  We investigate theoretically polygonal quantum rings and focus mostly on the
triangular geometry where the corner effects are maximal. Such rings can be
seen as short core-shell nanowires, a generation of semiconductor
heterostructures with multiple applications. We show how the geometry of the
sample determines the electronic energy spectrum, and also the localization of
electrons, with effects on the optical absorption. In particular, we show that
irrespective of the ring shape low-energy electrons are always attracted by
corners and are localized in their vicinity. The absorption spectrum in the
presence of a magnetic field shows only two peaks within the corner-localized
state domain, each associated with different circular polarization. This
picture may be changed by an external electric field which allows previously
forbidden transitions, and thus enables the number of corners to be determined.
We show that polygonal quantum rings allow absorption of waves from distant
ranges of the electromagnetic spectrum within one sample.
