  Higher-dimensional Dedekind sums are defined as a generalization of a recent
1-dimensional probability model of Dilcher and Girstmair to a d-dimensional
cube. The analysis of the frequency distribution of marked lattice points leads
to new formulae in certain special cases, and to new bounds for the classical
Dedekind sums. Upper bounds for the generalized Dedekind sums are defined in
terms of 1-dimensional moments. In the classical two-dimensional case, the
ratio of these sums to their upper bounds are cosines of angles between certain
vectors of n-dimensional cones, conjectured to have a largest spacial angle of
pi/6.
