  Nanostructures based on platinum, such as small clusters or STM-tips, often
exhibit an atomistic structure that relies upon one or very few strongly
under-coordinated platinum atoms. Here, we analyze a paradigmatic example, an
apex atom on a pyramidal platinum cluster employing the density functional
theory. We show that such a pristine platinum tip exhibits a spin polarization
of the apex atom with a remarkable robustness. Due to a depletion of the
projected density of states at the apex position, the apex-magnetization is
efficiently locked to about 0.6$\mu_\text{B}$.
