  Graphene is a new material that exhibits remarkable properties from both
fundamental and applied issues. This is a 2D matter system whose physical and
mechanical features have been approached by using tight binding model, first
principle calculations based on DFT and membrane theory. Graphene as a carbon
molecule has also hidden symmetries that motivated extensions in various
dimensions such as chain-type configurations, that are frequently observed as
the graphene bridge narrowed down to a few- or single-atom width, graphene
multi-layers thought of as electric capacitors, doped graphene to gain more
physical properties as well as cousin systems such as diamond and hyperdiamond.
In this work, we use tight binding model ideas and field theory method as well
as the hidden symmetries of the underlying crystals to study physical aspects
of 2D graphene and its homologues. We also study the relation between 2D
graphene with the Bori\c{c}i-Creutz fermions considered recently in literature
as an adequate model to perform numerical simulations in 4D lattice QCD where
the two Dirac zeros are interpreted in terms of the light quarks up and down.
