Canon:Rapier
From Dungeons and Dragons Wiki
The rapier is a long, thin bladed sword often with an elaborate guard protecting its hilt.
The image of a rapier in the PHB is completely rubbish.
The historical rapier had a blade usually between 38 and 42" long and would typically be diamond sectioned blade for all or most of the length. Rapiers were not fullered for a significant portion of its blade.