  Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD
given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond
lattice H_4. We first study the link between the H_4 and SU(5); then we refine
the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2,
\lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5)
satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions
of the zeros of the Dirac operator D in terms of the SU(5) simple roots
\alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental
weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal
lattice H_4^\ast. It is shown, amongst others, that these zeros live at the
sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2)
\gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the
lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector.
Other features such as differences with BBTW model as well as the link between
the Dirac operator following from our construction and the one suggested by
Creutz using quaternions, are also given.
  Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.
