Speaking of cutting edges.
Here's something:Single Edge - A bladed weapon that only has one cutting edge. It is advantageous as it can be pointed only to the opposing target. Though when trying to slash or hit in reverse, you need to turn the blade around.
Double Edge - A bladed weapon that has two cutting edge opposite of each other. It is advantageous and disadvantageous to the user as one of it's edges is also pointed towards you. Though if handled with right techniques, it can be very advantageous to the user.
Triple Edge - A non-classified bladed weapon. It is rare, probably you won't even find a branded and a named triple-edge bladed weapon, and quite possibly there's a reason. It's very disadvantageous. In the olden times, warfare with swords are one of the most common. There have been made single edge, and double edge weapons. There are also edgeless weapons, backswords and such. But why no triple edge? A sword can only be slashed through an enemy along it's flat surface. A triple edge means three edges on a sword, but there can only be two sides of a sword. So where does the other edge goes? Of course it'd be in the middle. Slashing will be a big problem, even if one side is used, as there will be a stopping force from one of the edges if attempt for a straight cut is made. You will need mundane amount of physical strength to cut through. Otherwise the blade will be as blunt as an edgeless blade and will prove very little in combat, and it will be most likely a mace rather than an actual sword. A triple edge sword though can prove effective like a thrust sword, as chain woven armor can be split and pierced through with it's edges, and do sufficiently large damage to the target.
Weiss Schnee rapier is not triple edge, it's a double edged blade to a pointed tip.
The middle part you see is called the "Central Ridge". Even if it's diamond-like structure, it's not considered a third edge.
A rapier doesn't need to be only for thrusting, though it's proven effective that way that it can be used for it as piercing through armor. But there's a reason why a rapier
CAN be made as a single edge, double edge, and even as an edgeless blade like an Estoc. Because there are some blades made specifically for usage, a katana is a long sword, curved, single edge blade used for slicing, a Bastard sword is a hand and a half sword that can be both used by two hands, or one hand with a shield on the off hand, a Zweihander is a heavy sword which requires two hands used to slash slow but powerful, and cannot be used for cavalry, some however see the rapier in its entire time-line and see that it never truly fits into any single definition[eg. Cut/Slash/Thrust/etc].
A rapier is a longsword, which is also a straight sword. So of course it would be given as a technique to be used like "half-sword", the technique of thrusting. Though that does not mean it cannot be used for slashing or cutting.
Though Weiss Schnee's sword may actually be a backsword, since it may have a "false edge". Due to it's fans it was called a rapier. Then again, we do not see any edge near the tip, and being a backsword it would need to be only single edged. As for the hilt is a complex, protective hilt, basket-like guard, which most rapiers actually use.
BUT STILL, we don't know if it's actually a rapier. It's only fan's speculations.
Though I don't know how'd you guys get into the topic of three-edge blades. I have made my point otherwise.
Plus I don't think we should be arguing about it from the first place, as I doubt the creator actually has any much ideas about swords, when actually making "fictional" weapons in the first place.
Edit:
I forgot to note that Weiss' rapier is actually like a "diamond rapier". It has "four edges", but it is actually still just a central ridge that provided additional thrust prowess as such a triple edge. It is still a double edge that is shaped like a diamond.
