A grenadier's mitre has no brim, and we carry a smooth bored musket, so this rifleman's discussion doesn't apply. However, when we go out as a hat company and wear the tricorn, the turn ups are not symmetrical. The left side is turned up for ease of shoulder carry. The back is turned up to clear any items being carried and the last side is turned up to make the three points. Since the officers don't carry muskets, their tricorns are turned up symmetrically.