  In higher-order topological insulators, bulk and surface electronic states
are gapped, while there appear gapless hinge states protected by spatial
symmetry. Here we show by ab initio calculations that the La apatite electride
is a higher-order topological crystalline insulator. It is a one-dimensional
electride, in which the one-dimensional interstitial hollows along the $c$ axis
support anionic electrons, and the electronic states in these one-dimensional
channels are well approximated by the one-dimensional Su-Schrieffer-Heeger
model. When the crystal is cleaved into a hexagonal prism, the 120$^\circ$
hinges support gapless hinge states, with their filling quantized to be 2/3.
This quantization of the filling comes from a topological origin. We find that
the quantized value of the filling depends on the fundamental blocks that
constitute the crystal. The apatite consists of the triangular blocks, which is
crucial for giving nontrivial fractional charge at the hinge.
