  This paper studies equable parallelograms whose vertices lie on the
Eisenstein lattice. Using Rosenberger's Theorem on generalised Markov
equations, we show that the set of these parallelograms forms naturally an
infinite tree, all of whose vertices have degree 4, bar the root which has
degree 3. This study naturally complements the authors' previous study of
equable parallelograms whose vertices lie on the integer lattice.
