The transneptunian region of the solar system is populated by a wide variety of icy bodies showing great diversity. The dwarf planet (136108) Haumea is among the largest TNOs and displays a highly elongated shape and hosts two moons, covered with crystalline water ice like Hamuea. Haumea is also the largest member of the sole TNO family known to date. A catastrophic collision is likely responsible for its unique characteristics. We report here on the analysis of a new set of observations of Haumea obtained with SINFONI at the ESO VLT. Combined with previous data, and using light-curve measurements in the optical and far infrared, we carry out a rotationally resolved spectroscopic study of the surface of Haumea. We describe the physical characteristics of the crystalline water ice present on the surface of Haumea for both regions, in and out of the Dark Red Spot (DRS), and analyze the differences obtained for each individual spectrum. The presence of crystalline water ice is confirmed over more than half of the surface of Haumea. Our measurements of the average spectral slope confirm the redder characteristic of the spot region. Detailed analysis of the crystalline water-ice absorption bands do not show significant differences between the DRS and the remaining part of the surface. We also present the results of applying Hapke modeling to our data set. The best spectral fit is obtained with a mixture of crystalline water ice (grain sizes smaller than 60 micron) with a few percent of amorphous carbon. Improvements to the fit are obtained by adding ~10% of amorphous water ice. Additionally, we used the IFU-reconstructed images to measure the relative astrometric position of the largest satellite Hi`iaka and determine its orbital elements. An orbital solution was computed with our genetic-based algorithm GENOID and our results are in full agreement with recent results.
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