  Recently, using supergravity analysis, a hyperbolic reflection group was
found to underlie the structure of wall-crossing, or the discontinuous moduli
dependence of the supersymmetric index due to the presence of walls of marginal
stability, of the BPS dyons in the N=4, d=4 compactification. In this paper we
work in the regime where four-dimensional gravity decouples and we show how the
presence of such a group structure can be easily understood as a consequence of
the supersymmetry of a system of (p,q) five-brane network, or equivalently the
holomorphicity of the Riemann surface wrapped by the appropriate M5 branes in
the Euclidean M-theory frame.
