometric models and (bottom right) SEM images. Column 3 are HRTEM images of the square area marked in the TEM images in Column 2 and corresponding FFT patterns (as insets). The outlines of the satellite NCs and the {111} planes are marked in the HRTEM images. 6

Supplementary Figure S7. SEM (left column) and TEM (right column) images of the edgesatellite Au/AgPd HMNCs with Au central NCs in different polyhedral shapes. The central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. 7

Supplementary Figure S8. Large area SEM images of the edge-satellite Au/AgPd HMNCs with Au central NCs in different polyhedral shapes. The central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. The HMNCs were monodisperse in size and shape. 8

Supplementary Figure S9. Identification of the exposed facets of edge-satellite NCs in Au/AgPd HMNCs. Au central NCs are (A) octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. Column 1 and 2 are TEM images of the HMNCs viewed from the <100> and <110> directions respectively. The characteristic projection angles of an octahedron (90 in <100> direction; 109.5 and 70.5 in <110> direction) are also indicated. The insets are the corresponding (bottom left) geometric models and (bottom right) SEM images. The arrows in (A2) show the two obtuse angles with a dark contrast. The arrows in (B2) show the V-shape contrast boundary. Column 3 are the HRTEM images of the square areas in the TEM images in Column 2 and corresponding FFT patterns (as insets). The outlines of the satellite NCs and the {111} planes are marked off in the HRTEM images. 9

Supplementary Figure S10. Ag underpotential deposition (UPD) on central NCs. UV-vis spectroscopy of (A) Au NCs and (B) Au@Pd NCs before and after mixing with AgNO 3 solution. (C) EDX and (D) XPS survey spectra of NCs prepared by ascorbic acid reduction of AgNO 3 in the presence of Au@Pd NCs. The inset in (D) is a high resolution XPS spectrum of Ag 3d. 10

Supplementary Figure S11. NCs formed by the addition of H 2 PdCl 4 solution to the growth solution containing Au octahedral central NCs and ageing for 10 min. (A) TEM images of NCs; (B) HRTEM image showing the corner area of a NC. 11

Supplementary Figure S12. Edge-satellite HMNCs formed with Au@Pd core-shell central NCs. (A) TEM image of Au@Pd central NCs used for the preparation of HMNCs. (B) HRTEM image showing the core-shell structure of the NCs. (C-F) Morphology of HMNCs produced with Au@Pd core-shell central NCs shown in (A): (C) TEM image; (D) SEM image of the HMNCs; (E) and (F) HRTEM images showing the edge regions of the HMNCs. 12

Supplementary Figure S13. Au NCs in different polyhedral shapes. (A) Octahedrons, (B) and (C) truncated octahedrons with small and large truncations respectively, and (D) cubes. Column 1-3 are TEM images, SEM images and geometric models with corresponding SEM images of individual NCs viewed in different orientations. 13

Supplementary Figure S14. SEM (left column) and TEM (right column) images of HMNCs with satellite NCs in various shapes. The exposed facets for the satellite NCs are (A and C) {100} or (B and D) a combination of {111} and {100} facets. (A and B) are corner-satellite HMNCs and (C and D) are edge-satellite HMNCs. 14

Supplementary Figure S15. Large area SEM images of HMNCs with satellite NCs in various shapes. The exposed facets for the satellite NCs are (A and C) {100} or (B and D) a combination of {111} and {100} facets. (A and B) are corner-satellite HMNCs and (C and D) are edge-satellite HMNCs. The HMNCs were monodisperse in size and shape. 15

Supplementary Figure S16. Identification of the exposed facets of the HMNCs with satellite NCs in various shapes. The exposed facets for the satellite NCs are (A and C) {100}, and (B and D) a combination of {111} and {100} facets. (A and B) are corner-satellite HMNCs and (C and D) are edge-satellite HMNCs. Column 1 and 2 are TEM images of the HMNCs viewed from the <100> and <110> directions respectively. The characteristic projection angles of an octahedron (90 in <100> direction; 109.5 and 70.5 in <110> direction) and those of a cube (90 in both <100> and <110> directions) are shown. The insets are the corresponding (bottom left) geometric models and (bottom right) SEM images. Column 3 are HRTEM images of the square areas in the TEM images in Column 2 and corresponding FFT patterns (as insets). The outlines of the satellite NCs and the {111} and {100} planes are marked off in the HRTEM images. The green and red outlines represent {100} and {111} facets respectively. 16

