yup, I think we can put this in the discovery index as well.(in fact I did, it is a very short article called D4.14)Klitzing wrote:[...]
so Wendy thus contributed to CRFebruary ...
[...]
Anyway what I was trying to say by investigating the symmetries, is trying to find out what (reflective) subsymmetries all symmetries have. This image is said to show the hierarchy of symmetries:
![Image](http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Polychoral_group_tree.png/400px-Polychoral_group_tree.png)
Besides, I realized the things I've posted before (about the perp-space/para-space of lace-cities etc., introducing the (...)(...)-notation) were exactly the representations of the polytopes in the corresponding (duo)prism-symmetry. Let's take the representation of ex like this:(2f)(o5o3o)+(F)(o5o3x)+(f)(x5o3o)+(x)(o5o3f)+(o)(o5x3o). Actually that is the representation of ex in ike-prism symmetry, it can be written as AFfxo ooxoo5oooox3oxofo&#zx. Similarly (o5o)(x5x)+(f5o)(o5x)+(o5f)(x5o)+(x5o)(o5f)+(o5x)(f5o)+(x5x)(o5o) is the representation of ex in 5×5-duoprism symmetry, as ofoxox5oofoxx xoxofo5xxofoo&#zx. Now apart from (duo)prism-symmetry, most things also have some kind of antiprism symmetry. The .3.3.-representation of the .5.3.3.-uniforms has tetrahedral antiprismatic symmetry, and the .5.-representation of id has pentagonal antiprismatic symmetry. I think a notation for this might be usefull as well, to be able to write down the id=>pent.el.gyrobirotunda partial expansion.
P.S have I already said Wendy's discovery is quite awesome?