G-structures have proven to be an effective tool to study supergravity vacua. Thus a 6 dimensional internal space must carry an SU(3)-strucure, and SCTVs happen to be good candidates for such spaces. After introducing the formalism of toric varieties, we will use the powerful tools that toric geometry provides us to develop systematic methods to construct SU(3)-structures on a wide class of SCTVs.

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