Of course, playing only one of them with no other context wouldn't sound like triplets, no matter what the note lengths were.
As already mentioned, playing the 1st & 3rd triplet gives you a swing beat.
Playing or even just emphasising only the 2nd triplet is more rare.
I can think of no finer example than this..
Tears for Fears - Everybody Wants to Rule the World.
Long quiet intro, track starts at about 34s
Finest use of the 2nd triplet I've ever heard.
The overall 'backbeat' of the track is distinctly a 'swing' 1st & 3rd triplets in heavy simple rotation.
However, the hi-hat pattern constantly emphasises the 2nd triplet, as does the rhythm guitar that is introduced in the second verse.
The [not too frequent] drum fills are worth waiting for as they also sit heavily on the 2nd triplet.
From comments - there appears to be a rights issue with the original video in the US. I found this one, from Spotify [who one would imagine are smart enough to get their rights.. ermm.. right]
It's a 30th anniversary Live version, & while the vocals are not as confident as the original, you do get a good chance to watch the drummer playing those 'middle triplets' on the hats all the way through.
I remember it took me a week to learn the limb independence to play that. Not easy at all.