  In the studied axisymmetric case of the central four-body problem, the axis
of symmetry is defined by two unequal-mass bodies, while the other two bodies
are situated symmetrically with respect to this axis and have equal masses.
Here, we consider a special case of the problem and assume that three of the
masses are equal. Using a recently found analytical solution of the general
case, we formulate the equations of condition for three equal masses
analytically and solve them numerically. A complete description of the problem
is given by providing both the coordinates and masses of the bodies. We show
furthermore how the three-equal-mass solutions are related to the general case
in the coordinate space. The physical aspects of the configurations are also
studied and discussed.
