  The considered model of baryon consists of three pointlike masses (quarks)
bounded pairwise by relativistic strings forming a curvilinear triangle.
Classic analytic solutions for this model corresponding to a planar uniform
rotation about the system center of mass are found and investigated. These
solutions describe a rotating curve composed of segments of a hypocycloid. The
curve is a curvilinear triangle or --- a more complicated configuration with a
set of internal massless points moving at the speed of light. Different
topological types of these motions are classified in connection with different
forms of hypocycloids in zero quark mass limit. An application of these
solutions to description of baryon states on the Regge trajectories is
considered.
