I came across this wonderful compound, triptycene.
Why is triptycene an aromatic compound, even though it is non-planar? I thought planarity was a requirement for aromaticity.
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The confusion arises because of a simplistic definition of aromaticity.
What matters for aromaticity is the planarity of the relevant part of the molecule. In triptycene there are three planar benzene groups joined together. Each is individually aromatic, but the whole molecule is not. Similarly, triphenyl-methane has three individually planar benzene groups, each of which is aromatic, but the molecule cannot be planar because of steric interactions between the groups. There are many other such examples of complex molecules containing an aromatic component attached to other things.
First of all, there's one thing you must know, aromaticity is a property of a ring system and not always of the molecule.
Small molecules like benzene and pyridine have only one ring, so it's "ok" to call them as aromatic, since they have only one ring system. But this approach can't be taken if you want to analyze, say, biphenyl.
Here, if you (incorrectly) try to analyze the whole molecule for aromaticity, you'd get 12 $\pi$ electrons, which is clearly a non-Huckel number, and hence you might infer it as non-aromatic. But however that approach is incorrect. However if I ask you Is biphenyl aromatic? what would you say? The answer is that it's meaningless to ask if biphenyl is aromatic or not. You may however ask Does biphenyl have aromatic ring systems in it?, which is a perfectly valid question.