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Starting from the classification of 6-dimensional Drinfeld doubles and theirdecomposition into Manin triples we construct 3-dimensional Poisson-Lie T-dualor more precisely T-plural sigma models. Of special interest are those that areconformally invariant. Examples of models that satisfy vanishing beta-functionequations with zero dilaton are presented and their duals are calculated. Itturns out that for "traceless" dual algebras they satisfy the beta-functionequations as well but usually with rather nontrivial dilaton. We also presentexplicit examples of several kinds of obstacles and difficulties present inconstruction of quantum dual models. Such concrete examples might be helpful infurther development and improvement of quantum version of Poisson-LieT-duality.Comment: 21 pages, minor typos corrected and clarifications adde

Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models