# Why does the image of cyclo[18]carbon look like a nonagon?

The $$\ce{C18}$$ allotrope cyclocarbon has been synthesized and imaged.[1] Science has most details behind a paywall, but this discussion includes an image:

In this octakaidecagonal molecule, each $$\ce{\color{blue}{C}}$$ is bonded viz. $$\ce{C-\color{blue}{C}#C}$$. Yet the above image looks like a nonagon. Why does every other carbon atom stand out as an obvious vertex while the others don't? My thoughts:

• The internal angles are close to $$180^\circ$$, making vertices hard to see. However, I wouldn't expect the internal angles of this octakaidecagon to differ much.
• I wonder if this molecule has a delocalised ring analogous to the one in benzene. On this idea, each of the nine visible edges could alternate between the states $$\ce{C-C#C}$$, $$\ce{C#C-C}$$. But this wouldn't explain why "odd" vertices have one appearance while "even" ones have another. I'm not convinced of this idea anyway, because it would average out to $$\ce{C=C=C}$$, unlike the $$1.5$$-bonds in benzene.

### References:

1. Kaiser, K.; Scriven, L. M.; Schulz, F.; Gawel, P.; Gross, L.; Anderson, H. L. An sp-hybridized molecular carbon allotrope, cyclo[18]carbon. Science 2019, eaay1914. DOI: 10.1126/science.aay1914.
• Aug 16, 2019 at 20:39

Nevertheless, the actual AFM images of $$\ce{C18}$$ are in Figs. 3Q and 3R. They are referred to as "AFM far" and "AFM close" respectively because of the height of the probe ($$\Delta z$$):
One can indeed see that there is 9-fold symmetry (technically, $$D_\mathrm{9h}$$). This implies that $$\ce{C18}$$ has a 'polyyne' structure in which there are two different types of bonds $$\ce{-C#C-C#C-\phantom{}}$$, rather than a 'cumulene' structure in which every bond is equivalent $$\ce{=C=C=C=C=}$$ (prior to this, computational studies had been equivocal as to which form was more stable).
Assigning the bright features in the “AFM far” images to the location of triple bonds, we observed curved polyyne segments with the expected number of triple bonds: 5 in $$\ce{C22O4}$$ and 8 in $$\ce{C20O2}$$. At small tip height, we observed sharp bond-like features with corners at the assigned positions of triple bonds and straight lines in between. This contrast was explained by CO tip relaxation, in that maxima in the potential energy landscape, from which the tip apex was repelled, were located above the triple bonds because of their high electron density. In between these maxima, ridges in the potential landscape led to straight bond-like features.
(The two bright spots outside the ring are due to individual $$\ce{CO}$$ molecules.)