  Higher-order topological insulators (HOTIs) are a newly discovered class of
topological insulators which exhibit unconventional bulk-boundary
correspondence. Very recently, the concept of HOTIs has been extended to
aperiodic quasicrystalline systems, where the topological band theory fails to
describe topological phases. More importantly, a novel HOTI phase protected by
an eightfold rotational symmetry, not found in crystalline materials, was
identified in the Ammann-Beenker tiling quasicrystals. Here we report the
discovery of a quasicrystalline HOTI in a dodecagonal quasicrystal. The
quasicrystalline HOTI supports twelve in-gap zero-energy modes symmetrically
distributed at the corners of the quasicrystal dodecagon. These zero-energy
corner modes are protected by a combination of a twelvefold rotational symmetry
and mirror symmetry, as well as particle-hole symmetry, which has no
crystalline counterpart.
