  Nielsen-Ninomiya theorem forbids Weyl fermions on the lattice which respect
the full hypercubic symmetry. By giving up this assumption in a specific way,
it is possible to formulate a lattice theory with a single Weyl fermion in four
dimensions and a sextet of Dirac particles in two dimensions. This way, the
meaning of the theorem in relation to the doubling problem on the lattice is
clarified. Whether the proposal will be suited for future lattice computations
will depend on the effects the extra particles will have in the interacting
theory.
