  We recall some basic aspects of line and line Complex representations, of
symplectic symmetry emerging in bilinear point transformations as well as of
Lie transfer of lines to spheres. Here, we identify SU(2) spin in terms of
(classical) projective geometry and obtain spinorial representations from
lines, i.e.~we find a natural non-local geometrical description associated to
spin. We discuss the construction of a Lagrangean in terms of line/Complex
invariants. We discuss the edges of the fundamental tetrahedron which allows to
associate the most real form SU(4) with its various related real forms covering
SO($n$,$m$), $n+m=6$.
