  Dissections of polytopes are a well-studied subject by geometers as well as
recreational mathematicians. A recent application in coding theory arises from
the problem of parameterizing binary vectors of constant Hamming weight which
has been shown previously to be equivalent to the problem of dissecting a
tetrahedron to a brick. Applications of dissections also arise in problems
related to the construction of analog codes.
  Here we consider the rectangle-to-rectangle dissection due to Montucla.
Montucla's dissection is first reinterpreted in terms of the Two Tile Theorem.
Based on this, a cube-to-brick dissection is developed in $\mathbb{R}^n$. We
present a linear time algorithm (in $n$) that computes the dissection, i.e.
determines a point in the cube given a point in a specific realization of the
brick. An application of this algorithm to a previously reported analog coding
scheme is also discussed.
