Hmmm - where is it defined as "three or more" notes?
Saying "unison" and "interval" have names doesn't really matter, as three notes has a name too, ie. a "triad".
I'm not sure that the triangle analogy is correct, though it does lend itself to supporting the "3 or more" perspective; you could equally come up with other things like "how many eyes do you need to perceive depth".