  Of the major deuterostome groups, the echinoderms with their multiple forms and complex development are arguably the most mysterious. Although larval echinoderms are bilaterally symmetric, the adult body seems to abandon the larval body plan and to develop independently a new structure with different symmetries. The prevalent pentamer structure, the asymmetry of Loven's rule and the variable location of the periproct and madrepore present enormous difficulties in homologizing structures across the major clades, despite the excellent fossil record. This irregularity in body forms seems to place echinoderms outside the other deuterostomes. Here I propose that the predominant five-ray structure is derived from a hexamer structure that is grounded directly in the structure of the bilaterally symmetric larva. This hypothesis implies that the adult echinoderm body can be derived directly from the larval bilateral symmetry and thus firmly ranks even the adult echinoderms among the bilaterians. In order to test the hypothesis rigorously, a model is developed in which one ray is missing between rays IV-V (Loven's schema) or rays C-D (Carpenter's schema). The model is used to make predictions, which are tested and verified for the process of metamorphosis and for the morphology of recent and fossil forms. The theory provides fundamental insight into the M-plane and the Ubisch', Loven's and Carpenter's planes and generalizes them for all echinoderms. The theory also makes robust predictions about the evolution of the pentamer structure and its developmental basis. *** including corrections (see footnotes) *** 
A hexamer origin of the echinoderms' five rays