Talk:Point groups in two dimensions
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[edit]It has been difficult for me to find good introductory material on the two-dimensional point groups, though I have had more success with searching for "rosette groups". I have found:
[http://www.math.ttu.edu/~drager/Classes/10MathCamp/handouts04.pdf Geometric Transformations and Wallpaper Groups: Symmetries of Geometric Patterns (Discrete Groups of Isometries)] is the best I could find. It's at 2010 Math Camp by Prof. Lance Drager.
It contains a proof that there are two infinite families of rosette groups: cyclic and dihedral.
It might also be nice to create some illustrations of elements in the group in action. Shall I do so? I'd make an illustration of rotation and reflection of a simple polygon - triangle or square or pentagon.
Lpetrich (talk) 17:10, 23 June 2011 (UTC)
- The foot diagrams are nice on the Frieze families. I've been working on a short summary article, with notations and simple diagrams, at List of planar symmetry groups. Tom Ruen (talk) 19:58, 23 June 2011 (UTC)
Needs more connection to rotational/reflection symmetry
[edit]I spent 15 minutes hunting wikipedia and google trying to make sense of this page, until I stumbled on rotational symmetry and reflection symmetry - I took one look at the images on the right sides of each page and instantly understood the entire Discrete Groups section. I'm not qualified to accurately insert the concepts into the page. — Preceding unsigned comment added by 98.225.79.39 (talk) 04:07, 9 March 2012 (UTC)
We could use some illustrations from other pages that demonstrate the symmetries, like from the Dutch version of this page: [1], and also from those symmetry pages. Like
| Cyclic group | Dihedral group |
|---|---|
| C1 (none) | D1 (bilateral) |
| C2 (up arrow, down arrow) | D2 (rectangle) |
| SO(2) (circle with direction) | O(2) (circle) |
I could work references to rotation and reflection symmetry into the text. Lpetrich (talk) 07:15, 9 March 2012 (UTC)
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