Glyptodendron is a Lower Silurian westonocerid characterized by compressed cyrtocones with a narrowly rounded dorsum and greatest width in the ventrolateral region.

Its generic etymology is modified from the Greek glypto (γλύφω) for "I engrave" and it "alludes to the depressed areoles" which Claypole erroneously interpreted from the superficial pits across the shell as being similar to those seen in lycopsid plants.

[1] Its specific epithet refers to it the locality from which the fossils were recovered by Leven Siler, a student of Professor E. W. Claypole (Antioch College, Yellow Springs, Ohio).

Though originally described as a plant fossil, fifteen years after its description, the type material of Glyptodendron was re-examined by noted paleontologist, August F. Foerste who recognized its true identity as a nautiloid.

[2] Foerste thought it might prove to be referable to the better known Cyrtoceras, a previously described nautiloid taxon.