  We show how to construct, for each $r \geq 3$, an ageometric, fully
irreducible $\phi\in Out(F_r)$ whose ideal Whitehead graph is the complete
graph on $2r-1$ vertices.
  This paper is the second in a series of three where we show that precisely
eighteen of the twenty-one connected, simplicial, five-vertex graphs are ideal
Whitehead graphs of fully irreducible $\phi \in Out(F_3)$. The result is a
first step to an $Out(F_r)$ version of the Masur-Smillie theorem proving
precisely which index lists arise from singular measured foliations for
pseudo-Anosov mapping classes.
  In this paper we additionally give a method for finding periodic Nielsen
paths and prove a criterion for identifying representatives of ageometric,
fully irreducible $\phi\in Out(F_r)$
