Figure 1.
Schematic diagram showing the self-assembly of a cube from (A) six untethered panels and (B) six tethered panels.
Since the number of conformations is greatly restricted by tethering as in (B), self-assembly occurs with much higher yield.
Figure 2.
Schematic diagram of the net geometry.
The diagram shows the (A) cube and (B) octahedron net geometry and illustrates the different kinds of topological connections and hinges.
Figure 3.
Schematic diagram of all the eleven 2D (A) cube and (B) octahedron nets.
Figure 4.
Cube folding dynamics and octahedral conformations.
Two distinct folding dynamics during self-assembly were observed for cube nets: (A) net 5 follows pathway 1 and (B) net 3 follows pathway 2. Pathway 1 was characterized by independent folding of two clearly distinguishable sections of the net, which came together when the central hinge folded. Nets following pathway 2 have different folding rates for different sections of the net. Octahedron nets can fold into (C) non-convex boat-shaped or (D) regular octahedra.
Figure 5.
(A–C) Cubes and octahedra were classified according to the following criteria. (Ai–iii) “A” cubes have no defects. (Bi, Biii) “B” cubes may have one misaligned face, or display slight underfolding or overfolding. (Ci–iii) “C” cubes are (Ci) severely twisted, (Cii) have a missing or unfolded face, or (Ciii) have a severely misfolded/misaligned face. (D) All 11 cube nets were capable of folding into “A” cubes. (E) All 11 octahedron nets were also capable of all self-assembling into “A” octahedra. There are two conformations of the folding of the octahedron nets: the regular octahedron and the non-convex octahedron (boat shape). A common defect observed in the folding of octahedron nets was (F) a tetrahedron. All of these are 200-micron scale structures.
Figure 6.
Distribution of defects in order of decreasing yield of “A” category (A) cubes and (B) octahedra.
Violet denotes “A” category polyhedra; maroon denotes “B” category polyhedra; yellow denotes “C” category polyhedra; and light blue denotes “D” category polyhedra.
Figure 7.
Trends of yield vs compactness.
(A–B) Scatter plots of the percentages of “A” cubes and octahedra as a function of the number of vertex connections. (C–D): Scatter plots of the percentages of “A” cubes and octahedra as a function of Rg. The trend lines have the following R-squared values. (A) y = 0.1478x−0.0219, R2 = 0.74; (B) y = 0.063x−0.2972, R2 = 0.74; (C) y = −0.0048x+1.7387, R2 = 0.49; (D) y = −0.0052x+1.4345, R2 = 0.77.