The atomic geometry of the (1×2) and (1×3) structures of the Pt(100) surface has been determined from a low-energy electron-diffraction intensity analysis. Both structures are found to be of the missing-row type, consisting of (111) microfacets, and with similar relaxations in the subsurface layers. In both reconstructions the top-layer spacing is contracted by approximately 20% together with a buckling of about 0.17 Å in the third layer and a small lateral shift of about 0.04 Å in the second layer. Further relaxations down to the fourth layer were detectable. The surface relaxations correspond to a variation of interatomic distances, ranging from -7% to +4%, where in general a contraction of approximately 3% for the distances parallel to the surface occurs. The Pendry and Zanazzi-Jona R factors were used in the analysis, resulting in a minimum value of RP=0.36 and RZJ=0.26 for 12 beams at normal incidence for the (1×2) structure, and similar agreement for 19 beams of the (1×3) structure. The (1×3) structure has been reproducibly obtained after heating the crystal in an oxygen atmosphere of 5×10-6 mbar at 1200 K for about 30 min and could be removed by annealing at 1800 K for 45 min after which the (1×2) structure appeared again. Both reconstructed surfaces are clean within the detection limits of the Auger spectrometer. CO adsorption lifts the reconstruction in both structures. After desorption at 500 K the initial structures appear again, indicating that at least one of the reconstructions does not represent the equilibrium structure of the clean surface and may be stabilized by impurities.