  The group of isometries of the hyperbolic 3-space is one of the simplest
non-commutative complex Lie groups. Its quotient by the maximal compact
subgroup naturally maps it back to the hyperbolic space. Each fiber of this map
is diffeomorphic to the real projective 3-space.
  The resulting map can be viewed as the simplest non-commutative counterpart
of the amoeba map introduced, in the commutative setting, by Gelfand, Kapranov
and Zelevinsky. The paper surveys basic properties of the non-commutative
amoebas and compares them against their commutative counterparts.
