In that picture it mentions how triangle wounds are impossible to stitch up. If that is true how would one treat a triangle puncture wound on the human body?
Triangular blades were created for pretty much one reason, and one reason only. The triangular cross section made a stronger blade, ensuring more damage was done in a charge/stab versus a flat blade.
The triangular blade was introduced in the early 1700's, mostly due to strength reasons. A triangular blade is less likely to bend/break when stabbing in a charge, especially if you hit a piece of armor, another weapon or bone. The cross section is much stronger in a triangle versus a flat blade.
There is anecdotal evidence galore about the wound, and the wiki states that it is harder to heal, as the scar tissue filling in the wound tends to pull apart the rest of the wound as it heals. I can find several anecdotal references, but nothing concrete to confirm this. There is also anecdotal evidence that the Geneva Convention bans triangular blades, however the language only states "weapons that cause unneeded suffering" (paraphrased).
Pretty much the only reason for them was strength, and as other weapons became better, the bayonet went back to a single/double blade, as they are much more useful in that shape in non combat situations (Cutting ropes, food, straps, etc).