  We show that asymptotically de Sitter black holes of negative mass can exist
in Lovelock gravity. Such black holes have horizon geometries with non-constant
curvature and are known as Exotic Black Holes. We explicitly examine the case
of Gauss-Bonnet gravity. We briefly discuss the positive mass case where we
show how the transverse space geometry affects whether a black hole will exist
or not.For negative mass solutions we shown how three different black hole
spacetimes are possible depending on the transverse space geometry. We also
provide closed form expressions for the geometric parameters to ensure that a
black hole spacetime is observed. We close with a discussion of the massless
case, where there are many different spacetimes that are permitted.
