  The $D$-dimensional Coulomb system serves as a starting point for generating
generalized atomic shells. These shells are ordered according to a generalized
Madelung rule in $D$ dimensions. This rule together with an {\it Aufbau
Prinzip} is applied to produce a $D$-dimensional periodic table. A model is
developed to rationalize the ordering of the shells predicted by the
generalized Madelung rule. This model is based on the introduction of an
Hamiltonian, invariant under the $q$-deformed algebra $U_q($so$(D))$, that
breaks down the SO($D+1$) dynamical symmetry of the hydrogen atom in $D$
dimensions. The $D=2$ case (Flatland) is investigated with some details. It is
shown that the neutral atoms and the (moderately) positive ions correspond to
the values $q=0.8$ and $q=1$, respectively, of the deformation parameter $q$.
