possible voicings of a 3 note chord include those 3 halfsteps in ANY and ALL of the 7.3 octaves.
your example is ok for when the 1,3,5 are only used once. But maybe you want 3 separate bass notes in 3 of the lower octaves, plus a 3rd in octave 4, and 2 5ths in octaves 5 and 6.
You could have that 3 note chord playing on 21-ish possible notes or any combination. And of course, you can omit notes of a chord and still call it that chord.
So usually spec'ing the arrangement for a chord is listing each individual octave that's playing it. And of course, rhythm comes into play and some of the notes aren't held for the full duration or start at the same time. So the arrangement is usually just plain spec'd in notation.