Supplementary Figure S17. Composition of corner-satellite Au/AgPd HMNCs. (A) STEM images and element maps of corner-satellite HMNCs with octahedral central NCs and cornersatellite NCs with {100} facets. (B)-(C) STEM images, element maps, and line scans of individual corner-satellite HMNCs oriented in the <100> and <110> directions. The insets in (B) and (C) are: (1) STEM image; (2-4) elemental mapping of Au, Pd and Ag respectively; (5) the geometric model and (6) Ag element map showing the locations of the satellite NCs according to the geometric model; (7) The line scan profile along the red line shown in (1). 17

Supplementary Figure S18. Composition of edge-satellite Au/AgPd HMNCs. (A) STEM images and element maps of edge-satellite HMNCs with octahedral central NCs and edgesatellite NCs with {100} facets. (B)-(C) STEM images, element maps, and line scans of individual edge-satellite HMNCs oriented in the <100> and <110> directions. The insets in (B) and (C) are: (1) STEM image; (2-4) elemental maps of Au, Pd and Ag respectively; (5) the geometric model and (6) Ag element map with dotted lines showing the most intense signal; (7) Line scan profile along the red line shown in (1). 18

Supplementary Figure S19. TEM images of octahedral NCs in different sizes. (A) 33 nm, (B) 61 nm, and (C) 83 nm. 19

Supplementary Figure S20. Au/AgPt HMNCs consisting of octahedral Au central NCs and corner-satellite AgPt bimetallic NCs in octahedral shape. The AgPt satellite NCs were not solid but porous dendritic NCs with an overall quasi-octahedral shape. (A) Low magnification SEM image. (B) TEM image of the HMNCs viewed from the <110> direction. The right insets are elemental maps of Au, Ag and Pt respectively. The bottom inset is the line scan across the dash line shown in the TEM image. Elemental mapping and line scan measurements revealed Au in the centre and Ag and Pt in the satellite NCs. The equal distribution of Ag and Pt signal throughout the satellite NCs confirmed the formation of AgPt bimetallic satellite NCs. (C) HRTEM image of the square region in the TEM image in (B) indicating that the AgPt satellite NCs were single crystals with some ill-defined {111} facets. 20

Supplementary Figure S21. Ternary Au/Pd/AgPd HMNCs with a Au central NC, a cubic Pd shell and satellite AgPd NCs on the edges of the Pd shell. (A) Low magnification SEM and (B) TEM images. The satellite NCs deposited exclusively on the edges of the central NCs resulting in an excavated cubic shape with a depression in each facet. The Au central NCs could be seen in the TEM image as regions of darker contrast overlaid with Moiré fringes. The Pd shell and AgPd bimetallic satellite NCs did not generate significant mass contrast because of the similar atomic weights of Ag and Pd. 21

Supplementary Figure S22. Cubic Au@Pd core-shell NCs. (A) TEM image; (B) SEM image with inset showing the geometric model of the cubic Au@Pd NCs; (C) TEM image of single Au@Pd NC viewed along <100> direction; and (D) HRTEM image of the square area in (C). Inset in (D) is the FFT pattern. 22

Supplementary Notes Supplementary Note 1: Architectural Diversity of HMNCs The shape and size of component NCs and their spatial relationship are the architecturedetermining elements of a HMNC. Metal NCs can now be synthesized in a variety of polyhedral shapes. The geometry of the polyhedral NCs can be further varied through truncations or overgrowths in the corners or promoting growth in certain directions to yield different degrees of truncation (or overgrowth) and aspect ratios. In addition, the polyhedral NCs can be fabricated in various sizes. Thus we have quite a large library of NCs that can be assimilated into HMNCs. These polyhedral NCs can be arranged in many varied ways to form different spatial relationships. In this way an unprecedented diversity of HMNCs can be created through the detailed engineering of their architecture-determining elements (Supplementary Figure S1). We will demonstrate the architectural diversity with a simple case in Supplementary Figure S2, where binary HMNCs were assembled from octahedral and cubic component NCs and their truncated forms (in different degrees of truncation); and satellite NCs on the corners of the central NC. 20 HMNCs with different architectures are used as examples in Supplementary Figure S2. The selected architectures from the top most row and left most column of Supplementary Figure S2 will be used to demonstrate our synthesis strategy. Furthermore, the HMNCs can also be prepared from different combinations of metals and possess more than two types of component NCs. The multi-component HMNCs display an even higher architectural diversity because each component NC, with its own morphology and relative spatial arrangement, can be assembled combinatorially to increase the number of possible HMNC variants. 23

