  An alternative framework underlying connection between tensor ${\rm
sl}_2$-calculus and spin networks is suggested. New sign convention for the
inner product in the dual spinor space leads to a simpler and direct set of
initial rules for the diagrammatic recoupling methods. Yet it preserves the
standard chromatic graph evaluations. In contrast with the standard
formulation, the background space is that of symmetric tensor spaces, which
seems to be in accordance with the representation theory of ${\rm SL}(2)$. An
example of Apollonian disk packing is shown to be a source of spin networks.
The graph labeling is extended to non-integer values, resulting in the
complex-values of chromatic evaluations.
