# Approximating triangles by squares

I have a simplicial complex $X$ embedded in $\mathbb{R}^n$ s.t. $|X|$ is an $n$-manifold. I would like to algorithmically construct a finite set $\Omega$ of $n$-cubes ("cube"=product of intervals) s.t. $\cup\Omega$ deformation retracts to $|X|$. Any hint? Intuition says that for a grid of small cubes one could define $\Omega$ to be set of all cubes from this grid having nonempty intersection with $X$. However, how small should be these cubes?

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