Supplementary Note 2: Structural analysis of corner-satellite Au/AgPd HMNCs The architectures of corner-satellite Au/AgPd HMNCs with central NCs in different polyhedral shapes (octahedrons, truncated octahedrons in different degrees of truncation (small and large), and cubes) are shown in Fig. 2 and Supplementary Figures S3-S6. A close examination of the EM images showed that each satellite NC was an octahedron seated on the corner of the central NC with the vertex of the latter as its geometric centre. For illustration, the geometric models of different polyhedral central NCs were compared with the geometric models and SEM images of the corresponding HMNCs viewed from the <100> directions (Supplementary Figure S5). The vertices of the central NCs and the geometric centre of each satellite NC in the HMNCs are marked as. Good agreements in terms of number and position were found between the vertices of the central NCs and the geometric centres of the satellite NCs. The increase in the number and proximity of corners in truncated octahedral central NCs resulted in some overlapping of the satellite NCs. The exposed {111} facets of the octahedral satellite NCs were further confirmed by analyzing the projection angles in the TEM images as shown in Supplementary Figure S6. An octahedral NC enclosed by {111} facets forms a rhombic projection with projection angles of 70.5 o and 109.5 o viewed from the <110> direction and a square projection with right angles from the <100> direction. These characteristic angles are marked in the TEM images of the HMNCs viewed from the <100> and <110> directions. The projection angles of the satellite NCs are consistent with the characteristic angles of an octahedron; thereby implicating the exposure of {111} facets. The exposed facets of the satellite NCs could also be inferred from the edge-on facets, i.e. facets parallel to the viewing directions which are projected as a line. An octahedron viewed from the <110> direction would have four facets projected edge-on as the boundary of the rhombus 24

projection. As outlined in the HRTEM images in Supplementary Figure S6, these boundaries are parallel to the {111} planes thereby confirming the exposure of {111} facets. Supplementary Note 3: Structural analysis of edge-satellite Au/AgPd HMNCs The architectures of edge-satellite Au/AgPd HMNCs with central NCs in different polyhedral shapes (octahedrons, truncated octahedrons with small and large truncations, and cubes) are shown in Fig. 2 and Supplementary Figure S7-S9. A depression in each facet can be clearly seen in the SEM images. There were two types of facets in the edge-satellite NCs: facets parallel to the surface of the underlying central NC (referred to as the outer facets) and facets facing the depressions (referred to as the inner facets). Both types of facets could be identified by TEM: outer facets from the outlines of TEM projections and inner facets from the contrast in the satellite NC projections. HMNCs with octahedral central NCs can be visualized as octahedrons with an excavated truncated trigonal pyramidal depression in each facet. The outlines of HMNCs in the TEM images are consistent with the projections of an octahedron suggesting that the outer facets of the satellite NCs were {111} facets. The inner facets were revealed by TEM imaged in the <110> direction. In this direction, the rhombic shaped projection showed a dark contrast in the two obtuse angle regions (arrows in Supplementary Figure S9A2). The contrast was caused by the two ridges parallel to the viewing direction. The facets of these two ridges were projected edgeon and defined the boundary of the dark region. The contrast boundary was parallel to the {111} planes, indicating that the inner facets of the depression were also {111} facets. 25

