  We prove the existence of higher-order topological insulators in: {\it i})
fourfold rotoinversion invariant bulk crystals, and {\it ii})
inversion-symmetric systems with or without an additional three-fold rotation
symmetry. These states of matter are characterized by a non-trivial
$\mathbb{Z}_2$ topological invariant, which we define in terms of symmetric
hybrid Wannier functions of the filled bands, and can be readily calculated
from the knowledge of the crystalline symmetry labels of the bulk band
structure. The topological invariant determines the generic presence or absence
of protected chiral gapless one-dimensional modes localized at the hinges
between conventional gapped surfaces.
