We present a first-principles study of the unreconstructed (001) surfaces of the half-metallic ferromagnet NiMnSb. Both terminations (MnSb and Ni) are considered. We find that half-metallicity is lost at the surfaces. After a discussion of the geometric relaxations and the spin-polarized surface band structure, we focus on topography images which are expected to be found with spin-polarized scanning tunneling microscopy. For the MnSb-terminated surface we find that only the Sb atoms are

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... reflecting a geometric buckling caused by relaxations. For the Ni-terminated surface we find a strong contrast between the images of forward and reverse tip-sample-bias of 0.5 eV, as well as a stripe-like image for reverse bias. We interpret these findings in terms of highly directional surface states which are formed in the spin-down gap region.