We scrutinize the Hipparcos parallax for the bright O supergiant \zeta Pup , and confirm that the implied distance of 332 \pm 11 pc 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 < 3.7 d ( with 95 % confidence ) , ruling out a proposed \sim 5.1-d value .
If the photometric period is the rotation period then i , the inclination of the rotation axis to the line of sight , is 33 { \fdg } 2 \pm 1 { \fdg } 8 .
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 } = 1.78 d 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 .