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''.



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> 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 $\lbrace 2, 3 \rbrace$)?
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Note that, for example, all braid groups are of this type.



Generalising right-angled Artin groups
These groups are called Artin groups of small type. See, for example, Crisp, John; Paris, Luis,
The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group. 
Invent. Math. 145 (2001), no. 1, 19–36.


