"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:
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