Is there an own name of the $(k-1)$ cells that are attached to a given $k$ cell (or in other words: of the $(k-1)$ cells that intersects a given closed $k$ cell, or yet another words: of the $(k-1)$ cells that are in the boundary of a given closed $k$ cell)?
Subquestion: Is there a notation for the relation beetween cells $A$ and $B$ that tells that $A$ is one less dimensional that $B$ and is attached to $B$?
I've seen facet, followed by ridge (k-2) and peak (k-3).