  In recent years, the role of crystal symmetries in enriching the variety of
TIs have been actively investigated. Higher-order TIs are a new type of
topological crystalline insulators that exhibit gapless boundary states whose
dimensionality is lower than those on the surface of conventional TIs. In this
paper, relying on a concrete tight-binding model, we show that higher-order TIs
can be smoothly connected to conventional TIs in a lower dimension without the
bulk-gap closing or symmetry breaking. Our result supports the understanding of
higher- order TIs as a stacking of lower-dimensional TIs in a way respecting
all the crystalline symmetry.
