The general shell form of cephalopods is also variable and important in their classification. The first mollusc page has a more complete listing of forms, but a few are shown here with real examples.
Straight cone-shaped cephalopods such as in the first photo (Carter Coll., Gg2) are called orthoconic or orthocone cephalopods. The word literally translates "perfect cone". Some Paleozoic nautiloids had a slightly modified version in which the cone is bent or curved, but not through a complete whorl. This form is called cyrtocone. A modification of this form in which the cone rapidly expands (i.e., is a short, fat cone) is called brevicone. If only the later, younger parts of the cone expand the form is ascocone. Finally, if the shell is more obviously bent through (or almost through) a complete whorl, without any contact between the aperture and the older part of the shell, the form is gyrocone.
In a few species the shell coils more obviously, but does not do so in the typical planispiral fashion generally associated with coiled cephalopods. The fragments of Turrelites (GSW Tax. Coll. 65017) shown below suggest a shell that was trochospirally coiled, as a gastropod shell is. (How would you prove Turrelites was not a gastropod?) Such a form is called heteromorphic. Some heteromorphic shells coiled completely irregularly rather than trochospirally.
Finally, the "normal" planispirally coiled cephalopods can accomplish coiling of three different patterns. The left photo below (Perisphinctites -- GSW Tax. Coll. 65028) coils in such a way that the dorsal (inside) margin of each coil just touches the venter (outside) of the whorl before. This is advolute (or evolute). Note that if the coils did not quite touch the shell would be gyrocone (see above). The middle photo shows a shell (Spenodiscus -- GSW Tax. Coll. 65019) in which each whorl partially covers the one before. (i.e., the Aperture overlaps the next earlier whorl). Such a shell is involute. On the right (Nautilus pompilius -- Carter Coll. RGi2) each whorl completely covers all the earlier formed whorls. Such a shell is convolute. (Refer back to the picture on the first cephalopod page to see the same species cut open to show two earlier whorls enclosed in the body whorl.)
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