  As is well known, crystals have discrete space translational symmetry. It was
recently noticed that one-dimensional crystals possibly have discrete
Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time
translational symmetry as well. In this paper, we classify the discrete
Poincar\'{e} groups on two- and three-dimensional Bravais lattices. They are
the candidate symmetry groups of two- or three-dimensional crystals,
respectively. The group is determined by an integer generator $g$, and it
reduces to the space group of crystals at $g=2$.
