We show that the solitonic branes of ten-dimensional IIA/IIB string theory must satisfy, upon toroidal compactification, a specific wrapping rule in order to reproduce the number of half-supersymmetric solitonic branes that follows from a supergravity analysis. The realization of this wrapping rule suggests that IIA/IIB string theory contains a whole class of so-called "non-standard" Kaluza-Klein monopoles.
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