When small truncated octahedrons were used as the central NCs, the HMNCs were truncated octahedrons with an excavated truncated trigonal pyramidal depression in the {111} facets and a square pyramidal depression in the {100} facets. The TEM projections of HMNCs showed the characteristics of a truncated octahedron. Since the satellite NCs had a square pyramidal depression on the {100} facets of the underlying central NC with no facets parallel to the latter, the outer facets were exclusively {111} facets. Two facets of the square pyramidal depressions were projected edge-on in the <110> directions thereby giving rise to a thickness contrast with a V-shape boundary (arrows in Supplementary Figure S9B2). The contrast boundary of the Vshape was parallel to the {111} planes indicating that the inner facets were {111} facets too. Edge-satellite NCs deposited on highly truncated octahedral and cubic central NCs had rough surfaces. A closer examination of the EM images showed that the edge-satellite NCs were made of linear assemblies of small NCs on the edges of the central NCs. From the HRTEM images, these linearly assembled small NCs were not randomly oriented, but epitaxially grown on the central NCs. Their TEM projection angles in the <110> and <100> directions are consistent with those of an octahedron, indicating that these small NCs were overlapping octahedrons bound by {111} facets. The outlines of the satellite NCs were parallel to the {111} planes as shown in the HRTEM images which further confirmed the exposure of {111} facets. Supplementary Note 4: Ag underpotential deposition (UPD) on central NCs Ag + can be reduced on the surface of a second metal, such as Au NCs 18-21 and Pd single crystals 22, up to a monolayer coverage at potentials lower than its standard reduction potential. This process is known as the UPD. The formation of Ag UPD on the metal NCs in this study was inferred from two experimental observations (Supplementary Figure S10): no significant reduction of Ag + 26

in the presence of central NCs; and the formation of a Ag deposit on the central NCs with thickness around one atomic layer. a) It is known that Ag + cannot be extensively reduced by ascorbic acid with CTAB capping agent at room temperature. 18 When the ascorbic acid reduction of AgNO 3 was carried out in the presence of CTAB-capped Au NCs or Au@Pd NCs, UV-vis spectroscopy could not detect the reduction of Ag + to a Ag 0 phase (Ag NCs or a sufficiently thick shell on the seed NCs) significantly enough to interfere with the surface Plasmon resonance (SPR) of Au and Au@Pd central NCs to cause peak and intensity shifts in the latter (Supplementary Figure S10A-B). The lack of significant spectral changes after the central NC solutions were aged with AgNO 3 in sufficiently high concentrations suggests that no significant reduction of Ag + to Ag 0 had taken place. b) That said the reduction of Ag + did occur on the Au or Au@Pd surface up to a monolayer by the UPD process. The experimental evidence was provided by EDX and XPS. The results from the Au@Pd NCs will be used here as an example. The composition of Au@Pd NCs after mixing with the AgNO 3 solution in the presence of ascorbic acid and CTAB was analysed. EDX analysis detected a trace amount of Ag (3.73 atom%) on the NCs (Supplementary Figure S10C), which agrees well with the calculated value of 3.2 atom% for a Ag monolayer on a 55 nm octahedral NC. XPS of the same sample (Supplementary Figure S10D) measured the Ag atom% to be ~15.65 %. Since the XPS penetration depth is typically around 3 nm, the low Ag concentration measured by XPS suggests that the Ag layer on the NC surface was much thinner than 3 nm and was around one atomic layer thick. 27

Supplementary Note 5: Edge-selective deposition through Pd-coating on the central NCs Edge-satellite HMNCs were prepared by adding H 2 PdCl 4 solution to the central NC solution and ageing the mixture for 10 min before the addition of AgNO 3 solution. The TEM images taken after aging showed clear Moiré fringes with alternating bright and dark bands (Supplementary Figure S11A). These Moiré fringes, which are characteristic of Au@Pd core-shell NCs because of the Au and Pd lattice mismatch, suggest the formation of a Pd-coating on the Au central NCs during aging. The Pd-coating could also be identified in the HRTEM image (Supplementary Figure S11B) as a light contrast skin about 1.5-2 nm in thickness over a darker Au central NC. The lattice of the Pd-coating was in registration with the lattice of the central Au NC. For confirmation that edge-selective deposition was assisted by the Pd-coating on Au central NCs, Au@Pd NCs (with a 5 nm thick Pd shell) were used as the central NCs in the preparation of HMNCs (Supplementary Figure S12). Specifically the Au@Pd central NC solution was mixed with AgNO 3 solution and H 2 PdCl 4 solution in the same order as that used to promote the formation of corner-satellite HMNCs. Interestingly only edge-satellite HMNCs were formed in this case; showing that Pd-coating was essential for the edge-selective deposition of satellite NCs. Supplementary Note 6: Structural analysis of Au/AgPd HMNCs with satellite NCs in various shapes Fig. 3 and Supplementary Figure S14-S16 show the architectures of corner- and edge-satellite HMNCs where the exposed facets of the satellite NCs were {100}, or a combination of {100} and {111}. The central NCs were all octahedral. These two types of corner-satellite HMNCs could be visualized as octahedral central NCs with cubic or truncated octahedral satellite NCs on their six corners. The cubic shape satellite NCs are clearly identifiable in the SEM images. 28

