  We define a notion of facets-pairing structure and its seal space on a nice
manifold with corners. We will study facets-pairing structures on any cube in
detail and investigate when the seal space of a facets-pairing structure on a
cube is a closed manifold. In particular, for any binary square matrix $A$ with
zero diagonal in dimension n, there is a canonical facets-pairing structure
$F_A$ on the n-dimensional cube. We will show that all the closed manifolds
that we can obtain from the seal spaces of such $F_A$'s are neither more nor
less than all the generalized real Bott manifolds --- a special class of real
toric manifolds introduced by Choi, Masuda and Suh.
