crystals*

We propose that the noncentrosymmetric hexagonal ABC crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. Six pairs of Weyl points and one pair of Dirac points coexist in the Brillouin zone. All twelve Weyl points are located in the k_z = 0 plane at about 0.25 eV above the Fermi energy and are related by the C_6v point group symmetry. The existence of the Weyl points is confirmed by calculations of the Berry flux and the surface Fermi arcs. The Dirac points, which can be considered as double Weyl points with zero Chern number, occur along the C_6z rotational axis and are protected by C_6v point group symmetry. The Dirac points in the z axis are about 0.11 eV below the Fermi energy and form two electron pockets. We study topological phase transitions as a function of the HgPb buckling in SrHgPb and other material realizations of related topological semimetals that occur in the family of hexagonal ABC crystals. Our finding should provide a realistic and promising platform for studying the interplay between Dirac points and Weyl points, and for understanding their effects on transport and optical properties.