  In the hypersphere soliton model (HSM), we study the geometrical inner
structures and the ensuing charge distributions of the nucleons by exploiting
the aspect of the HSM where the hypersphere soliton is described by an extended
object possessing the parameter $\lambda$ $(0\le\lambda<\infty)$ which
corresponds to the radial distance from the center of $S^{3}$ to the foliation
leaves of the hypersphere soliton. To do this, we investigate the foliation and
topology related with geometry on a hypersphere described by
$(\mu,\theta,\phi)$. Exploiting the so-called scanning algorithm we study
geometrical relations between spherical shell foliation leave on a northern
hemi-hypersphere $S^{3}_{+}$ and that on a flat equatorial solid sphere $E^{3}$
which contains the center of $S^{3}$. We then elucidate the physical meaning of
$\mu$ in $S^{3}$ of radius $\lambda$ by showing that $\mu$ plays the role of an
auxiliary angle to fix the radius $\lambda\sin\mu$ of the $S^{2}$ spherical
shell sharing the center of $S^{3}(=S^{2}\times S^{1})$, at a given angle
$\mu$. Next, using the charge density profiles of nucleons with $\mu$
dependence, we construct the nucleon fractional charges of spherically
symmetric and nontrivial distributions. In the HSM we note that the proton and
neutron charges do not leak out from the hypersphere soliton, and the positive
and negative charges in the neutron are confined inside and outside its core,
respectively. Explicitly we predict the fractional volumes and charges of the
neutron. The proton and neutron are shown to be described by a topological
structure of two Hopf-linked M\"obius strip type twist circles in $S^{3}$. We
also note that the characteristic ratio of the hypersphere volume to the
corresponding solid sphere one is given by a geometrical invariant related with
hyper-compactness.
