  Certain spontaneously broken gauge theories contain massless magnetic
monopoles. These are realized classically as clouds of non-Abelian fields
surrounding one or more massive monopoles. In order to gain a better
understanding of these clouds, we study BPS solutions with four massive and six
massless monopoles in an SU(6) gauge theory. We develop an algebraic procedure,
based on the Nahm construction, that relates these solutions to previously
known examples. Explicit implementation of this procedure for a number of
limiting cases reveals that the six massless monopoles condense into four
distinct clouds, of two different types. By analyzing these limiting solutions,
we clarify the correspondence between clouds and massless monopoles, and infer
a set of rules that describe the conditions under which a finite size cloud can
be formed. Finally, we identify the parameters entering the general solution
and describe their physical significance.
