O CHEM QUESTION

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ITW

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Quiz question regarding a 3,3-dimethyl-bicyclo[4.0.3]nonatetraene:

*Picture attached

My teacher is insisting that this is an aromatic compound, due to the fact that the pi bond between 1 and 2 can break and form an anion, giving the ring to the left 6 pi electrons to resonate with

I simply disagree, since using the same logic would imply a pentalene, for example, would also be aromatic which is commonly held to be antiaromatic.

This would contradict the requirement that the delocalization of electrons decreases the energy of the molecule.

Any help, explanation, or literature would be appreciated.
 

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Are those 2 methyl groups?? Or hydrogen?

Edit: I see from the name they are methyl groups. So the C there is sp3 hybridized, breaking the conjugation. Not aromatic (nonaromatic)
 
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