  We argue that the T-duality phenomenon is not exclusively a stringy effect
but it is relevant also in the context of the standard point particle dynamics.
To illustrate the point, we construct a four-parametric family of
four-dimensional electro-gravitational backgrounds such that the dynamics of a
charged point particle in those backgrounds is insensitive to a particular
permutation of the parameters although this very permutation does alter the
background geometry. In particular, we find that a direct product of the
Euclidean plane with the two-dimensional Euclidean black hole admits a
point-particle T-dual with asymptotically negative curvature. For neutral
particles, this point-particle T-duality picture gets slightly modified because
the T-duality map is no longer defined everywhere but only on a dense open
domain of the space of states. We suggest a possible interpretation of this
phenomenon in terms of a point particle T-fold.
