Given that the primitive basis vectors of a lattice are
a = (a/2)(x + y),
b = (a/2)(y + z),
c = (a/2)(z + x)

where x, y, and `z are unit vectors in the x-, y- and z-directions of a Cartesian coordinate system.
a) Determine the Bravais lattice.
b) Calculate the volume of the primitive unit cell.