Haeckel, 1881, emend. Riedel, 1967
Cephalis spherical or subspherical, relatively small, often poreless or sparsely perforate. It usually bears an apical horn. Internal spicule small and inconspicuous. With one or more, sometimes up to over 10, usually well-developed postcephalic segments. Generally, cap- or helmet-shaped, or conical in overall outline.
The following species of this family are treated in the present volume:
Artostrobus annulatus
Clathrocyclas cassiopeiae
Cornutella profunda
Corocalyptra cervus
Corocalyptra columba
Corocalyptra kruegeri
Cycladophora davisiana
Cyrtopera laguncula
Dictyocephalus papillosus
Dictyophimus gracilipes
Dictyophimus hirundo
Dictyophimus infabricatus
Eucyrtidium acuminatum
Eucyrtidium anomalum
Eucyrtidium hexastichum
Lipmanella bombus
Lipmanella dictyoceras
Litharachnium tentorium
Lithopera bacca
Lithostrobus hexagonalis
Perypiramis circumtexta
Pterocanium elegans
Pterocanium praetextum
Pterocanium trilobum
Pterocyrtidium dogieli
Sethoconus anthocyrtis
Theopilium tricostatum