  We investigate how geometry influences spin dynamics in polygonal magnetic
nanotubes. We find that lowering the rotational symmetry of nanotubes by
decreasing the number of planar facets, splits an increasing number of
spin-wave modes, which are doubly degenerate in cylindrical tubes. This
symmetry-governed splitting is distinct form the topological one recently
observed in cylindrical nanotubes. Doublet modes with half-integer or integer
multiple azimuthal periods of the number of facets, split to singlet pairs with
lateral standing-wave profiles of opposing mirror-plane symmetries.
Furthermore, the polygonal geometry facilitates the hybridization of modes with
different azimuthal periods but the same symmetry, manifested in avoided level
crossings. These phenomena, unimaginable in cylindrical geometry, provide new
tools to control spin dynamics on nanoscale. The presented concept can be
generalized to nano-objects of versatile geometries and order parameters,
offering new routes to engineer dynamic response in nanoscale devices.
