the parietals were not random growths but specific traits that could be used to determine the evolution of horned dinosaurs, if only it could be analyzed how they corresponded among species. Sampson, in the paper describing Achelousaurus in 1995, therefore introduced a generalized numbering system for such parietal processes, counting them from the midline to the side of the frill. This was applied to the Centrosaurinae as a whole in 1997. The large spikes of Achelousaurus correspond to "Process 3" spikes of other centrosaurines and were similar to those of Einiosaurus, though curved more to the sides, similar to Pachyrhinosaurus. They were shorter and thinner than the corresponding spikes of Styracosaurus. Between these spikes, on both sides of the central frill notch, were two small tab-like processes ("Process 2") that were directed towards the midline. Innermost "Process 1" spikes, as present in Centrosaurus, are lacking with Achelousaurus. The frill had two large paired openings, the parietal fenestrae, with a midline parietal bar between them. A linear row of rounded swellings ran along the top of the parietal bar, which may be homologous to the spikes and horns in the same area of some Pachyrhinosaurus specimens. A row of relatively small processes ran along the parietal shield margin from the "Process 3" spikes outwards, for a total per side of seven. They were largely equal in size, causing the P4 process to be reduced in comparison to the P3. These lower processes appear to have been capped by epoccipitals, bones that lined the frills of ceratopsids. In Achelousaurus these epoccipitals, which start as separate skin ossifications or osteoderms, fuse with the underlying frill bone to form spikes, at least in the third position. In 2020, it was denied that these processes were separate ossifications. In the most mature individuals, the front-most P6 and P7 processes would be less imbricated relative to each other, rotated around their longitudinal axes. Keratin sheaths The bosses on the skull of Achelousaurus may have been covered in a keratinous sheath in life, but their shape in a living animal is uncertain. In 2009, the paleontologist Tobin L. Hieronymus and colleagues examined correlations between skull morphology, horn, and skin features of modern horned animals, and examined the skull of centrosaurine dinosaurs for the same correlates. They proposed that the rugose bosses of Achelousaurus and Pachyrhinosaurus were covered by thick pads of cornified (or keratinized) skin, similar to