What group might represent the symmetries of these carbon rings?

[askmathquestions]

The carbon rings in the upper-middle of this page https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/react3.htm such as corannulene or coronene possess symmetries. But, they are not the typical dihedral arrangements of points, like a single hexagon or single pentagon or single equilateral triangle.

So, what group represents the symmetries of tiles of hexagons, or tiles of triangles and so on?

 

[fresh_42]

The carbon rings in the upper-middle of this page https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/react3.htm such as corannulene or coronene possess symmetries. But, they are not the typical dihedral arrangements of points, like a single hexagon or single pentagon or single equilateral triangle.

So, what group represents the symmetries of tiles of hexagons, or tiles of triangles and so on?

This cannot be answered in such a generality. Every molecule has its own (not necessarily different) symmetry group. All that can be said is, that if $n$ is the number of vertices, then it is a subgroup of $\operatorname{Sym}(n),$ i.e. a finite group, which is more of a trivial fact than an answer.

This is subject to crystallography.