  We scrutinize the Hipparcos parallax for the bright O supergiant zeta Pup,
and confirm that the implied distance of 332+/-11pc appears to be reliable. We
then review the implications for the star's physical parameters, and the
consequences for the interpretation of P(phot), the 1.78-d photometric period.
The equatorial rotation period is <3.7d (with 95% confidence), ruling out a
proposed ~5.1d value. If the photometric period is the rotation period then i,
the inclination of the rotation axis to the line of sight, is 33.2+/-1.8
degrees. The inferred mass, radius, and luminosity are securely established to
be less than canonical values for the spectral type, and are not in agreement
with single-star evolution models. The runaway status, rapid rotation, and
anomalous physical properties are all indicative of an evolutionary history
involving binary (or multiple-star) interaction. We perform simple starspot
modelling to show that the low axial inclination required if P(rot) = 1.78d has
testable spectroscopic consequences, which have not been identified in existing
time series. If P(phot) is directly related to drivers of systematic,
high-velocity stellar-wind variability (`discrete absorption components') in
zeta Pup, antisolar differential rotation is required. Model line profiles
calculated on that basis are at variance with observations.
