An Artin group $G$ is determined by its Coxeter matrix $M$. This is a symmetric $n \times n$ matrix with entries from $\lbrace 2, 3, \ldots, \infty \rbrace$ that determine the relations between the generators of the group. If all of the entries are in $\lbrace 2, \infty \rbrace$ then we say that $G$ is a ``right-angled Artin group''.
Is there a name for an Artin group in which all of the entries of its Coxeter matrix are in $\lbrace 2, 3, \infty \rbrace$ (or alternatively $\lbrace 2, 3 \rbrace$)?
Note that, for example, all braid groups are of this type.