It was hypothesized that egg-laying Papilio butterflies could use polarizational colours as a cue to detect leaf orientation and to discriminate between shiny and matt leaves. These hypotheses would be supported if the following general questions were answered positively: (1) Can surface orientation be unambiguously coded by the polarizational colours perceived by polarization-sensitive colour vision systems? (2) Are the changes in the polarizational colours due to retinal rotation significantly different between shiny and matt surfaces? Using video polarimetry, we measured the reflection-polarizational characteristics of a shiny green hemisphere in the red, green and blue spectral ranges for different solar elevations and directions of view with respect to the solar azimuth as well as for sunlit and shady circumstances under clear skies. The continuously curving hemisphere models numerous differently oriented surfaces. Using the polarization- and colour-sensitive retina model developed earlier, we computed the polarizational colours of the hemisphere, and investigated the correlation between colours and local surface orientation. We also calculated the maximal changes of the polarizational colours of shiny and matt hemispheres induced by rotation of the retina. We found that a surface with any orientation can possess almost any polarizational colour under any illumination condition. Consequently, polarizational colours cannot unambiguously code surface orientation. Polarization sensitivity is even disadvantageous for the detection of surface orientation by means of colours. On the other hand, the colour changes due to retinal rotation can be significantly larger for shiny surfaces than for matt ones. Thus, polarizational colours could help discrimination between shiny and matt surfaces. The physical and perceptional reasons for these findings are explained in detail. Our results and conclusions are of general importance for polarization-dependent colour vision systems.