Johnson extends the operator to work with a placeholder 1 nodes, which removes mirrors, doubling the size of the fundamental domain and cuts the group order in half. In general this operation only applies to individual mirrors bounded by even-order branches. The 1 represents a mirror so [2p] can be seen as [2p, 1 ], [ 1,2p], or [ 1,2p, 1 ], like diagram or , with 2 mirrors related by an order-2p dihedral angle. The effect of a mirror removal is to duplicate connecting nodes, which can be seen in the Coxeter diagrams: = , or in bracket notation:[1,2p, 1 ] = [ 1,p, 1 ] = [p].