  Bonnor's map in General Relativity is duality between (dimensionally reduced)
vacuum gravity and static truncation of electro-vacuum theory. It was used as a
tool to generate an exact solution of electro-vacuum from some vacuum solution.
It can be expected that similar dualities will be useful for solution
generation in higher-dimensional theories too. Here we study such maps within a
class of theories in dimensions $D\leq 6$ using oxidation of D=3 cosets and
consistent truncation of the corresponding theories. Our class includes those
theories whose D=3 symmetries are subgroups of $G=O(5,4)$. It contains
six-dimensional minimal supergravity, five-dimensional minimal and $U(1)^3$
supergravities and a number of four-dimensional theories which attracted
attention recently in the search of exact solutions. We give explicit
reduction/truncation formulas relating different theories in dimensions $D=4,
5, 6$ in terms of metrics and matter fields and discuss various alternative
duality chains between them.
