Description: The Triquetrorhabdulaceae are elongate nannoliths formed of three laths arranged back-to-back, in optical continuity. The two most common species are Triquetrorhabdulus carinatus (Oligocene and Early Miocene) and T. rugosus (Middle and Late Miocene).

Nannolith structure and crystallography: In T. carinatus the three laths are similar and are arranged at 120° to each other; the nannolith is thus radially symmetrical in cross-section. The optic axis of the nannolith is parallel to the length, consequently they show strong birefringence and straight, length fast, extinction, in any common orientation. The laths are normally featureless, very well preserved specimens, however, sometimes show a fine transverse striation, resembling the rodded ultrastructure of T. rugosus (e.g. Perch-Nielsen 1977 pl. 36/6).

T. rugosus is formed of three dissimilar laths. The two basal laths are broad and meet at a shallow angle. The third, median, lath is low, and curved in plan view. All three laths often show a rodded ultrastructure, perpendicular to the length. This is always clearest on the broader of the basal laths. In addition subsidiary ridges sometimes form on the basal laths. The optic axis of the laths is perpendicular to their length and in the plane of the median ridge; it is therefore vertical when the basal plates are horizontal, and the median ridge vertical. This is the usual rest position of the nannolith, which is consequently dark in cross-polars. An alternative, only slightly less common, position is for the median ridge to be pointing downward, the basal plate is then tilted from the horizontal; in this orientation the nannolith shows weak birefringence, with straight, but length-slow extinction.

Thus these two species have distinctly different structures and optical orientations: T. carinatus has three identical laths with the optic axis parallel to their length; T. rugosus has three dissimilar laths with the optic axis perpendicular to their length. Of the minor species T. auritus, T. challengeri, and T. milowii all show the same structure as T. carinatus and were plainly derived from it. Conversely, T. rioi, T. striatus, T. extensus and T. finifer all show the same structure as T. rugosus.

Orthorhabdus serratus superficially appears to be a third distinct type since it shows birefringence, but with the opposite orientation to T. carinatus (i. e. length-slow). However, this species can be considered a variant of the T. rugosus pattern, with a larger median lath (compare Figs. 56/E & F). Since the median lath is larger than the basal laths the nannolith usually rests on its side, and so shows strong birefringence. The two species are readily separable on other grounds: O. serratus has strongly differentiated ends; is bilaterally symmetrical; and does not obviously have the rodded ultrastructure of T. rugosus. Nonetheless their similarity is striking, particularly when compared to T. carinatus. This suggests that T. rugosus is more likely to be related to O. serratus than to T. carinatus.