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S. D. SAMPSON ET AL.
The parietal can be subdivided into three primary components: (1) a robust, longitudinal midline bar, (2) a posterior transverse ramus, forming a ‘T’ with the parietal bar and possessing a variety of hooks, spikes and/or horns, and (3) lateral rami with scalloped margins bearing variably developed accessory elements or ‘epoccipitals’. The median bar is typically robust, convex dorsally and concave ventrally, with a deep ventral groove. Dorsal undulations on the parietal median bar are common to virtually all centrosaurines, juvenile through adult. The undulations range from two to six with four or five being typical. Development of these midline processes varies from low rugosities (AMNH 5351, Centrosaurus nasicornis) to prominent bumps (AMNH 3998, Monoclonius crassus) to well-developed spikes and hooks in some adult pachyrhinosaurs (TMP 86.55.211, Pachyrhinosaurus sp.). Near the anterior end of the median bar, there is a transverse constriction or neck which broadens further anteriorly into a well-developed sutural complex for the frontals, and a deep depression, the posterior portion of the frontal fontanelle complex (Sternberg, 1927). In adults, the posterior transverse ramus of the parietal forms a generally thick, well developed margin with a complex variety of taxonomicallyspecific processes. The anteriorly-directed lateral rami round out the frill, enclose the parietal fenestrae, and include contact surfaces for the squamosals. A U-shaped midline notch on the posterior border is often present with much variation within species. Some specimens possess a deep emargination in this region while others have virtually a horizontal border and lack this feature. Parietal processes—whether hooks, horns, spikes, or simple outgrowths—number between five and seven per side, varying between and within taxa and even on opposite sides of the same parietal (NMC 8795, Centrosaurus longirostris). For the purposes of discussion, we present here a system of numbering parietal processes from medial to lateral (Fig. 8), with the assumption that equivalently numbered processes are homologous. Thus, the anteriorly directed hooks of Centrosaurus are referred to as process 1 and the large, medially directed horns become process 2. Processes further lateral are numbered sequentially. Three genera—Einiosaurus, Achelousaurus and Pachyrhinosaurus—apparently lack parietal outgrowths homologous to process 1 in Centrosaurus and Styracosaurus. Thus, the most medial process on the periphery of the parietal in the former group is designated process 2. The centrosaurine squamosal is roughly rectangular in outline and short in comparison to that of chasmosaurines in which the squamosal is triangular and much longer, often reaching the posterior frill margin. The posterolateral portion of the centrosaurine squamosal forms part of the scalloped lateral margin of the frill. Processes number between three and six with four or five being typical. There is much intraspecific variation in the number of these outgrowths; a sample of six squamosals from an Einiosaurus bonebed shows variation between three and five epoccipitals per specimen. A single individual may vary in the number of scallops on opposite squamosals (AMNH 5239, Centrosaurus flexus). The ventral (internal) surface of the squamosal shows several characteristic ridges and grooves, the sutural contacts for the quadrate and exoccipital. The exoccipital slots into a deep groove with a heavy osseous lateral ridge. The quadrate is wedged behind the anteromedial border of the exoccipital groove. The squamosal contacts the posterolateral surface of the parietal with a simple butt suture that is variably grooved on the contact surface but generally concave. In most forms, the posteromedial margin of the squamosal ‘steps down’ and the medial contact with the