Analysis of filament orientations in one micrograph each of SOL and EDL. (A and D) Filament orientations in simple lattice (A; all filaments have same orientation; mean deviation angle = 0°) and no-three-alike superlattice (D; in any group of three filaments, in a line or forming a triangle, one filament is rotated by 60° with respect to the other two, which are identical; mean deviation angle for any three adjacent filaments = 30°). (B) Histogram for SOL micrograph showing mean deviation angle for the six filaments surrounding the central filament in a hexagon. The histogram peaks near 10°, close to the expected 0° for a simple lattice. (C) Deviation angle for adjacent filaments in SOL considered pairwise. The histogram peaks near to 0°, as expected for a simple lattice. (E) Mean deviation angle for the six filaments surrounding the central filament in a hexagon for EDL micrograph. The peak is close to 30°, as expected for a no-three-alike superlattice. (F) Deviation angle for adjacent filaments in EDL considered pairwise. There are two peaks, close to 0 and 60°, as expected for a no-three-alike superlattice (see D). Note: The relatively broad spread of the angle data is due partly to imperfections in the filament lattice, as seen in bending of the lines of filaments (Fig. 3), and partly to imperfections in particle picking due to thin filament proximity to thick filaments. Both factors affected the accuracy of angle determination. See also Fig. S5.