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$\zeta$ Phoenicis is a bright binary system containing B6V and B8V stars. Ithas deep total and annular eclipses, a slightly eccentric orbit with a periodof 1.669 d, apsidal motion and a third body on a wider orbit. The TransitingExoplanet Survey Satellite light curve and published radial velocities of thissystem are analysed to determine masses of 3.91 +/- 0.06 Msun and 2.54 +/- 0.03Msun and radii of 2.84 +/- 0.02 Rsun and 1.89 +/- 0.01 Rsun. The resultingdistance to the system is in agreement with its trigonometric parallax. Thephysical properties of the stars, with the exception of the effectivetemperature of the secondary component, can be matched by the predictions ofseveral sets of theoretical stellar evolutionary models for a solar chemicalcomposition and an age of 70 to 90 Myr. A spectroscopic analysis of this systemis encouraged for the determination of the photospheric chemical composition ofthe stars, plus improved measurements of their masses and effectivetemperatures.

Rediscussion of eclipsing binaries. Paper I. The totally-eclipsing B-type system zeta Phoenicis