High-pressure ice polymorphs are important for our understanding of hydrogen bonding and exist in the interior of the earth and icy moons. Nonetheless, spectroscopic information about them is scarce, where no information about their optical properties in the near-infrared (NIR) region is available at all. We here report NIR spectra of six ice polymorphs differing in terms of their density and O-atom topology, namely, ices II, IV, V, VI, IX, and XII, in comparison with the known spectra of ice Ih. By contrast to earlier work, we do not use mulling agents or transmission of thin films but use diffuse reflectance on powdered samples in liquid nitrogen. The first overtone of the OH-stretching mode is identified as the marker band most suitable to distinguish between these ices. There is a clear blue shift of this band that increases with increasing topological density in addition to a significant narrowing of the band.