THE standard carbon-arc synthesis for fullerenes also produces graphitic microtubules with helical structures 1. In most cases the cylindrical tubes are closed by polyhedral caps, some being first transformed into a conical shape before closure 2. Here we present images from transmission electron microscopy of a further kind of growth morphology, in which cone-like growth is transformed into cylindrical growth by the incorporation of a defect that induces negative curvature. We suggest that the defect in the hexagonal network responsible for negative curvature may be a single heptagonal ring. Three-dimensional, open negatively curved graphitic structures have been proposed recently by Terrones and Mackay 3. We discuss more generally the effect of pentagons and heptagons on the growth morphologies of these tubules, and the constraints on the number of pentagonal defects imposed by tube closure.