  Despite its simple crystal structure, layered boron nitride features a
surprisingly complex variety of phonon-assisted luminescence peaks. We present
a combined experimental and theoretical study on ultraviolet-light emission in
hexagonal and rhombohedral bulk boron nitride crystals. Emission spectra of
high-quality samples are measured via cathodoluminescence spectroscopy,
displaying characteristic differences between the two polytypes. These
differences are explained using a fully first-principles computational
technique that takes into account radiative emission from ``indirect'',
finite-momentum, excitons via coupling to finite-momentum phonons. We show that
the differences in peak positions, number of peaks and relative intensities can
be qualitatively and quantitatively explained, once a full integration over all
relevant momenta of excitons and phonons is performed.
