  The Benalcazar-Bernevig-Hughes (BBH) model [Science 357, 61 (2017)],
featuring bulk quadrupole moment, edge dipole moments, and corner states, is a
paradigm of both higher-order topological insulators and topological multipole
insulators. In this work, we generalize the BBH model to arbitrary dimensions
by utilizing the Clifford algebra. For the generalized BBH model, the
analytical solution of corner states can be directly constructed in a unified
way. Based on the solution of corner states and chiral symmetry analysis, we
develop a general boundary projection method to extract the boundary
Hamiltonians, which turns out to be the BBH models of lower dimension and
reveals the dimensional hierarchy.
