Context : Aims : We determine the physical properties ( spin state and shape ) of asteroid ( 21 ) Lutetia , target of the ESA Rosetta mission , to help in preparing for observations during the flyby on 2010 July 10 by predicting the orientation of Lutetia as seen from Rosetta . Methods : We use our novel KOALA inversion algorithm to determine the physical properties of asteroids from a combination of optical lightcurves , disk-resolved images , and stellar occultations , although the latter are not available for ( 21 ) Lutetia . Results : We find the spin axis of ( 21 ) Lutetia to lie within 5° of ( \lambda = 52 ° , \beta = -6 ° ) in Ecliptic J2000 reference frame ( equatorial \alpha = 52 ° , \delta = +12 ° ) , and determine an improved sidereal period of 8.168 270 \pm 0.000 001 h. This pole solution implies the southern hemisphere of Lutetia will be in “ seasonal ” shadow at the time of the flyby . The apparent cross-section of Lutetia is triangular as seen “ pole-on ” and more rectangular as seen “ equator-on ” . The best-fit model suggests the presence of several concavities . The largest of these is close to the north pole and may be associated with large impacts . Conclusions :