terminology for simplicial sets

In something I've been thinking about recently, the condition on a simplicial set that all faces of non-degenerate simplices are non-degenerate seems to play a significant role. Does anyone know whether this condition has been considered previously, and if so whether it has a standard name? The condition is of course satisfied by those simplicial sets which are derived from simplicial complexes in the standard way, but it's more general: it allows the possibility that two (formally) different faces of a non-degenerate simplex might coincide, as long as they're not degenerate. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]