I see what you mean. Still I would argue that both tritones and minor thirds only appear to possess the symmetrical property as a result of temperament. It doesn't exist 'in nature' as such.
The frequency ratios that they represent, 7/5 and 6/5, respectively, don't lend themselves to the same type of symmetry. If you have a tritone, 7/5, you would need a 10/7 ratio to make the octave, which would be a different interval (although close).
With a minor third (6/5), if you were to stack the intervals starting from let's say 500 Hz, you would go to 600, 720, 864, and 1036.8, and you'd be off 36.8 Hz from the octave.
The frequency ratios that they represent, 7/5 and 6/5, respectively, don't lend themselves to the same type of symmetry. If you have a tritone, 7/5, you would need a 10/7 ratio to make the octave, which would be a different interval (although close).
With a minor third (6/5), if you were to stack the intervals starting from let's say 500 Hz, you would go to 600, 720, 864, and 1036.8, and you'd be off 36.8 Hz from the octave.