Is there a pictorial or symbolic way to represent each distinct symmetry of a polyhedron?
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1It is just a particular case of the answer you expect, but this is at least a start: http://en.wikipedia.org/wiki/Dihedral_group – Surb Aug 25 '14 at 10:07
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Here are a few other pages worth a look: Polyhedral group, List of spherical symmetry groups, Point groups in three dimensions (and pages linked to them) – Jean-Claude Arbaut Aug 25 '14 at 10:11
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None of these seem to provide a unique way to list each distinct symmetry? The sphere-like thing seems to classify the entire group "in general" by a single diagram. – ina Aug 25 '14 at 22:54
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Well, sure: You name the generating symmetries $\rho_0, \rho_1, \rho_2$ and the various symmetries are $\rho_0 \rho_1 \rho_2$ or $\rho_2 \rho_0 \rho_1 \rho_0 \rho_2$ or whatever. Are you looking for something more? – Nick Matteo Aug 26 '14 at 20:23
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Looking for a particular pictorial diagram (unique for each configuration), rather than operators – ina Aug 27 '14 at 20:29
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also, can you explain more about how to reduce to get a base set of generating symmetries? – ina Aug 27 '14 at 20:30