Just as a sidenote: In Computer Graphics (and according to Grassmann's law) colour is a three dimensional quantity.
https://en.wikipedia.org/wiki/YUV
Scroll down a bit and look at the Notes section. Colors seem to have different shapes. Red occupies a corner of the cube. Cyan a whole edge. Trying to flatten the space by removing the lights and darks just doesn't work.
Color is weird.
Without seeing the cube viz in my link, I'm likely to look at CIELAB and say, "oh, sure, but you can just take out the brightness and then it's all flat again." The cube makes it clear what happens when you do that.