Square projections in both <110> and <100> directions in the TEM images confirmed the exposure of {100} facets. Truncated octahedral satellite NCs had a more spherical appearance in the SEM images; and the outlines of their projections in HRTEM were parallel to either {111} or {100} planes, confirming the presence of both {111} and {100} facets. Edge-satellite HMNCs where the satellite NCs were bound by {100} facets appeared as three intercepting identical square prisms which were perpendicular to one another. The right projection angles viewed from the <110> and <100> directions confirmed the exposure of {100} facets. Edge-satellite HMNCs with satellite NCs enclosed by both {100} and {111} facets could be seen as truncated octahedrons with excavated truncated trigonal pyramidal depressions only in the {111} facets. The TEM projections showed the characteristics of a truncated octahedron. In this case, there were also facets parallel to the {100} facets of the central NCs. Therefore, the outer facets were a combination of {111} and {100} facets. The inner facets of the depression could be characterized by the outlines of the darker regions at the two obtuse corners where two ridges were projected parallel to the viewing directions with their facets projected edge-on. The parallelism to {100} planes indicated that the inner facets of the depression were {100} facets. Supplementary Note 7: Composition of Au/AgPd HMNCs The chemical composition of Au/AgPd HMNCs was analyzed by STEM-EDX. Corner- and edge-satellite HMNCs with octahedral central NCs; and satellite NCs with {100} facets; were chosen as examples and shown in Supplementary Figure S17 and S18 respectively. Cornersatellite HMNCs which were viewed in the <100> and <110> directions had a cross shape as shown in the STEM image and corresponding elemental maps (Supplementary Figure S17A). Elemental maps and line scans of <100> and <110> oriented corner-satellite HMNCs are given 29

in Supplementary Figure S17B and S17C respectively. Corner-satellite HMNCs with octahedral central NCs had six satellite NCs. When the HMNCs were oriented in the <100> direction, the six satellite NCs would appear differently as shown in Supplementary Figure S17B5: four as branches of the cross shape and the other two superimposed with one above and the other below the centre of the central NC. Elemental mapping detected Ag and Pd signals all over the cross shape with higher percentages of these metals in the centre. Au, on the other hand, was detected in the central regions only. Line scan measurements confirmed the same trend in elemental distribution with the intensities of the Ag and Pd signals in the centre nearly doubling those at the two sides. For corner-satellite HMNCs oriented in the <110> direction (where the octahedral central NC was projected as a rhombus with two sharp angles and two obtuse angles), the six satellite NCs would appear in the way shown in Supplementary Figure S17C5: one at each sharp corner of the rhombic projection of the central NCs and two superimposed at each obtuse corner. In elemental mapping, Ag and Pd were detected at the four corners of the rhombic projection of the central NCs with higher percentages of their presence in the obtuse corners. Line scans showed stronger Ag and Pd signals at the two sides corresponding to the corner-satellite NCs and a stronger Au signal in the centre corresponding to the central NCs. Edge-satellite HMNCs oriented near their <100> direction showed a square projection with a cross in the middle which was marked off in the STEM image and the element maps in Supplementary Figure S18A. The intense signals in the Ag and Pd elemental maps formed a cross shape (Supplementary Figure S18B). For the edge-satellite HMNCs oriented in the <110> direction, the Ag and Pd signals formed a ф shape in the element maps (rotated 90 o in Supplementary Figure S18C) corresponding to the edges of the rhombic projection of the 30

octahedral central NC. The equal distribution of Ag and Pd signals for both corner- and edgesatellite NCs confirms the formation of the bimetallic AgPd NCs. 31

