Sword Design
The bronze sword that Thorn is being compared to is called a kopis and is a traditional form of ancient Greek sword. It’s curved forward and shaped somewhat like a larger version of a kukri. It’s more sharply curved than Thorn and has a convex tip, for a number of reasons; this makes it less suitable for thrusting. Thorn is more similar in profile to some of the thinner forms of the Illyrian sica, which has a longer, thinner, and less sharply curved blade. Unlike a normal sica (or a kopis, or a khopesh, or a falcata, or a kukri, or…you get the point), Thorn is sharpened on both edges. There are a number of reasons for this, mostly related to how much more you can get away with as a swordsmith when the material you’re working with will be made supernaturally durable. Mundane blacksmiths have to manage an inherent property of steel, which is that harder (i.e., able to take and retain a sharper edge) alloys will also be less tough (i.e., they will be brittle and prone to shatter).
So swordsmiths will generally use a variety of methods to compensate for this issue. With a sword like a sica which has one side distinctly more favored than the other, a common solution is to leave the other edge unsharpened. This lets you use a thicker spine and often use a tougher, softer alloy in that portion of the blade, while keeping the edge hard (and therefore sharp). This also lends the blade more weight (and thus momentum) and focuses that weight more towards the tip, which is why a kukri or kopis can cut in ways more associated with an axe than a knife. Fullers (grooves) and ridges in the center of a blade are also used to help strengthen the blade without adding as much weight.
None of this is relevant to Thorn. It is supernaturally tough and sharp, without much concern needed for the blade’s shape and composition in the process. This means that the blade can be thinner without becoming fragile, that the material can be hard enough to take an edge without losing toughness, and that momentum doesn’t matter much (since even a light swing will be sufficient most of the time, and Kyoko is unnaturally strong in any case, which further reduces the importance of weighting). This is also why Thorn can have such extensive silver and amber inlay; those materials don’t represent a structural weakness when none of this is happening in a natural way. As a result, while it has the forward-swept shape of a sica, it is very much sharpened on both edges. In theory this means it could also be used with the outer side of the curve as the focus, similar to a sabre; however, the way the hilt is shaped would make this an awkward grip from an ergonomic standpoint. The point also has a distinct enough hawkbill profile that it would be rather awkward to thrust with it in that position. So Kyoko will pretty much always be using it more like a sica, focusing on the inner edge of the curved blade.