  In this paper, we study the (singular) universal cover of an affine
hypertoric variety. We show that it is given by another affine hypertoric
variety, and taking the universal cover corresponds to taking the
simplification of the associated hyperplane arrangement. Also, we describe the
fundamental group of the regular locus of an affine hypertoric variety in
general. In the latter part, we show that the hamiltonian torus action is block
indecomposable if and only if $\mathbb{C}^*$-equivariant symplectic structures
on the associated hypertoric variety are unique up to scalar. In particular, we
establish the analogue of Bogomolov's decomposition for hypertoric varieties,
which is proposed by Namikawa for general conical symplectic varieties. As a
byproduct, we show that if two affine (or smooth) hypertoric varieties are
$\mathbb{C}^*$-equivariant isomorphic as varieties, then they are also the
hamiltonian torus action equivariant isomorphic as symplectic varieties. This
implies that the combinatorial classification actually gives the classification
of these varieties up to $\mathbb{C}^*$-equivariant isomorphisms.
