Rapiers are typically not sharp on the sides of the blade. A rapier is a slender and agile sword primarily designed for thrusting rather than cutting. Its blade is typically long, narrow, and triangular or diamond-shaped in cross-section. The sharpness of a rapier is concentrated along the pointed tip and the leading edge, which is the edge that faces the opponent during a thrust.

The purpose of a rapier is to deliver precise and accurate thrusting attacks, targeting vulnerable areas of an opponent's body. The narrow, tapered blade allows for excellent point control and penetration while minimizing resistance during the thrust.

While some historical variations of rapiers might feature small sharpened edges on the sides of the blade near the tip, these are generally not meant for cutting but rather to create additional puncture wounds during thrusting attacks.

It's important to note that rapier designs can vary, and there might be exceptions or variations in specific historical examples. If you are considering acquiring or studying a rapier, it's advisable to consult reputable sources, historical references, or experienced experts who can provide accurate information about the specific rapier type or period you are interested in.

Always prioritize safety and familiarize yourself with the laws and regulations regarding sword ownership and usage in your jurisdiction. If you plan to practice with a rapier or any bladed weapon, seek proper training and guidance from qualified instructors who can teach you the appropriate techniques and safety protocols.