For a simplicial complex $X$ with an action of a discrete group $G$, we can impose the following condition, namely that if $g\in G$ stabilizes a given simplex $\sigma\subseteq X$, then $g:\sigma\to\sigma$ is in fact the identity map. This condition is nice because it implies that the quotient $X/G$ is glued out of simplices (rather than simplices modulo a finite group of permutations of their vertices).

Is there a standard term for this condition (or any related one) on the action $G\curvearrowright X$?