  We study the fundamental group of the configuration space of $n$ ordered
points on the circle no three of which are equal. We compute it for $n<6$ and
describe its homology for $n=6$. We also show how, for arbitrary $n$, this
group can be assembled from planar braid groups, relate it to the pure cactus
group and construct a cubical complex homotopy equivalent to its classifying
space.
