  For any finite reflection group $W$ on $\mathbb{R}^{N}$ and any irreducible
$W$-module $V$ there is a space of polynomials on $\mathbb{R}^{N}$ with values
in $V$. There are Dunkl operators parametrized by a multiplicity function, that
is, parameters associated with each conjugacy class of reflections. For certain
parameter values, called singular, there are nonconstant polynomials
annihilated by each Dunkl operator. There is a Gaussian bilinear form on the
polynomials which is positive for an open set of parameter values containing
the origin. When $W$ has just one class of reflections and $\dim V>1$ this set
is an interval bounded by the positive and negative singular values of
respective smallest absolute value. This interval is always symmetric around
$0$ for the symmetric groups. This property does not hold in general, and the
icosahedral group $H_{3}$ provides a counterexample. The interval for
positivity of the Gaussian form is determined for each of the ten irreducible
representations of $H_{3}$.
