  We examine in detail the relative equilibria of the 4-vortex problem when
three vortices have equal strength, that is, $\Gamma_{1} = \Gamma_{2} =
\Gamma_{3} = 1$, and $\Gamma_{4}$ is a real parameter. We give the exact number
of relative equilibria and bifurcation values. We also study the relative
equilibria in the vortex rhombus problem.
