I'm sorry to disagree, but the first and last knives in Fernando's picture are not "facones". Yes, I know that what I'm saying is contrary to a fairly established belief, but it's about these things that usually pays handsomely to listen to the natives. Although in this case the "natives" are Argentinians, so listening to them may be a bit... tiresome... (

joking, joking, just joking...)
It's one of those anthropological things that defy clear categorization and that are subjected to some local variations, but
as a general trend, these little (or not so little) single-edged knives with the off-centred handle, integral bolster and frequently richly decorated with embossed silver and even gold, are in fact called
cuchillos criollos ("Criollo" knives), found in the south-western part of South America (Argentina, Uruguay...), and still in production (and use) today.
See:
An undecorated example:
and, although the pic is smaller, here's one of the big exemplars:
I don't know the exact details, but I do know that one may recognize regional variations of those through morphological features of the knife and its decorations, like the shape of the drag or the button/clip.
On the other hand, a
facón is an unmistakable fighting weapon, much bigger, sometimes made from a cut-down or broken sword blade, and, as such, frequently double-edged. the hilt is usually centred and they normally (although not always) feature a handguard.
See:
"A
facón? This is not a
facón...
THIS is a
facón!"
It is also worth mentioning that this terminology is still in use today.
The credit goes to that Argentinian who managed to make all this information past my thick skull..