  We investigate the properties of an edge-centered honeycomb lattice, and show
that this lattice features both spin-1/2 and spin-1 Dirac-Weyl fermions at
different filling fractions f (f=1/5,4/5 for spin-1/2 and f=1/2 for spin-1).
This five-band system is the simplest lattice that can support simultaneously
the two different paradigmatic Dirac-Weyl fermions with half-integer spin and
integer spin. We demonstrate that these pseudo-relativistic structures,
including a flat band at half-filling, can be deduced from the underlying
Kagome sublattice. We further show that the signatures of the two kinds of
relativistic fermions can be clearly revealed by several perturbations, such as
a uniform magnetic field, a Haldane-type spin-orbit term, and charge density
waves. We comment on the possibility to probe the similarities and differences
between the two kinds of relativistic fermions, or even to isolate them
individually. We present a realistic scheme to realize such a system using cold
atoms.
