  The main purpose is to describe the evolution of $\Xt = \Xs \wedge_- \Xss,$
with $\X(s,0)$ a regular polygonal curve with a nonzero torsion in the
3-dimensional hyperbolic space. Unlike in the Euclidean space, a nonzero
torsion implies two different helical curves. However, recent techniques
developed by de la Hoz, Kumar, and Vega help us in describing the evolution at
rational times both theoretically and numerically, and thus, the similarities
and differences.
  Numerical experiments show that the trajectory of the point $\X(0,t)$
exhibits new variants of Riemann's non-differentiable function whose structure
depends on the initial torsion in the problem. As a result, with these new
solutions, it is shown that the smooth solutions (helices, straight line) in
the hyperbolic space show the same instability as displayed by their Euclidean
counterparts and curves with zero-torsion. These numerical observations are in
agreement with some recent theoretical results obtained by Banica and Vega.
