  A polyuble of a Manin triple can be regarded as the ``$n$-th power'' of it,
which plays an important rule in the study of Poisson geometry, mathematical
physics and Lie theory. In this paper, we first construct an isomorphism
between the $mn$-ble and the $n$-ubles of $m$-uble by colored graph and point
out it is unique. Then, we construct a class of Poisson homogeneous spaces and
obtain a class of Poisson homeomorphisms between them based on the first main
result. Last, we apply first two main results to multi-flag varieties as well
as multi-double flag varieties and construct a class of global Poisson
isomorphisms between them as well as their $T$-leaves.
