On my question Why does the French sixth sound more dissonant than the others?, I got this answer from Ben I.:
It's because the French 6th chord has an extra tritone.
If we take an A♭ Augmented 6th chord, we would have:
A♭ C D F♯
F♯are both tritones.
Caters had wrote this comment on Ben I.'s answer:
So, it is like a diminished 7th (which is also 2 overlapping tritones) but based on the major chord instead?
Both the Fr. 6 and dim7 are made of two overlapping tritones. The question is, are there any chords that are made of two overlapping tritones other than the dim7 and the Fr. 6?