  We study the geometric aspects of two exotic bialgebras S03 and S14
introduced in math.QA/0206053. These bialgebras are obtained by the
Faddeev-Reshetikhin-Takhtajan RTT prescription with non-triangular R-matrices
which are denoted $R_{03}$ and $R_{14}$ in the classification of Hietarinta,
and they are not deformations of either GL(2) or GL(1/1). We give the spectral
decomposition which involves two, resp., three, projectors. These projectors
are then used to provide the Baxterisation procedure with one, resp., two,
parameters. Further, the projectors are used to construct the noncommutative
planes together with the corresponding differentials following the Wess-Zumino
prescription. In all these constructions there appear non-standard features
which are noted. Such features show the importance of systematic study of all
bialgebras of four generators.
