  In the paper we present new examples of unexpected varieties. The research on
unexpected varieties started with a paper of Cook II, Harbourne, Migliore and
Nagel and was continued in the paper of Harbourne, Migliore, Nagel and Teitler.
Here we present three ways of producing unexpected varieties that expand on
what was previously known. In the paper of Harbourne, Migliore, Nagel and
Teitler, cones on varieties of codimension 2 were used to produce unexpected
hypersurfaces. Here we show that cones on positive dimensional varieties of
codimension 2 or more almost always give unexpected hypersurfaces. For
non-cones, almost all previous work has been for unexpected hypersurfaces
coming from finite sets of points. Here we construct unexpected surfaces coming
from lines in $\mathbb{P}^3$, and we generalize the construction using
birational transformations to obtain unexpected hypersurfaces in higher
dimensions.
