  We propose a new contact relation between polytopes. Intuitively, we say that
two polytopes are in strong contact if a small enough object can pass from one
of them to the other while remaining in their union. In the first half of the
paper we prove that this relation is indeed a contact relation between
polytopes, which turns out not to be the case for arbitrary regular closed in
Euclidean spaces sets. In the second half we study the universal fragments of
the logics of the resultant contact algebras. We prove that they all coincide
with the set of theorems of a standard quantifier-free formal system for
connected contact algebras, which also coincides with the universal fragments
of the logics of a variety of (classes of) contact algebras of interest.
