When it comes to dice, what's the appropriate way to denote the number of their sides/faces?
A six-sided die or a four-faced die?
Or have these two no difference for natives?
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I'd go with 'sided' as a Brit.
Just to note, though, that very many people don't know what a 'die' is. They will use the word 'dice' for singular or plural.
Right or wrong, if you call it a 'six-sided dice', everyone will know what you mean, and only the true pedants will correct your usage of 'dice'.
In fact I got the OED to agree with me…
The form dice (used as plural and singular) is of much more frequent occurrence in gaming and related senses than the singular die.
Both the OED & Wikipedia use both terms, sides and faces, so this may be one of familiarity, rather than absolute correctness.
As an American from the midwest, "sided" would be the term used by the general public, and everyone I've heard refer to dice after about grade-8 correctly uses the singular and plural forms, "die" and "dice" respectively.
As a tabletop gamer, we additionally use a particular jargon: Instead of referring to "sides" of dice, we use a shorthand. We would refer to a die by a "d" concatenated with the number of sides on that die. Therefore, a "six-sided die" would simply be a "d6" read aloud as "dee six". Ten of those dice would be "10d6", read aloud as "ten dee six". Even friends who aren't gamers pick this up really quickly. It's a lot faster to refer to gaming dice this way, since we often have handfuls of dice to cast that can look like "6d6 + 4d12 + 1d20", and they all have special uses.
To my ear, "these dice each have 6 faces" and "these dice each have 6 sides" are completely interchangeable. Either "sides" or "faces" is a perfectly normal word to use.
However I would never used the phrase "6-faced dice". I would know what it meant instantly, but it sounds unusual enough to be "wrong". Only "6-sided dice" sounds normal.
So to the question in the title, I would say either is fine and there is no difference. But with the usage in the question body I would say only "-sided" is acceptable - though I wouldn't lose sleep over it, as "-faced" would be understood to mean exactly the same thing, it just sounds weird.
Language conventions are strange and arbitrary sometimes.
While neither is incorrect, and both would be understood, "sided" is much more idiomatic. One can see this using Ngrams.
Incidentally, despite what one of the other answers suggests, for the singular "die" remains much more common than "dice", at least in the corpus that Google uses. (I used this phrasing to try to avoid any doubt over whether the singular or plural was meant, or whether the word was being used in a different context. Results for "a six-sided die" versus "a six-sided dice" are similar.)