  In this paper, we present a new solution of the vacuum Einstein equations in
five dimensions which is a static black hole with hyperscaling violation and
with a three-dimensional horizon modeled by one the eight Thurston geometries,
namely the Nil geometry. This homogeneous geometry is non-trivial in the sense
that it is neither of constant curvature nor a product of constant curvature
manifolds. Using the Hamiltonian formalism, we identify the mass and entropy of
the black hole solution. Curiously enough, in spite of the fact that the
entropy turns to be negative, the mass is positive and the first law of
thermodynamics holds. We also discuss the extension in higher dimension.
