  The $n$-skeleton of the canonical cubulation $\cal C$ of $\mathbb{R}^{n+2}$
into unit cubes is called the {\it canonical scaffolding} ${\cal{S}}$. In this
paper, we prove that any smooth, compact, closed, $n$-dimensional submanifold
of $\mathbb{R}^{n+2}$ with trivial normal bundle can be continuously isotoped
by an ambient isotopy to a cubic submanifold contained in ${\cal{S}}$. In
particular, any smooth knot $\mathbb{S}^{n}\hookrightarrow\mathbb{R}^{n+2}$ can
be continuously isotoped to a knot contained in ${\cal{S}}$.
