The genus Helicoprion (Chondricthyes, Euchondrocephali) is preserved primarily by a continuous spiral root that forms the base for more than 130 teeth. Helicoprion is found globally in Lower Permian marine rocks and at least 100 specimens exist in public collections worldwide. Ten species of the genus are reviewed in the context of new morphometric analyses conducted on dozens of specimens. Helicoprion whorls share a common inner spiral geometry that results in exponential growth of tooth and root dimensions. Novel growth equations permit calculation of whorl diameter, volution number and tooth count from incomplete specimens. The results of meristic and geometric analyses identify taxobases that distinguish three emended species concepts. Differentiation of form is evident among specimens only after the second volution or roughly the 85th tooth. Helicoprion davisii has widely spaced, stout teeth with tall cutting surfaces and is distinguished from H. bessonowi, which has narrow, closely spaced teeth with short cutting surfaces. Helicoprion ergassaminon is an intermediate form, having narrow, closely spaced teeth with tall cutting surfaces. Several large specimens in the study are too dissimilar to place in the new emended species concepts.