Up until 2013, the only known fossils of this genus on record were their teeth, which were arranged in a "tooth-whorl" strongly reminiscent of a circular saw. As the skeletons of chondrichthyid fish are made of cartilage, including those of Helicoprion and other eugeneodonts, the entire body disintegrates once it begins to decay, unless exceptional circumstances preserve it. It was not until the discovery of the skull of a related genus of eugeneodont, Ornithoprion, that it was realized that the tooth-whorl was in the lower jaw. The tooth-whorl represented all of the teeth produced by that individual in the lower jaw, in that as the individual grew, with the older, smaller teeth being moved into the center of the whorl by the appearance of larger, newer teeth. Models of Helicoprion‍ "​s tooth-whorl have been made. Author of the 1994 book Planet Ocean: A Story of Life, the Sea, and Dancing to the Fossil Record, author Brad Matsen and artist Ray Troll describe and depict an example. They say that there were no teeth in the animal"s top row besides the crushing teeth for the whorl to cut against. The two envision the living animal to have a long and very narrow skull, creating a long nose akin to the modern-day goblin shark. According to their studies, the fossils that have been found are essentially a growth ring, as each set of new teeth pushes the previous set into the whorl. The images that Troll has devised are an educated guess at best. Helicoprion‍ "​s true physical identity remained hidden in 280-million-year-old rocks.Comparisons with other eugenodontids suggest that Helicoprion may have grown up to 3–4 metres (9.8–13.1 ft) long.
For over a century, it was not certain where the tooth-whorl was located in the lower jaw. Older reconstructions placed the whorl in the front of the lower jaw. A 2008 reconstruction, created by Mary Parrish under the direction of Robert Purdy, Victor Springer and Matt Carrano for the Smithsonian, places the whorl deeper into the throat,although other studies did not accept this conclusion.A 2013 study based on new data places the tooth-whorl at the back of the jaw, where the tooth-whorl occupied the entire mandibular arch.
In the article, "Helicoprion in the Anthracolithic (Late Paleozoic) of Nevada and California, and its Stratigraphic Significance", author Harry E. Wheeler describes another Helicoprion fossil, based on the species H. sierrensis, collected by J. H. Menke, that once resided in the University of Nevada, Mackay Museum in 1931. (The fossil"s current location is not known) According to Meller, Helicoprion’s mouth is its most distinct trait. The mouth consists of a whorl separated into 3 ј volutions. The biggest diameter is about 170 millimetres (6.7 in). The whorls have a separation of about 1 millimetre (0.039 in) in the first volution, and it goes to about 8 millimetres (0.31 in) at the largest whorl displayed. The specimen has a total of about 32 teeth in the first volution, 36 in the second and 41 in the last. The teeth at the end of the first volution are about 7 millimetres (0.28 in) long and measure about 2.4 inches (61 mm) width reaching about 40 millimetres (1.6 in) long and 9.5 wide at the end of the third. The teeth are symmetrically opposed to one another.
Additionally, other extinct fish, such as onychodontiformes, have analogous tooth-whorls at the front of the jaw, suggesting that such whorls are not as big of an impediment to swimming as suggested in Purdy"s hypothesis. While no complete skulls of Helicoprion have been officially described, the fact that related species of chondrichthyids had long, pointed snouts suggests that Helicoprion did as well.
Fossils of Helicoprion species first appear in Upper Carboniferous marine strata, proliferate greatly during the Permian, and eventually disappear during the Early Triassic. Fossils have been found in the Ural Mountains, Wandagee Mountain of Western Australia, China(together with the related genera Sinohelicoprion and Hunanohelicoprion), and Western North America, including the Canadian Arctic, Mexico, Idaho, Nevada, Wyoming, Texas, Utah, and California. Due to the fossils" locations, it is speculated that the various species of Helicoprion lived off the southwestern coast of Gondwana, and later, Pangaea.
Helicoprion was first described by Alexander Karpinsky in 1899 from a fossil found in Artinskian age limestones of the Ural mountains.Karpinsky named the type species Helicoprion bessonowi. Oliver Perry Hay originally described the species.
Helicoprion ferrieri was originally described as a species of the genus Lissoprion in 1907, from fossils found in the Phosphoria Formation of Idaho. An additional specimen, tentatively referred to H. ferrieri was described in 1955. That specimen was found in Wolfcampian age quartzites exposed on China Mountain, six miles southeast of Contact, Nevada. The 100 millimetres (3.9 in) wide fossil consists of 1 ѕ whorls and about 61 preserved teeth. Due to weathering the rest of the fossil was lost and the preserved section is distorted from slippage of the host rock.
Helicoprion jingmenense was described from of a nearly complete tooth whorl with 4¹⁄₃ volutions (part and counterpart) found in the Lower Permian Qixia Formation of Hubei Province, China. The specimen is very similar to H. ferrieri and H. bessonowi, though, it differs from the former by having teeth with a wider cutting blade, and a shorter compound root, and differs from the latter by having fewer than 39 teeth per volution.
In 2013, a group of paleontologists discovered the true arrangement of Helicoprion"s toothwhorl.In the same year, 2 specimens of an as yet undescribed species of Helicoprion were discovered. The first specimen suggests an animal that reached 10 meters in length, while the second specimen, nicknamed "Bois", suggests an animal that exceed 12 meters. This suggests that this species of Helicoprion is the largest known eugeneodont.

