I have in possession a German helmet, namely an M40(?) with a factory mark of Q66. The Q stands for Quist, a German factory that produced these helmets in Esslingen. What I do not understand about this particular helmet is the decals on the sides. The swastikas on the decals are reversed. My best guess on why this is the case is perhaps the man who owned this helmet (his name is on the leather lining inside the helmet. I can't clearly make it out) hand-painted it incorrectly. Any insight on this matter would be greatly appreciated. The helmet: http://imgur.com/a/ZrNQa
You might want to try /r/whatisthisthing or maybe /r/antiques. Perhaps one of the military subs can help, but as I don't frequent them I can't be sure. The swastica being backward might be for the same reason modern uniforms have the flag in reverse, to look like the wearer is always advancing.