In this genus Brongniart[865] included two species, _Hexapterospermum stenopterum_ and _H. pachypterum_: the shell is hexagonal in transverse section, each angle being prolonged as a narrow flange. In one of the sections figured by Brongniart (fig. 495, E) the ribs are not fissured: this is said to be a feature distinguishing _Hexapterospermum_ from _Ptychotesta_, but the occurrence of a fissured rib in another section suggests that in the structure of the ribs there is no essential difference between the two genera. In _Ptychotesta pachypterum_ the testa is prolonged at the chalazal end as in _Polylophospermum_, and it is possible that there is no generic difference. Williamson described a cast from the Coal Measures of Lancashire as _Hexapterospermum_ [= _Hexagonocarpus_] _Noegerrathi_[866] (fig. 506, H), but in the absence of anatomical characters it is preferable to avoid the use of Brongniart’s term and to assign them to Renault’s genus _Hexagonocarpus_[867]. Similarly the seeds referred by Dr P. Bertrand[868] to _Hexapterospermum_ may appropriately be included in the genus _Hexagonocarpus_. [Illustration: Fig. 495. A, _Polypterospermum Renaultii_. B, _Ptychotesta tenuis_. C, D, _Polylophospermum_ _stephanense_; _sa_, sarcotesta; _s_, spaces; _v_, vascular bundles. E, _Hexapterospermum stenopterum_. F, _Diplotesta avellana_. G, _Taxospermum_ _Grüneri_. H, _Diplotesta Grand’Euryana_. (After Brongniart; C, after Oliver.)] =Polypterospermum.= Brongniart. This generic name was proposed for an ovoid seed from St Étienne described as _Polypterospermum Renaultii_[869]; hexagonal in section with six deep and sharp flanges at the angles alternating with six secondary ridges distinguished by their blunter edges and slightly smaller depth (fig. 495, A). Without further anatomical details it is hardly possible to say whether or not the species represents a well-defined generic type, but it is not improbable that a fuller knowledge would confirm Brongniart’s institution of a new generic designation. The seeds described by Arber[870] and Kidston[871] respectively as _Radiospermum ornatum_ and _Polypterospermum ornatum_ are transferred to _Polygonocarpus_ on the ground that they afford no evidence of anatomical characters of the _Polypterospermum_ type. =Pachytesta.= Brongniart. Brongniart[872] established this genus for some unusually large seeds (fig. 496, A) from the Coal Measures of France reaching a length of 11–12 cm. and resembling in form and size a hen’s egg. Petrified examples have been described by Brongniart and Renault[873], and Oliver[874] has given a lucid statement of the more interesting features of this Permo-Carboniferous genus. _Pachytesta gigantea_ (Grand’Eury).