Recently a new model for the structure of columnar graphite whiskers has been proposed; this model includes the presence of five-rings of carbon atoms, as in the fullerenes. The whiskers are assumed not to be single crystals but have geometrically well defined textures. Their unusual diffraction patterns exhibit rotation symmetry of high multiplicity. The wide variety of the observed multiplicities is explained by assuming small changes in the conical shape of the whiskers. We describe a series of electron diffraction experiments which have been performed on fracture cones of these graphite whiskers. These experiments confirm unambiguously the proposed microstructure.