We discuss the different discrete duality symmetries in six dimensions
that act within and between (i) the 10-dimensional heterotic string c
ompactified on T-4, (ii) the 10-dimensional type IIA string compactifi
ed on K3 and (iii) the 10-dimensional type IIB string compactified on
K3, In particular we show that the underlying group-theoretical struct
ure of these discrete duality symmetries is determined by the proper c
ubic group C/Z(2). Our group theoretical interpretation leads to simpl
e rules for constructing the explicit form of the different discrete t
ype II duality symmetries in an arbitrary background. The explicit dua
lity rules we obtain are applied to construct dual versions of the 6-d
imensional chiral null model.