Simple set

Template:Multiple issues The three-dimensional 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. (After gluing the first pair of opposite faces the cube looks like a thick washer, after gluing the second pair — the flat faces of the washer — it looks like a hollow torus, the last gluing — the inner surface of the hollow torus to the outer surface — is physically impossible in three-dimensional space so it has to happen in four dimensions.)