A three dimensional Dirac Semimetal: (a) Crystal structure and (b) Brillouin zone of newly proposed material, BiO2 in the β-cristobalite structure. (c) shows the map of energy vs. momentum for BiO2, which exhibits linear dispersion and Dirac points at the Fermi energy at the X points in the Brillouin zone. This band structure can be viewed as a three-dimensional generalization of graphene.