  The Florides solution, proposed as an alternative to the interior
Schwarzschild solution, represents a static and spherically symmetric geometry
with vanishing radial stresses. It is regular at the center, and is matched to
an exterior Schwarzschild solution. The specific case of a constant energy
density has been interpreted as the field inside an Einstein cluster. In this
work, we are interested in analyzing the geometry throughout the permitted
range of the radial coordinate without matching it to the Schwarzschild
exterior spacetime at some constant radius hypersurface. We find an interesting
picture, namely, the solution represents a three-sphere, whose equatorial
two-sphere is singular, in the sense that the curvature invariants and the
tangential pressure diverge. As far as we know, such singularities have not
been discussed before. In the presence of a large negative cosmological
constant (anti-de Sitter) the singularity is removed.
