  Strong Steiner $\omega$-categories are a class of $\omega$-categories that
admit algebraic models in the form of chain complexes, whose formalism allows
for several explicit computations. The conditions defining strong Steiner
$\omega$-categories are traditionally expressed in terms of the associated
chain complex, making them somewhat disconnected from the $\omega$-categorical
intuition. The purpose of this paper is to characterize this class as the class
of polygraphs that satisfy a loop-freeness condition that does not make
explicit use of the associated chain complex and instead relies on the
categorical features of $\omega$-categories.
