Illustrated Glossary of Organic Chemistry

Nonaromatic: A molecule that is neither aromatic or antiaromatic.

1,3,5-Hexatriene is nonaromatic because it does not have a closed loop of p orbitals and because it is acyclic. Verify with a model.

In its most stable conformation (the tub; shown here) cyclooctatetraene is nonaromatic (and also not conjugated) because the atoms which host its p orbital loop are not planar. Verify with a model.