  In this paper, we study and describe the universal Poisson deformation space
of hypertoric varieties concretely. In the first application, we show that
affine hypertoric varieties as conical symplectic varieties are classified by
the associated regular matroids (this is a partial generalization of the result
by Arbo and Proudfoot). As a corollary, we obtain a criterion when two quiver
varieties whose dimension vector have all coordinates equal to one are
isomorphic to each other. Then we describe all 4- and 6-dimensional affine
hypertoric varieties as quiver varieties and give some examples of
8-dimensional hypertoric varieties which cannot be raised as such quiver
varieties. In the second application, we compute explicitly the number of all
projective crepant resolutions of some 4-dimensional hypertoric varieties by
using the combinatorics of hyperplane arrangements.
