  We consider four-dimensional de Sitter, flat and anti de Sitter branes
embedded in a six-dimensional bulk spacetime whose dynamics is dictated by
Lovelock theory. We find, applying a generalised version of Birkhoff's theorem,
that all possible maximally symmetric braneworld solutions are embedded in
Wick-rotated black hole spacetimes of Lovelock theory. These are warped
solitonic spaces, where the horizons of the black hole geometries correspond to
the possible positions of codimension-2 branes. The horizon temperature is
related via conical singularities to the tension or vacuum energy of the
branes. We classify the braneworld solutions for certain combinations of bulk
parameters, according to their induced curvature, their vacuum energy and their
effective compactness in the extra dimensions. The bulk Lovelock theory gives
an induced gravity term on the brane, which, we argue, generates
four-dimensional gravity up to some distance scale.
  As a result, some simple solutions, such as the Lovelock corrected
Schwarzschild black hole in six dimensions, are shown to give rise to
self-accelerating braneworlds. We also find that several other solutions have
self-tuning properties. Finally, we present regular gravitational instantons of
Lovelock gravity and comment on their significance.
