The allotropes of carbon. Three forms (or 'allotropes') of pure carbon are diamond, graphite and buckminster fullerene (or 'buckyballs'). In all three allotropes the carbon atoms are joined by strong covalent bonds but in such different arrangements that the properties of the allotropes are very different.he allotropes of carbon. Three forms (or 'allotropes') of pure carbon are diamond, graphite and buckminster fullerene (or 'buckyballs'). In all three allotropes the carbon atoms are joined by strong covalent bonds but in such different arrangements that the properties of the allotropes are very different.