  We study the role of the edges in determining the features of the topological
phase in a quasicrystalline higher order topological insulator. We consider a
specific model consisting of two stacked Haldane models with opposite Chern
number and a $30^\circ$ twist, whose structure is crystallographically
equivalent to that of the graphene quasicrystal. We find that the gap-opening
in the low energy spectrum of the higher order topological insulator occurs at
different energies when different kinds of edges are considered. Crucially,
bearded bonds appear to be necessary for the gap to appear close to the charge
neutrality point. In the more realistic case of zigzag edges, the gap opens
symmetrically in the electron and hole sectors, away from zero energy. We
explain our findings by inspecting the edge-bands of the decoupled bilayer, in
the approximation of quasi-periodicity.
