  Different compactifications of six-dimensional string theory on $M_4 \times
T^2$ are considered. Particular attention is given to the roles of the reduced
modes as the $S$ and $T$ fields. It is shown that there is a discrete group of
invariances of an equilateral triangle hidden in the model. This group is
realized as the interchanges of the two-form fields present in the intermediate
step of dimensional reduction in five dimensions. The key ingredient for the
existence of this group is the presence of an additional $U(1)$ gauge field in
five dimensions, arising as the dual of the Kalb-Ramond axion field strength.
As a consequence, the theory contains more four-dimensional $SL(2,R)$
representations, with the resulting complex scalar axidilaton related to the
components of the Kaluza-Klein vector fields of the naive dimensional
reduction. An immediate byproduct of this relationship is a triadic
correspondence among the fundamental string, the solitonic string, and a
singular Brinkmann pp wave.
