"jr" <cre### [at] gmailcom> wrote:
I have no idea (yet) what "C3" and "C4" symmetries
> might be; on the ever-increasing ToDo list.

Those are symmetry groups.  They're used to define, and simplify geometric
permustations (at least in chemistry wrt to molecule shapes and electron orbital
/ energy states)
https://en.wikipedia.org/wiki/Group_theory#Chemistry_and_materials_science

https://en.wikipedia.org/wiki/Group_theory

C refers to a cylcical group, where the number refers to how many dicrete ways
you can arrange something and have it be "different".

A circle is C1
A "double semicircle", theta, "half moon" is C2, since you can rotate it 180
deg, and so you have 2 symmetric orientations.
triangles C3
Squares C4
pentagons C5
Hexagons C6

It gets a bit complicated when you start looking at even the simple, yet
non-trivial structures
https://www.globalsino.com/EM/page3137.html

which is every bit as "fun" as it looks.  Especially when your Inorganic
Chemistry professor is ... special.  ;)

It would certainly be interesting to have a library of transforms that would
reorient things based upon symmetry groups, and then it would probably be
possible to analyze a given object to determine what symmetry group it was
in....

(and NO, at this point I'm not doing that.  :P  )


- BW

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