Supplementary Methods Synthesis of polyhedral Au NCs Au NCs in various polyhedral shapes (octahedral, truncated octahedral with different degrees of truncation and cubic) were prepared first and used as the central NCs for the preparation of heterogeneous metallic nanocrystals (HMNCs). Synthesis of Au octahedral seed NCs. Au octahedral NCs were prepared first and used as seeds for the preparation of larger octahedral or other types of polyhedral NCs. The synthesis of Au octahedral seed NCs was based on a seed-mediated growth method using small Au NCs as seeds. For the preparation of small Au seed NCs, 7 ml 75 mm CTAB solution was prepared at 30 o C to dissolve the CTAB. 87.5 µl 20 mm HAuCl 4 solution was added to the CTAB solution. 0.6 ml of an ice-cold NaBH 4 solution (10 mm) was then injected quickly into the mixture under vigorous mixing to form a brown seed solution. Stirring continued gently at 30 o C for 2 to 5 hours to decompose the excess NaBH 4. The seed solution was then diluted 100 fold with ultrapure water. A growth solution was separately prepared by adding 25 µl 20 mm HAuCl 4 solution and 0.387 ml 38.8 mm ascorbic acid (in that order) into 12.1 ml 16.5 mm CTAB solution in a clean test tube at 28 o C with thorough mixing after each addition. 0.15 ml of the diluted seed solution was added to the growth solution and thoroughly mixed. The mixture was left unperturbed at 28 o C overnight. The color of the solution changed to pink indicating the formation of Au NCs. Synthesis of octahedral Au NCs. 5 ml of the octahedral Au seed solution was added to 12.5 ml of a growth solution containing 16 mm CTAB, 0.04 mm HAuCl 4 and 1.2 mm ascorbic acid to enlarge the octahedral Au NCs (to edge length of 45 nm). The mixture was thoroughly mixed and left unperturbed overnight. For the growth of larger octahedral NCs (edge lengths of 61 nm and 32

83 nm), 5 ml and 2 ml of the 45-nm octahedral Au NC solution were added to 12.5 ml of the abovementioned growth solution respectively. Synthesis of truncated octahedral Au NCs. 5 ml of the octahedral Au seed solution was added to 12.5 ml of growth solution. The growth solution for truncated octahedral Au NCs with small truncations was 16 mm CTAB, 0.04 mm HAuCl 4 and 2 mm ascorbic acid. For truncated octahedral Au NCs with large truncations, the growth solution contained 16 mm CTAB, 0.08 mm HAuCl 4 and 4 mm ascorbic acid. The mixture was thoroughly mixed and left unperturbed overnight. Synthesis of cubic Au NCs. The growth solution in this case contained 16 mm CTAB, 0.2 mm HAuCl 4 and 9.5 mm ascorbic acid. 6.5 ml of the octahedral seed solution was added to 12.5 ml of the growth solution to initiate the growth of cubic NCs. The mixture was thoroughly mixed and left unperturbed overnight. Synthesis of HMNCs. Synthesis of Au/AgPt HMNCs. The preparation of Au/AgPt HMNCs was similar to the preparation of corner-satellite Au/AgPd HMNCs except that H 2 PdCl 4 in the growth solution was replaced by H 2 PtCl 6 at the same concentration, and the reaction time was extended to one week. In particular, 36 µl 5 mm AgNO 3 and 0.155 ml 38.8 mm ascorbic acid were added to 3 ml octahedral Au NC solution. After thorough mixing, 60 µl 100 mm HCl and 42 µl 5 mm H 2 PtCl 6 were added in turns to the octahedral Au NC solution. The solutions were mixed well and left on the shaker for one week. 33

Synthesis of ternary Au/Pd/AgPd HMNCs. For the synthesis of ternary Au/Pd/AgPd HMNCs, a cubic Pd shell was grown on the Au octahedral central NCs. Specifically 0.375 ml 5 mm H 2 PdCl 4 and 0.644 ml 38.8 mm ascorbic acid were added to 12.5 ml of Au octahedral seed solution. The mixture was thoroughly mixed and left unperturbed overnight. For the deposition of satellite AgPd NCs on the cubic Au@Pd NCs, 36 µl 5 mm AgNO 3 and 0.155 ml 38.8 mm ascorbic acid were added to 3 ml cubic Au@Pd NC solution. After thorough mixing, 60 µl 100 mm HCl and 60 µl 5 mm H 2 PdCl 4 were added consecutively to the cubic Au@Pd NC solution. The solutions were mixed well and left on the shaker overnight. 34