 
Parahelicoprion clerci

Parahelicoprion is an extinct genus of eugeneodontid, shark-like holocephalid from the Permian of the Ural Mountains and South America. Its name is a derivation of Helicoprion, from the Ancient Greek words "Nearly coiled saw", another holocephalid that shares similar traits to it, including the helical whorl of teeth. One of the primary qualities that separate Parahelicoprion from the aforementioned Helicoprion is the shape, thickness and angle of the tooth whorl. This whorl sharks teeth protrude outwards not like a tightly coiled saw but instead a curved arrangement of cutting blades indicating it relied less on crushing slow-moving invertebrates and catching squid and other small mollusk prey, but inflicting traumatic damage against more durable, faster prey. Their teeth grew at a much slower pace than that of other whorl-tooth sharks, resulting in a depreciated spiral, growly only half of the teeth a Helicoprion would grow in its life time. The tooth spiral also was able to indicate the age of the eugeneodontidans in question.
Parahelicoprion was a nektonic carnivore that preyed upon a variety of different species, using its blade-like teeth to cut at exposed flesh like a hatchet or wedge. Many different prey species were identified at the beginning of the Permian, from sarcopterygian fish ill-equipped to deal with large predators (Menaspis and Petalodus being common prey items), xenacanthid sharks, plentiful species of ammonite and trilobite, and due to its size, other smaller eugeneodontids. Parahelicoprion is even believed to participate in cannibalism of its own species.

Edestus giganteus

Sarcoprion

Sarcoprion (Ancient Greek for "flesh saw") is an extinct genus of eugeneodontid holocephalid from the Permian of Greenland. Similar to other eugeneodontids like Edestus and Heliocoprion, it was best known for its extremely bizarre tooth morphology compared to other species of sharks and their closest relatives, the chimaeras. Compared to other members of Helicoprionidae (Teeth of Agassiz), its "tooth whorls" were found to be in sharper, more compact and in better condition than other sharks of the time, and refrained from growing to extremely unwieldy forms that would raise questions about its ability to feed properly.The Genus contains one species, Sarcoprion edax ("gluttonous flesh saw"), found in Permian-aged marine strata of Meddelelser om Grшnland.
Sarcoprion had a jaw and mouth structure which allowed it to be more hydrodynamic, reducing the size and shape of the tooth whorl and increasing the size of the rostrum. Sarcoprion is thought to have pursued smaller, fast moving prey similar to today"s Mako shark. Estimations on its size suggested an average of 6-8 meters (20 - 26 feet) from the two specimens discovered in Greenland.
Using the compact tooth whorl during hunting, Sarcoprion hunted a large variety of different species, diving at them with high speed and sawing vulnerable areas.Any creatures that were wedged between its rostrum and its teeth were vertically thrashed to inflict maximum damage.

