Seventeen trigonoceratid genera are listed in the Treatise. All but one are found in the Lower Carboniferous of Europe and equivalent Mississippian of North America.(ibid Kummel)
Mississippian Genera from North America alone
Mississippian Genera from North America and Europe (L Carb)
Mississippian (L Carb) Genera from Europe
Lower Permian Central Asia
Trigonoceras, type genus, named by Hyatt, 1844, is unique among the Trigonoceratidae in the Treatise. It is the only genus included that has a subtriangular whorl section consisting of a broad concave venter and narrow dorsum. The remaining can be divided on the basis of shell morphology into those that are smooth, at least on the outer whorl, those with numerous equal longitudinal ribs or lirae, and those with prominent longitudinal ridges separated by wide grooves or sulci.(ibid Kummel)
Those with smooth whorls include Leuroceras and Mesochasmoceras; those with numerous longitudinal ribs or lirae include Chouteauoceras, Discitoceras, and Rineceras; and those with prominent, wide spaced, longitudinal ridges are such as Stroboceras and Vestinautilus.
Trigonoceratid genera can also be grouped on the basis of the suture which may be essentially straight and transverse or slightly sinuous, or may have a well defined ventral lobe, or a ventral saddle. Those with straight or slightly sinuous sutures are Apogonoceras, Diodoroceras, Discitocdras, Rineceras, Stroboceras, and Thrincoceras; with a discernible ventral lobe: Aphelaeceras, Epistroboceras, Lispoceras, Maccoyoceras, Pararineceras, Subclymenia, and Vestinutilus; and with a ventral saddle: Chouteauoceras and Leuroceras.
Ventral saddles are also found in the Centroceratidae in Carlloceras and Phacoceras, in the Grypoceratidae in Stenopoceras and Parastenopoceras, and in the Syringonautilidae.(ibid Kummel)