We present optical spectrophotometric observations of the X-ray binary star Her X-l, The majority of line absorption and emission originates on or near the mass-losing primary with distributions over the inner face of the star, consistent with irradiation by X-rays from the environs of the compact companion, He II lambda 4686 Angstrom emission is detected and found to be distributed closely about the neutron star and is a likely tracer of the accretion flow, Variations from orbit-to-orbit are a consequence of the 35-d quasi-periodicity that has been previously found over the entire observable spectrum, The mechanism providing the 35-d period is considered to be the precession of a tilted and twisted accretion disc about the neutron star, In order to determine the plausibility of the twisted-disc model we reconstruct the expected shadow of the disc across the heated inner face of the donor star, Large-scale emission structure is reproduced, but the model fails to synthesize finer observational details predicted by recent theoretical calculations.