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We perform a systematic search for N=1 Minkowski vacua of type II stringtheories on compact six-dimensional parallelizable nil- and solvmanifolds(quotients of six-dimensional nilpotent and solvable groups, respectively).Some of these manifolds have appeared in the construction of string backgroundsand are typically called twisted tori. We look for vacua directly in tendimensions, using the a reformulation of the supersymmetry condition in theframework of generalized complex geometry. Certain algebraic criteria toestablish compactness of the manifolds involved are also needed. Although theconditions for preserved N=1 supersymmetry fit nicely in the framework ofgeneralized complex geometry, they are notoriously hard to solve when coupledto the Bianchi identities. We find solutions in a large-volume,constant-dilaton limit. Among these, we identify those that are T-dual tobackgrounds of IIB on a conformal T^6 with self-dual three-form flux, and henceconceptually not new. For all backgrounds of this type fully localizedsolutions can be obtained. The other new solutions need multiple intersectingsources (either orientifold planes or combinations of O-planes and D-branes) tosatisfy the Bianchi identities; the full list of such new solution is given.These are so far only smeared solutions, and their localization is yet unknown.Although valid in a large-volume limit, they are the first examples ofMinkowski vacua in supergravity which are not connected by any duality to aCalabi-Yau. Finally, we discuss a class of flat solvmanifolds that may lead toAdS_4 vacua of type IIA strings.Comment: 75 pages, 1 figure. v.2: minor corrections, references added; v3:  several changes and clarification

A scan for new Script N = 1 vacua on twisted tori