A Kakutani-von Neumann map is the push-forward of the group rotation (Z_2,+1)
to a unit simplex via an appropriate topological quotient. The usual quotient
towards the unit interval is given by the base 2 expansion of real numbers,
which in turn is induced by the doubling map. In this paper we replace the
doubling map with an n-dimensional generalization of the tent map; this allows
us to define Kakutani-von Neumann transformations in simplexes of arbitrary
dimensions. The resulting maps are piecewise-linear bijections (not just mod 0
bijections), whose orbits are all uniformly distributed; in particular, they
are uniquely ergodic w.r.t. the Lebesgue measure. The forward orbit of a
certain vertex provides an enumeration of all points in the simplex having
dyadic coordinates, and this enumeration can be translated via the
n-dimensional Minkowski function to an enumeration of all rational points. In
the course of establishing the above results, we introduce a family of
{+1,-1}-valued functions, constituting an n-dimensional analogue of the
classical Walsh functions.