Acanthoeca spectabilis is one of the most common loricate choanoflagellates found in marine biofilms everywhere. However, it is special for two reasons; firstly, it is probably the most distinctive member of the small nudiform clade of loricate choanoflagellates. Secondly, the lorica chamber of Acanthoeca comprises a closely wound left-handed coil of costae that is unique amongst choanoflagellates. Mathematical analysis of the lorica chamber shows that the helical costae undergo two turns. This species, more than any, demonstrates that the helical coiling of costae can only be achieved by a rotational movement generated by the cell during lorica assembly. Comparison of the lorica morphology of Acanthoeca with that of the closely related genus Polyoeca indicates that the helical costae of Acanthoeca are probably homologous with the outer longitudinal costae of Polyoeca. This is unusual because helical costae are usually the innermost layer of costae. However, since there is no 'true' inner layer in the chamber of Acanthoeca the outer layer of costae are adjacent to the cell surface and therefore available for coiling. In contrast to tectiform choanoflagellates, which number more than one hundred species and inhabit a wide variety of microniches, the six known extant nudiform species must either represent a minor evolutionary development or be the remnants of a previously more extensive radiation.