There's a classic story that uses a chemestry text as a Rosetta Stone to get a toehold on an exo-archeological expedition, because the properties of the elements prove to be something known to be in common with the aliens.
The elements are the same. But how might aliens organize and represent them?
Different (perhaps better) ways of laying out the table are already well documented.
But this XKCD cartoon (link for explain xkcd commentary) got me thinking...
Meanwhile, I have thought about alien alphabets and digits in the past. Considering a simple letterform (as opposed to a complex ideograph) it's actually very hard to invent something that's not already in Unicode for some writing system, as there are only so many ways to combine a small number of elementary strokes.
So, my question is: how might an alien race depict the compact symbols for elements that are somehow evocative of their nature? Suppose that the elegant symbols are applied to the lightest elements (and those known/important in antiquity) and the full table can be formed by adding modifications to the basic symbol to move to heavier rows.
The element's nature would be the bonding structure (count or shape), but I didn't want to limit it to that in case someone has other inspiration; the fact that carbon has so many hybrid bond types might be more important than any specific bond represented.
They could be like our symbols for astrology objects, used only for those things and not related to general writing. But it would be coolest if they were normal characters, exploiting the geometric nature of their (alphabetic or syllabic) writing system. (An ideographic writing system using pictograms of the Lewis bonding structure is just too lame. So emphasis on relatively simple character shapes: think ☿ not 辰星.)
Reopen: Jim2B says he has an objective answer; see his comments. So, it doesn't have to be "opinion based". Give it a try; you can always close it again if it's no good, but he's a high-ranked poster and I expect something good and interesting.