  We propose a quantum symmetry reduction of loop quantum gravity to Bianchi I
spacetimes. To this end, we choose the diagonal metric gauge for the spatial
diffeomorphism constraint at the classical level, leading to an
$\mathbb{R}_{\text{Bohr}}$ gauge theory, and quantise the resulting theory via
loop quantum gravity methods. Constraints which lead classically to a suitable
reduction are imposed at the quantum level. The dynamics of the resulting model
turn out to be very simple and manifestly coincide with those of a polymer
quantisation of a Bianchi I model for the simplest choice of full theory
quantum states compatible with the Bianchi I reduction. In particular, the
"improved" $\bar{\mu}$ dynamics of loop quantum cosmology can be obtained by
modifying the regularisation of the Hamiltonian constraint with similar ideas,
in turn yielding insights into the full theory dynamics.
