  We demonstrate that the linear quotient singularity for the exceptional
subgroup G in Sp(4,C) of order 32 is isomorphic to an affine quiver variety for
a 5-pointed star-shaped quiver. This allows us to construct uniformly all 81
projective crepant resolutions of the quotient singularity C4/G as hyperpolygon
spaces by variation of GIT quotient, and we describe both the movable cone and
the Namikawa Weyl group action via an explicit hyperplane arrangement. More
generally, for the n-pointed star shaped quiver, we describe completely the
birational geometry for the corresponding hyperpolygon spaces in dimension 2n -
6; for example, we show that there are 1684 projective crepant resolutions when
n = 6. We also prove that the resulting affine cones are not quotient
singularities for n >= 6.
