  Based on their formation mechanisms, Dirac points in three-dimensional
systems can be classified as accidental or essential. The former can be further
distinguished into type-I and type-II, depending on whether the Dirac cone
spectrum is completely tipped over along certain direction. Here, we predict
the coexistence of all three kinds of Dirac points in the low-energy band
structure of CaAgBi-family materials with a stuffed Wurtzite structure. Two
pairs of accidental Dirac points reside on the rotational axis, with one pair
being type-I and the other pair type-II; while another essential Dirac point is
pinned at the high symmetry point on the Brillouin zone boundary. Due to broken
inversion symmetry, the band degeneracy around accidental Dirac points is
completely lifted except along the rotational axis, which may enable the
splitting of chiral carriers at a ballistic p-n junction with a double negative
refraction effect. We clarify their symmetry protections, and find both the
Dirac-cone and Fermi arc topological surface states.
