  We show that Guilfoyle's exact solutions of the Einstein-Maxwell equations
for spherical symmetric static electrically charged matter with a
Reissner-Nordstr\"om exterior possess a bewildering plethora of different types
of solutions. For the parameter space of the solutions we use two normalized
variables, $q^2/R^2$ and $r_0/R$, where $q$ is the total electric charge, $r_0$
is the radius of the object, and $R$ is a length representing the square root
of the inverse energy density of the matter. The two other parameters, the mass
$m$ and the Guilfoyle parameter $a$, both dependent on $q$, $r_0$ and $R$, are
analyzed in detail. The full parameter space of solutions $q^2/R^2\times r_0/R$
is explored with the corresponding types of solutions being identified and
analyzed. The different types of solutions are regular charged stars, including
charged dust stars and stars saturating the Buchdahl-Andr\'easson bound,
quasiblack holes, regular charged black holes with a de Sitter core, regular
black holes with a core of phantom charged matter, other exotic regular black
holes, Schwarzschild stars, Schwarzschild black holes, Kasner spacetimes,
pointlike and planar naked singularities, and the Minkowski spacetime. Allowing
for $q^2<0$, in which case it is not possible to interpret $q$ as electric
charge, also yields new solutions, some of which are interesting and regular,
others are singular. Some of these types of solutions as well as the matter
properties have been previously found and studied, here the full spectrum being
presented in a unified manner.
