whether gluing the faces of tetrahedron in pairs would get a manifold?

whether gluing the faces of tetrahedron in pairs would get a manifold?

I think gluing the faces of tetrahedron in pairs would get a manifold.
Because gluing in pairs will make the result of gluing without boundary
and there is not Y structure in the result.
But it is not enough for proving it is a manifold. I want to know whether
there are any references about the question.