  Traditional topological insulators often rely on band inversions driven by
nonuniform hopping textures and spin-orbit coupling, as exemplified in the
Su-Schrieffer-Heeger and Kane-Mele models. We present a novel approach
utilizing the spatial nature of sublattice symmetry to induce nontrivial
topological insulating properties characterized by second-order corner states
without band inversion. To substantiate our proposal, we design a photonic
crystal with non primitive translational symmetry, demonstrating unique
directional waveguide edge modes and localized corner modes.
