Pentacone reciprocal lattice

Even though it looks like a Klingon bi-directional interstellar ramjet, this is a 3D contour plot (the 700 electron scattering-unit isosurface) of a 118-atom carbon pentacone's reciprocal lattice. The non-central spikes (rows of blobs) intersect the model at top and bottom at a distance of g100 = 1/(2.13[A]) or about 0.48 reciprocal Angstroms from the "DC peak" at the center.
Note: The mouse allows you to re-orient and or spin the specimen, while the Shift key plus vertical mouse motion allows zooming in on the model for a closer look. Hitting the Home key allows you to return to the original point of view.
More on reciprocal lattices may be found here, while another example of naturally-occuring ``starship shapes'' may be found here and here.

One design element for the above structure is the 30-spike set of harmonics for zig-zag rows in the pentacone faces, shown below.

Another design element in the reciprocal lattice of a pentacone is the 30-spike set of harmonics for the adjacent atom-pair (armchair) rows in the pentacone faces, shown below. Although they don't appear in the contour plot above because they didn't meet the intensity threshold, their triple-intersections account for the bright near-g110 spots seen in diffraction patterns, and they provide elements of structure for possible starship shield-generators and/or cloaking-devices. The fact that the triple intersections occur just off the spike centers does not alter pentacone powder patterns because the projected areas don't increase. The significantly off-axis double intersections (points don't quite touch in the model below), however, do result in a powder diffraction satellite peak, thanks to the coherency spike that comes from viewing adjacent sheets along the bisector of the angle between them.

Copyright P. Fraundorf (2005) UM-StL Physics and Astronomy.