PROOF GAME "ODDITIES"
Symmetric diagrams are cool in chess problems. But symmetric play leading to a symmetric diagram is usually uncool, because it's repetitive and too obvious. Asymmetric play leading to a symmetric diagram is very cool (a) because it's more varied (b) it's paradoxical (c) it's rarer/harder to design.This is not an area where I have done much work, but it does interest me. It reminds me of Colonel George Sicherman's "Polyhex Oddities" described on www.mathpuzzle.com, where he makes a symmetric shape from an odd number of identical asymmetric tiles. I've stolen the name.
I will try to collect here over time symmetric positions in an odd number of plys. This was the theme of the retro composition tourney in Messigny, 1997. It's not an area that I've been very active, but I would like to do more work here in the future.
More humbly, here are all the PGs of 3.5 moves.