  The effects of frustration on extended supersolid states is a largely
unexplored subject in the realm of cold-atom systems. In this work, we explore
the impact of quasicrystalline lattices on the supersolid phases of dipolar
bosons. Our findings reveal that weak quasicrystalline lattices can induce a
variety of modulated phases, merging the inherent solid pattern with a
quasiperiodic decoration induced by the external potential. As the lattice
becomes stronger, we observe a super quasicrystal phase and a Bose glass phase.
Our results, supported by a detailed discussion on experimental feasibility
using dysprosium atoms and quasicrystalline optical lattice potentials, open a
new avenue in the exploration of long-range interacting quantum systems in
aperiodic environments. We provide a solid foundation for future experimental
investigations, potentially confirming our theoretical predictions and
contributing profoundly to the field of quantum gases in complex external
potentials.
