  ccc-Autoevolutes are closed constant curvature space curves which are their
own evolutes. A modified Frenet equation produces constant curvature curves
such that the curve on $[0, \pi]$ is congruent to the evolute on $[\pi, 2\pi]$
and vice versa. Closed curves are then congruent to their evolutes. If the
ruled surface spanned by the principal normals between curve and evolute is a
M\"obius band then the curve is its own evolute. We use symmetries to construct
closed curves by solving 2-parameter problems numerically. The smallest
autoevolute which we found is a trefoil knot parametrized by three periods $[0,
6\pi]$.Our smallest closed solution of the ODE is parametrized by two periods.
