I didn't know that. Wouldn't that make the spectral locus pretty incomplete when viewed on an RGB monitor or printed with a printer that only uses CMYK?
That is correct. There is no display nor printer that can reproduce such saturated red, green and blue colors as depicted in the CIE (x,y)-chromaticity diagram (AKA spectral locus).
For the RGB cube and 2D x,y-chromaticity diagram, there is a way to transform the cube into spectral locus representation, but the opposite is not true. RGB values can be transformed into CIE-XYZ values using a linear transformation. XYZ values then can be further transformed into x,y coordinates which are the basis of the spectral locus diagram. However, along the way, the Y (luminance) component is lost and only 2D graph projected. Not knowing the luminance values, one cannot get back to XYZ, thus precluding calculation of RGB values. As Eric Chan pointed out, the RGB gamut (and cube) shown in your previous post
would not match the x,y-diagram. However if you had a hypothetical RGB color space (gamut) that has primaries of the spectral locus, then there would be a mathematical translation going in direction RGB->XYZ>x,y. Prolem is that while RGB space is linear, x,y-chromaticity diagram is not. That means that same changes in the RGB cube would not correspond to perceived changes in the x,y diagram.
Some more details and pictures are at this webpage
. For transformation of sRGB space to XYZ (->y,y), see equation VII-inv.