The domain and range of the CIECAM16 forward transformation was numerically determined and visualized for CIE standard illuminants, using a linear programming approach that provides the gamuts and colour solids for optimum colours. The effect of the surround, adapting luminance, and luminance of the background on the range of the CIECAM16 forward transformation were individually analyzed, showing that their ranges increased when the surround changed from dark to dim or average, the adapting luminance increased, or the luminance of the background decreased. The proposed methodology for the determination and visualization of the domain and range of the CIECAM16 forward transformation can be used for any illuminant, as well as for CIECAM02, CAM16, CAM02-UCS and CAM16-UCS. The findings of this paper not only solve the long-term unresolved domain and range problems of the CIE colour appearance models, but also find applications in cross-media colour reproduction. Furthermore, it was also found that some non-CIE colours are inside the International Color Consortium Profile Connection Space (ICC PCS), and some CIE colours are not included in that space.