  We prove a conjecture of Crapo and Penne which characterizes isotopy classes
of skew configurations with spindle-structure. We use this result in order to
define an invariant, spindle-genus, for spindle-configurations.
  We also slightly simplify the exposition of some known invariants for
configurations of skew lines and use them to define a natural partition of the
lines in a skew configuration.
  Finally, we describe an algorithm which constructs a spindle in a given
switching class, or proves non-existence of such a spindle.
