Peripetoceras is a genus in the Clydonautilacean

Clydonautilaceae

The Clydonautilaceae is a superfamily within the nautiloid order Nautilida characterized by smooth, generally globular, shells with nearly straight sutures, in early forms but developing highly differentiated sutures in some later forms...

 family, Liroceratidae

Liroceratidae

Liroceratidae is an extinct family of nautilids, shelled marine molluscs, belonging to the Clydonautilaceae, consisting of generally smooth, involute, nautiliconic forms with a small umbilicus...

. It can be recognized by its smooth, involute shell with a deep small umbilicus with rounded shoulders and steep convex wall; whorl section with flattened venter, rounded ventral shoulders and convergent slightly convex flanks; suture with slight ventral and lateral lobes; and small siphuncle located dorsally of the center.

Peripetoceras ranges from the Lower Carboniferous

Carboniferous

The Carboniferous is a geologic period and system that extends from the end of the Devonian Period, about 359.2 ± 2.5 Mya , to the beginning of the Permian Period, about 299.0 ± 0.8 Mya . The name is derived from the Latin word for coal, carbo. Carboniferous means "coal-bearing"...

 (Upper Mississippian) to the Permian

Permian

The PermianThe term "Permian" was introduced into geology in 1841 by Sir Sir R. I. Murchison, president of the Geological Society of London, who identified typical strata in extensive Russian explorations undertaken with Edouard de Verneuil; Murchison asserted in 1841 that he named his "Permian...

and has been found in Europe (England and Germany), Russia and China.