  There are contextual sets of multiple qubits whose commutation is
parametrized thanks to the coset geometry $\mathcal{G}$ of a subgroup $H$ of
the two-generator free group $G=\left\langle x,y\right\rangle$. One defines
geometric contextuality from the discrepancy between the commutativity of
cosets on $\mathcal{G}$ and that of quantum observables.It is shown in this
paper that Kleinian subgroups $K=\left\langle f,g\right\rangle$ that are
non-compact, arithmetic, and generated by two elliptic isometries $f$ and $g$
(the Martin-Maclachlan classification), are appropriate contextuality filters.
Standard contextual geometries such as some thin generalized polygons (starting
with Mermin's $3 \times 3$ grid) belong to this frame. The Bianchi groups
$PSL(2,O\_d)$, $d \in \{1,3\}$ defined over the imaginary quadratic field
$O\_d=\mathbb{Q}(\sqrt{-d})$ play a special role.
