Why is the CMYK space four sided in chromaticity charts In chromaticity charts the CMYK color space is usually four-sided. I've lately had to read quite a few charts and it suddenly dawned to me that I don't really understand why. It has just not been something I've needed to think about until now.



Image 1: A sample CIE31 chromaticity graph showing the spaces*.

One of my working hypotheses is that it is actually a triangle. This triangle just clips for some reason. But there might be other reasons such as non-ideality of the color primaries, or bad plane. So why is it squarish?

* This image is not so clearly a polygon, like it's usually depicted as, but it's the best one I had at hand.
There are two aspects to this:


The traditional chromaticity graph is actually a two-dimensional slice of a three-dimensional volume.  The slice usually used is one that matches up (more or less) to the fully-saturated primaries of an RGB-based colorspace; the full RGB colorspace is a tetrahedron.
CMYK is a four-primary colorspace, with primaries that are not linearly independent.  This makes the full volume a complex shape.  Further, at least one (black) and possibly all four of the primaries don't lie on the plane of the 2D chromaticity graph.


The CMYK space is four-sided because it's a 2D slice of a complex 3D shape that (probably) doesn't lie on any of the surfaces of that shape.