# notation for symmetry types

I am reading an article and in one of the sections the article mentions the symmetry group.

The symmetry group of one of the objects the article talks about is the dihedral group of order 12, using this as an example the article talks about symmetry types denoted as : I,G,DD,R2,SD,D.

What is the meaning of the notation ? It's easy to see from the article that I is the id, but that's all I managed to figure out.

Edit: : link to the article - page 7 in the pdf, table 1 it is also said that "we define a symmetry type to be conjugacy class of subgroups of G"

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It would help enormously if you indicated where this article could be found (ideally linked to it). – Qiaochu Yuan Mar 23 '12 at 23:07
@QiaochuYuan - added – Belgi Mar 23 '12 at 23:10
These are all defined in Table 1 on page 93 under the Effect column. $I$ does nothing, $G$ rotates $\pm\pi/3$, $DD$ rotates $\pm2\pi/3$, $R2$ by $\pi$, $SD$ are reflections through a coordinate plane and $D$ are reflections through a coordinate axis. – bgins Mar 23 '12 at 23:26
@bgins: No, Table I defines the operations; Table II defines the symmetry types. – joriki Mar 23 '12 at 23:27
Well together, they certainly define the meaning of the notation, dont't they? By the way, there is also another notation in Conway's relatively new book. It would be nice to see the lattice of subgroups for these. I think the reason they define the symmetry type as a conjugacy class is because each symmetry should be invariant, for example, under the effect of rotations or reflections. But I think this is all made clearer when you view them in a lattice. – bgins Mar 23 '12 at 23:39