This paper continues the
investigations of previous papers in this series, and attention is confined to
exceptional arcs. Given a special constructing sequence for an exceptional arc, the
associated sequence of local linking matrices is defined, and the cofinality class of this
sequence is shown to be an invariant of the oriented local arc type of the exceptional
arc. This paper also gives a set of sufficient conditions for an arc to have a
constructing sequence.
The paper closes with examples which show that there exist uncountably
many locally nonamphicheiral exceptional arcs of any penetration index.
No two of the locally nonamphicheiral exceptional arcs exhibited here can
be distinguished by the invariant of nonoriented local arc type developed
previously.
