- Test of moderate size, depressed with uniformly rounded sides.
- Apical disc large, with large subcircular periproct. Apical disc plating dicyclic. Periproctal membrane covered in small uniform platelets.
- Ambulacral zones moderately broad and straight; not expanded adorally.
- Pore-pairs in weakly offset triads. Ambulacral plating compound in triads with all three elements extending to the perradial suture. Large primary tubercle to each compound plate and with a narrow zone of granules perradially at most.
- Interambulacral plates a little wider than tall; dominated by large primary tubercle with a large areole and small mamelon. All tubercles perforate and non-crenulate. Rest of plate covered with heterogeneous granulation, including small interradial secondary tubercles.
- Spines long and slender, without cortex; primary spines solid with medulla in cross-section; secondary spines with a hollow lumen.
- Sphaeridium on each compound plate from peristome to apex.
- Auricles of perignathic girdle small and upright, not meeting perradially.
- Lantern with deep foramen magnum and grooved teeth.
- C. cubensis Agassiz, 1869; Recent, Caribbean.
- C. mirabilis (Doderlein, 1885); Recent, Japan.
- C. porphyrogigas Anderson, 2009; Recent, New Zealand and Australia.
- C. indica (de Meijere, 1903); Recent, Philippines.
- C. hawaiiensis Clark, 1907; Recent, Hawaii.
- C. novaezealandiae Pawson, 1964; Recent, Australasia.
- C. otagoensis McKnight, 1968; Recent, New Zealand.
- C. alanbakeri Rowe, 1989; Recent Tasman Straight.
- C. annulata Mortensen, 1940; Recent, Malay Archipelago.
- C. diomedeae Mortensen, 1939; Recent, Gulf of Panama.
- C. capensis H. L. Clark, 1923; Recent, South Africa.
- C. pulchella (Agassiz & Clark, 1907); Recent, Pacific, including New Zealand.
- C. superba H. L. Clark, 1925; Recent, Indian Ocean.
- C. depressa Koehler, 1927; Recent, Maldive Islands.
- C. ameghinoi de Loriol, 1902; Miocene, Patagonia.
- C. chalmasi (Cotteau, 1882); Bajocian and Bathonian, France.
- C. tuberculata Wright, 1860; Oxfordian, Upper Jurassic, England.