Context : The transneptunian region of the solar system is populated by a wide variety of icy bodies showing great diversity in orbital behavior , size , surface color , and composition . Aims : The dwarf planet ( 136108 ) Haumea is among the largest transneptunian objects and is a very fast rotator ( \sim 3.9h ) . This dwarf planet displays a highly elongated shape and hosts two small moons that are covered with crystalline water ice , similar to their central body . A particular region of interest is the Dark Red Spot ( DRS ) identified on the surface of Haumea from multiband light-curve analysis ( Lacerda et al . 2008 ) . Haumea is also known to be the largest member of the sole TransNeptunian Objects ( TNO ) family known to date , and an outcome of a catastrophic collision that is likely responsible for the unique characteristics of Haumea . Methods : We report here on the analysis of a new set of near-infrared Laser Guide Star assisted observations of Haumea obtained with the Integral Field Unit ( IFU ) Spectrograph for INtegral Field Observations in the Near Infrared ( SINFONI ) at the European Southern Observatory ( ESO ) Very Large Telescope ( VLT ) Observatory . Combined with previous data published by Dumas et al . ( 2011 ) , and using light-curve measurements in the optical and far infrared to associate each spectrum with its corresponding rotational phase , we were able to carry out a rotationally resolved spectroscopic study of the surface of Haumea . Results : We describe the physical characteristics of the crystalline water ice present on the surface of Haumea for both regions , in and out of the 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 ( 1.45 \pm 0.82 % by 100 nm ) 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 \mu m ) with a few percent of amorphous carbon . Improvements to the fit are obtained by adding \sim 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 . Conclusions :