A group generated by the elements P_i for i = 1, ..., n subject to (P_i P_j)^(M_(i j)) = 1, where M_(i j) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p, q, r)] for the Coxeter group generated by the nodes of a Y-shaped Coxeter-Dynkin diagram whose three arms have p, q, and r graph edges. A Coxeter group of this form is finite iff 1/(p + 1) + 1/(q + 1) + 1/(r + 1)>1.

bimonster | building | Coxeter-Dynkin diagram