It turns out that the chromaticity chart is harder to read than I anticipated. The CMYK slice is actually triangular of sorts its just that the chromaticity chart is not really linear.

The chromaticity chart is made with the assumption that light is a spectra. The curved arc is the pure spectral color of the rainbow. Everything in between is interpolated edge values.


[![enter image description here][1]][1]

**Image 1**: Visible specturm on the edge, interpolations on surface. 

Now magentas are a bit peculiar. They only exist in our brains interpretation, thus they can not be measured. Magentas are sort of virtual colors that make the color circle full. This means that when you move from absence of blue towards absence of green your line kinks since the graph has no well defined direction for magenta's. This makes a 4th corner where none should be located.

Magentas are thus a bit of virtual colors that only exist in our brain. Not in physics, they are 2 spectra interleaved. There are off course many such metamers.

  [1]: https://i.sstatic.net/COa4K.png