Mechanisms for shaping and folding sheets of cells during development are poorly understood. An example is the complex reorganisation of the forebrain neural plate during neurulation, which must fold a sheet into a tube while evaginating two eyes from a single contiguous domain within the neural plate. We, for the first time, track these cell rearrangements to show that forebrain morphogenesis differs significantly from prior hypotheses. We postulate a new model for forebrain neurulation and demonstrate how mutations affecting two signalling pathways can generate cyclopic phenotypes by disrupting normal cell movements or introducing new erroneous behaviours.