Any smooth knot Sn ↪ Rn+2 is isotopic to a cubic knot contained in the canonical scaffolding of Rn+2

The n-skeleton of the canonical cubulation C of Rn+2 into unit cubes is called the canonical scaffolding S. In this paper, we prove that any smooth, compact, closed, n-dimensional submanifold of Rn+2 with trivial normal bundle can be continuously isotoped by an ambient isotopy to a cubic submanifold contained in S. In particular, any smooth knot S-n hooked right arrow Rn+2 can be continuously isotoped to a knot contained in S.