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High Quality Content by WIKIPEDIA articles! Triple torus or three-torus can refer to one of the two following concepts, both related to a torus. Three-dimensional torus The three-dimensonal torus, or triple torus, is defined as the Cartesian product of three circles, mathbb{T}^3 = S^1 times S^1 times S^1. In contrast, the usual torus is the Cartesian product of two circles only. The triple torus is a three-dimensional compact manifold with no boundary. It can be obtained by gluing the three pairs of opposite faces of a cube.