The fossil in the image above belongs to a genus of trilobites that lived from the Mid-Ordovician to the end of the Silurian. Distinguishing characters of Sphaerexochus include the massive inflation of the glabella, the central section of the trilobite head, which became almost spherical. The cheeks on either side of the glabella, in contrast, remained fairly small. The inflated glabella was marked on each side in the posterior part by a deep furrow that run in a curve from the side to the posterior margin. In the photo above, this furrow marks out the circular section that looks a bit like a large eye; the actual eye can just be made out in the photo (I think) as a crescent-shaped structure on the cheek below the glabella. The rear outer corners of the cheeks were more or less blunt in adult individuals, generally lacking the prominent cheek-spines of many other trilobites (small spines were present in juveniles). The spines on the trilobite's rear end (the pygidium) were also blunt and stout.
Přibyl et al. (1985) recognised four subgenera within Sphaerexochus, and this classification was largely supported by Congreve & Lieberman (2011) in a phylogenetic analysis (one of the subgenera, Onukia, is not known from well-preserved material and hence could not be analysed by Congreve & Lieberman). One of the subgenera, Korolevium, retained short cheek-spines as adults; they were absent in other subgenera. The remaining two subgenera, Sphaerexochus and Parvixochus, were distinguished by features of the hypostome, a plate on the underside of the head that covered the mouth in life. Korolevium and Parvixochus were both extinct by the end of the Middle Ordovician, but the Sphaerexochus subgenus sailed on and passed through the mass extinction event at the end of the Ordovician apparently unscathed (Congreve & Lieberman 2011).