Benzocyclobutadiene is the simplest polycyclic hydrocarbon, being composed of an aromatic benzene ring fused to an anti-aromatic cyclobutadiene ring.
Though the benzene ring is stabilized by aromaticity, the cyclobutadiene portion has a destabilizing effect.
This results into it being a non-aromatic compound - neither behaving as aromatic nor an antiaromatic one.
[1] For this reason, benzocyclobutadiene will readily dimerize or polymerize and it reacts as a dienophile in Diels-Alder reactions.
[2] Benzocyclobutadiene is used in the production of the pharmaceutical drug naflocort.