Tetragonoceras is an extinct prehistoric nautiloid genus from the nautilid

Nautilida

The Nautilida constitute a large and diverse order of generally coiled nautiloid cephalopods that began in the mid Paleozoic and continues to the present with a single family, the Nautilidae which includes two genera, Nautilus and Allonautilus, with six species...

 family Tetragonoceratidae that lived during the Middle Devonian

Devonian

The Devonian is a geologic period and system of the Paleozoic Era spanning from the end of the Silurian Period, about 416.0 ± 2.8 Mya , to the beginning of the Carboniferous Period, about 359.2 ± 2.5 Mya...

, found in Canada.

Tetragonoceras has an openly spiralled, gyroconic shell with an almost square cross section, but with the venter on the outer rim broader than the dorsum on the inner. The sides are flattish and converge slightly on the dorsum and the ventro-lateral shoulders are angular. The suture of Tetragonoceras has slight lateral and ventral lobes separated by subangular saddles. The siphuncle

Siphuncle

The siphuncle is a strand of tissue passing longitudinally through the shell of a cephalopod mollusk. Only cephalopods with chambered shells have siphuncles, such as the extinct ammonites and belemnites, and the living nautiluses, cuttlefish, and Spirula...

 is ventral and tubular. (Kummel 1964.). A member of the Tetragonoceratidae, Tetragonoceras is also a component of the superfamily Tainocerataceae

Tainocerataceae

The Tainocerataceae is a superfamily in the cephalopod order Nautilida characterized by straight to loosely coiled shells, generally with a degressed, such that the width is greater than the height, to quadrate whorl section. Many bore spines, ribs, frills, wings, or nodes...

.