Structural characteristics of the spherically averaged internally folded density or reciprocal form factor B(r) are studied within the Hartree-Fock framework for 103 neutral atoms, 54 singly charged cations, and 43 anions in their ground state. The function B(r) is classified throughout the Periodic Table into three types: (i) monotonic decrease from the origin, (ii) maximum at r=0 and a negative minimum at r>0, and (iii) a local maximum at r=0 and a pair maximum-minimum out of the origin. A detailed study of the corresponding properties for individual subshells as well as their relative weight for the total B(r) is also carried out. For completeness, the analytical B(r) for hydrogenlike atoms in both ground and excited states is also analyzed. (C) 2004 American Institute of Physics.