  Interplanetary Coronal Mass Ejections are the manifestation of solar
transient eruptions, which can significantly modify the plasma and magnetic
conditions in the heliosphere. They are often preceded by a shock, and a
magnetic flux rope is detected in situ in a third to half of them. The main aim
of this study is to obtain the best quantitative shape for the flux rope axis
and for the shock surface from in situ data obtained during spacecraft
crossings of these structures. We first compare the orientation of the flux
ropes axes and shock normals obtained from independent data analyses of the
same events, observed in situ at 1AU from the Sun. Then, we carry out an
original statistical analysis of axes/shock normals by deriving the statistical
distributions of their orientations. We fit the observed distributions using
the distributions derived from several synthetic models describing these
shapes. We show that the distributions of axis/shock orientations are very
sensitive to their respective shape. One classical model, used to analyze
interplanetary imager data, is incompatible with the in situ data. Two other
models are introduced, for which the results for axis and shock normals lead to
very similar shapes; the fact that the data for MCs and shocks are independent
strengthen this result. The model which best fit all the data sets has an
ellipsoidal shape with similar aspect ratio values for all the data sets. These
derived shapes for the flux rope axis and shock surface have several potential
applications. First, these shapes can be used to construct a consistent ICME
model. Second, these generic shapes can be used to develop a quantitative model
to analyze imager data, as well as constraining the output of numerical
simulations of ICMEs. Finally, they will have implications for space weather
forecasting, in particular for forecasting the time arrival of ICMEs at the
Earth.
