  Aims: We present a magnetic Doppler imaging study from all Stokes parameters
of the cool, chemically peculiar star HD 24712. This is the very first such
analysis performed at a resolving power exceeding 10^5.
  Methods: The analysis is performed on the basis of phase-resolved
observations of line profiles in all four Stokes parameters obtained with the
HARPSpol instrument attached at the 3.6-m ESO telescope. We use the magnetic
Doppler imaging code, INVERS10, which allows us to derive the magnetic field
geometry and surface chemical abundance distributions simultaneously.
  Results: We report magnetic maps of HD 24712 recovered from a selection of
FeI, FeII, NdIII, and NaI lines with strong polarization signals in all Stokes
parameters. Our magnetic maps successfully reproduce most of the details
available from our observation data. We used these magnetic field maps to
produce abundance distribution map of Ca. This new analysis shows that the
surface magnetic field of HD 24712 has a dominant dipolar component with a weak
contribution from higher-order harmonics. The surface abundance distributions
of Fe and Ca show enhancements near the magnetic equator with an underabundant
patch at the visible (positive) magnetic pole; Nd is highly abundant around the
positive magnetic pole. The Na abundance map shows a high overabundance around
the negative magnetic pole.
  Conclusions: Based on our investigation and similar recent four Stokes
parameter magnetic mapping studies, we present a tentative evidence for the
hypothesis that Ap stars with dipole-like fields are older than stars with
magnetic fields that have more small-scale structures. We find that our
abundance maps are inconsistent with recent theoretical calculations of atomic
diffusion in presence of magnetic fields.
