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

Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank