  In the present paper, we investigate the question if the skeleton of a
Mumford curve of genus two can be tropicalized faithfully in dimension three,
i.e. if there exists an embedding of the curve in projective three space such
that the tropicalization maps the skeleton of the curve isometrically to its
image. Baker, Payne and Rabinoff showed that the skeleton of every analytic
curve can be tropicalized faithfully. However the dimension of the ambient
space in their proof can be quite large.
  We will define a map from the skeleton to the tropicalization of the
Jacobian, which is an isometry on the cycles. It allows us to find principal
divisors and simultanously to determine the retractions of their support on the
skeleton which is necessary to calculate their tropicalization.
  It turns out that a Mumford curve of genus two whose cycles of its skeleton
are either disjoint or share an edge of length at most half of the length of
the cycles, can be tropicalized faithfully in dimension three.
