  We present numerical evidence for the existence of several types of static
black hole solutions with a nonspherical event horizon topology in $d\geq 6$
spacetime dimensions. These asymptotically flat configurations are found for a
specific metric ansatz and can be viewed as higher dimensional counterparts of
the $d=5$ static black rings, dirings and black Saturn. Similar to that case,
they are supported against collapse by conical singularities. The issue of
rotating generalizations of these solutions is also considered.
