The use of 3D-polar coordinate representations of the RGB colour space is widespread, although many of these representations, such as HLS and HSV, have deficiencies rendering them unsuitable for quantitative image analysis. Three prerequisites for 3D-polar coordinate colour spaces which do not suffer from these deficiencies are suggested, and the results of the derivation of three colour spaces based on these prerequisites are presented. An application which takes advantage of their good properties for the construction of colour histograms is also discussed.