So, the only solution, as displayed in my rough drawing below, is to choose these hypothetical colors outside the visible color range. No matter which colors you choose, there will always be colors outside of the gamut (the range of your shape) because the lines of your shape will always have a straight edge, and the spectrum itself is curved. The point being that any 3 primaries would mathematically be like drawing a basic triangle or polygon on this graph. Note there are other new RGB technologies available to expand this range already.
I have drawn out 2 (approximate) areas showing how much of this color range can be reproduced with the current CMYK and RGB standards. This diagram below is something I’ve drawn to help you understand this concept, and it might make more sense as you keep reading – the graph itself is the CIE 1931 Color System and the colors reflect all of the colors that we can see.
And because this range of colors actually ranges on a curve rather than a flat edge (don’t even ask me the maths here), it’s impossible to choose any number of primary colors within the gamut of colors that would mix to create every color that we can see. The CIE 1931 Color System was created to capture the full gamut of colors that humans can see. In simple terms, imaginary primaries are hypothetical colors that humans are incapable of seeing. (I googled this and the Wikipedia page was literally titled “impossible color”) This is what happens when we let mathematicians get involved in art.
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