Orodus

Orodontidae is an extinct family of cartilaginous fish that lived from the late Pennsylvanian to the early Permian in what is now North America.
Described by crushing teeth, with a wide base and a crown.Known teeth of this type up to 110 mm in diameter, belonging to very large fish,perhaps as long as 10 m (31ft).
The genus Orodus was described by L. Agassiz in 1838 from the early Carboniferous of Bristol (England). The teeth were attributed to a wide variety of fish (eugeneodonts, hybodont sharks) - and indeed, this form of teeth could converge in different groups of cartilage. In the 1980s, in the black deep-water shales of coal age in North America (Indiana), the bodies of fish with horodontal teeth were found. Samples originate from the Late Carboniferous (Westphal) Staunton and Linton formations. The sediments of these formations are the so-called cyclotems, where deep-water sediments alternated with shallow ones. At the same time, deep-sea sediments accumulated under anoxic conditions (for example, under conditions of high hydrogen sulfide concentration, as in the Black Sea) and the bodies of fish were well preserved.
Orodus greggi and O. micropterygius were large fish - skeletons are known up to 4 meters in length, although there could be individuals much larger.They have a long body, rounded stupid head. Sky-square cartilage is poorly defined, possibly fused with neurocranium. Meckel"s cartilage of the lower jaw is short and extended. The paired fins are tiny. The dorsal fin, apparently, is one, shifted backwards (undescribed representatives of the group with two dorsal fins are known). Caudal fin semi-lunar, not high. Anal fin and fin spines not. The body is covered with cyclomorial scales, which are more complex on the back, downward scales are simplified, turning into cloves. Remains of the Oordus skeleton from the carboniferous of England were found together with the shells of predatory ostracods that ate on the corpse of a fish.
These enormous fishes apparently lived in the water column and ate some invertebrates with hard covers (ammonites, equeries, floating gastropods). All orodont found in marine sediments. 3-4 genera are described: Orodus (early carbon - early Perm of Europe and North America), Leiodus (early carbon of North America), Mesodmodus (early carbon of North America) and Hercynolepis (late Devonian of Europe).Orodus teeth are also known from the Middle Carboniferous near Moscow.

Pseudomegachasma

Pseudomegachasma ("false megamouth") is an extinct genus of filter-feeding shark that was closely related to the modern sand tiger shark.It is known from Cretaceous strata in Russia and the United States, and is the only known planktivorous odontaspid, as well as the oldest known planktivorous elasmobranch. It most likely derived from its closest relative, the piscivorous shark Johnlongia. As its name suggests, it was originally classified under Megachasma, before it was found to be an odontaspid.
The new lineage, named Pseudomegachasma, is represented by two extinct species – Pseudomegachasma casei (formerly known as Eorhincodon casei) from RF’s Belgorod and Volgograd provinces and P. comanchensis (formerly Megachasma comanchensis) from the U.S.
These sharks were 20 -25 feet (6-8 m) long and had small teeth very similar to the modern-day megamouth shark (Megachasma pelagios).
Pseudomegachasma means ‘false megamouth shark’ due to its dental features superficially nearly identical to the modern-day, plankton-eating megamouth shark.E. casei and M. comanchensis are two Cretaceous taxa initially described as putative planktivorous elasmobranchs, but the type specimens of these two taxa were subsequently reinterpreted to represent taphonomically abraded teeth of an odontaspidid, Johnlongia.
Pseudomegachasma sharks lived in warm oceans during the age of the dinosaurs about 100 million years ago.
Pseudomegachasma would represent the oldest known plankton-feeding shark in the fossil record.These sharks would have evolved independent of the four known lineages of modern-day planktivorous cartilaginous fishes: the megamouth sharks, basking sharks, whale sharks, and manta rays.

Chlamydoselachus goliath

Chlamydoselachus is a genus of sharks and the sole extant member of the family Chlamydoselachidae, in the order Hexanchiformes. It contains two extant and several extinct species. The most widely known species still surviving is the frilled shark (Chlamydoselachus anguineus).It is known as a living fossil, along with Chlamydoselachus africana, also known as the Southern African frilled shark, which is only found along coastal areas of South Africa. The only two extant species of this genus are deep-sea creatures which are typically weakened in areas closer to the surface.