  We study all five-, six-, and one eight-vertex type two-state solutions of
the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13}
A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of
these solution. Starting with algebraic solutions, whose parameters have no
specific interpretation, and then using these symmetries we can construct a
parametrization where we can identify global, color and spectral parameters. We
show in particular how the distribution of these parameters may be changed by a
change of gauge.
