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The chromaticity diagram is said to describe all colors visible to the human eye. However, I have also read that all visible colors are contained in a 3D color space – very similar to a cone – and that the chromaticity diagram is only a cross section at the plane X+Y+Z=1

Chromaticity diagram

What is the relation of the chromaticity diagram and any other cross section in the 3D cone?

XYZ Color space

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"It's a cross section with plane x+y+z=1" is true in one of the numerous at a glance same looking color systems. That one is 1931 CIExyY, where the luminance is an independent component, x and y define the seen hue and chromaticity, but in a quite cryptic way.

Hopefully you are not searching any profound meanings or hidden connections between this shape and spiritual world. This is an arbitary math creation, a result of some practical math specs and numerous tests with a mass of people how they see colors.

The flatiron shape is the limit of perceived maximum chromaticity, humans cannot see any difference if the color is further away from the neutral point in xy plane. Those colors outside the flatiron curve actually do not even exist, because there's no way to create negative sensations in the eye.

The colors which are often stamped inside the flatiron are decorative ones, a big part of the flatiron interior isn't possible to be show in color on computer screens or as printed in CMYK.

The story is all in all highly complex. You should start the studies from this:

https://en.wikipedia.org/wiki/CIE_1931_color_space

Warning: The article is written like math texts. If you let your eyes scan it and pick something here and there, you'll get nothing. Everyhing is written in a way that you must remember and understand what's said above.

xyY system is still far from the predictable linearity of CIELab or the equivalent HCL.

In the very beginning you should notice that RGB and CMYK in computers and printers are ways to produce colors. Those early systems such as 1931 CIEXYZ or the flattened version of it 1931 CIExyY were developed as math models for seen colors. CIE had some goals to enhance the already existing models such as the numbers must be in practical range.

CIE is the International Commission on Illumination. Short name CIE is taken from its French title, the Commission Internationale de l´Eclairage

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The chromaticity diagram maps how humans sense color and what physicist call color (wavelength of light). It does not really explain anything else. Though due to its nature its good for explaining how a limited wavelength thing is shown. Also its true that the chromaticity diagram as drawn is just a slice and that the mapping eventually is not the same on all slices, but this is a bit more complicated then necessary to understand things.

The way you read the chart is that on the outer arc there is human sensing to pure one wavelength data. And data in between is between two points of pure wavelength. But it also prodicts that you can mix wavelengths for same color in many ways. Also from the chart you can see that magenta does not exist, its a pure illusion of human sensing apparatus.

are colors a cone? Well yes there are descriptions that define color as a cone. There are lots and lots of spaces used to describe color, each with their own problems and benefits. The reason for this is simply because color is not spatial, it is missing several qualifications for this to be true. So generating a space and drawing conclusions as a space does not universally make sense the same way as space does, so you need different systems for different properties.

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