The original resource
"Tables for Group Theory" By Peter Atkins, Mark Child and Courtenay Phillips (1970). I have been using this 2008 version, in which Pg. 37 has the following table:
Some minor inconsistencies
These inconsistencies don't bother me as much as the ones in the next section, but I'm mentioning them because the existence of these inconsistencies could possibly offer a simple explanation for the ones that I describe in the next section (i.e. maybe they simply didn't put much effort into perfecting the diagrams).
- For C4 one of the lines is black instead of purple
- For C6 there's extra purple lines which seem to be spurious
- For C4, C5 and C6 some lines are different sizes when compared to the other lines in the same diagram, or when comparing the diagrams of C5 and C5h.
- If the Cnv series approaches a cone as n→∞, then the Dnh series would approach a circle as n→∞, but this is not depicted.
More uncomfortable inconsistencies
For the inconsistencies that were listed in the previous section, I'm comfortable concluding that the first three were just issues with aesthetics (poor work on the graphics), and that the other inconsistency was simply an oversight.
For the following two, I'm a bit more uncomfortable because they seem much less accidental:
- The purple lines in C4-C6 are perfectly parallel with beige lines, but for C2 and C3 they are not. This seems much less accidental than coloring a line black when all other such lines are purple.
- The purple lines in the Cn and Cnh series are just thin straight lines, but the Dn series has triangles. Perhaps in the Dn series, since there's two different types of appendages (beige and purple), they felt the need to use thicker triangles rather than just thin lines, so that the difference between the two types is made more obvious than it would be if they were just thin lines with different colors (rather than thick triangles with different colors). I'll ask a question about this inconsistency in a separate post, in line with the one question per post policy.
Are the C2 and C3 diagrams simply in error? For example, is there actually a molecule with a structure like depicted in the C2 diagram, or is it meant to be just a straight horizontal line with two appendages, like the O-O bond with two H appendages in H2O2, rather than a 3D diamond with two appendages?