Trimming corners and cutting darts before stretching and cross-stitching all seams cleanly opened, leaving no excess material in the way of drawing the now finished cover over its dome construction; after which the newly attached border is to be wrapped over the padded crown, joining the fur directly onto its satin lining.
My first thought when starting work on the hat was to create the fabric component and strengthen it from the inside out using small separate pieces of interfacing for each of the faces, an idea quickly cast aside upon realising doing so would never give a strong enough effect like the selected approach does.