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Why are some annulenes such as [14] and [18]annulenes are aromatic even though they are not fully planar as cited by Wikipedia? What does it mean that they can achieve planar form?

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It means very little, at least in terms of stabilization. Perfectly planar or not, larger aromatic rings bring less stability than smaller ones, so they react more like mere conjugated polyenes than what we think of as "aromatic rings". See the fourth paragraph here.

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