Hausdorff metric on faces of the $n$-cube

The Hausdorff metric on all faces of the unit $n$-cube ($\mathrm I^n$) is considered. The notion of a cubant is used; it was introduced as an $n$-digit quaternary code of a $k$-dimensional face containing the Cartesian product of $k$ frame unit segments and the face translation code within $\mathrm I^n$. The cubants form a semigroup with a unit (monoid) with respect to the given operation of multiplication. A calculation of Hausdorff metric based on the generalization of the Hamming metric for binary codes is considered. The supercomputing issues are discussed.