While it's true any sword sharpened on one side and not on the other could be called "monoedged", in this case what is being implied is a blade with an edge that is one molocule thick and incredibly sharp. The blade does of course get dulled with use, but the scabbard it is kept in resharpens it with every unsheathing.
Melee: Attacks with this trait can be used during close combat without penalty.
Penetrating: When a weapon with this trait successfully hits, it has D3 Armor Penetration against the target.
Parry: Every ability that grants a fighter a Parry adds one use to a pool that refreshes each time this fighter initiates close combat or is declared as a close combat target, and empties at the end of the Fight action. Parry uses can be spent from this pool to force an Engaged enemy fighter to re-roll one successful close combat hit. However, if an attacker is outside a fighter's vision arc they must spend two Parry uses to force the enemy fighter to re-roll a successful hit.