  In this work, it is shown that there is a continuous function $\mu:[0,1]
\longrightarrow \mathbb{C}$ such that $\mathsf{P}^\mathsf{I}(\mu(\alpha)) = 0$,
$\forall \alpha \in [0,1]$, where $\mathsf{P}^\mathsf{I}$ is a Type I reduced
Ito polynomial. In addition, demonstrations are given for basic properties of
the Karpelevi{\v{c}} region, including a rigorous, but elementary argument
showing that points on the boundary of the Karpelevi{\v{c}} region are {\it
extremal} whenever $n> 3$.

Spectral Theory;Complex Variables