  The supersolid phase of a dipolar Bose-Einstein condensate has an intriguing
excitation spectrum displaying a band structure. Here, the dressing of an
impurity in a one-dimensional dipolar supersolid with the excitations of the
supersolid is studied. The ground-state energy of the supersolid polaron is
calculated using a variational path integral approach, which obtained accurate
results for other polaron systems within the Bogoliubov and Fr\"ohlich
approximations. A divergence is observed at the superfluid-supersolid phase
transition. The polaron radius is also computed, showing that for strong
impurity-atom interactions, the polaron can become localized to a single
droplet, behaving like a small solid-state polaron.
