  We construct modular spaces of all 6-dimensional real semisimple Drinfeld
doubles, i.e. the sets of all possible decompositions of the Lie algebra of the
Drinfeld double into Manin triples. These modular spaces are significantly
different from the known one for Abelian Drinfeld double, since some of these
Drinfeld doubles allow decomposition into several non-isomorphic Manin triples
and their modular spaces are therefore written as unions of homogeneous spaces
of different dimension. Implications for Poisson-Lie T-duality and especially
Poisson-Lie T-plurality are mentioned.
