Trying to understand reduction of color dimension in colorblind case
Let's start with a quick overview of the different types of dichromats in man:


Protanopes have no functional red cones. Red appears as black. Certain shades of orange, yellow, and green all appear as yellow. 
Deuteranopes have no functional green cones. They tend to see reds as brownish-yellow and greens as beige. 
Tritanopes have blue-yellow color blindness and lack blue cone cells. Blue appears green and yellow appears violet or light grey.


Now color vision can be modeled with the Hering model, where there are two opponent channels, namely red-green and blue-yellow. These opponent channels determine color vision. Because of these two limbs, color space is often represented as triangles, rather than cubes as in your post. Fig. 1 shows the color space in trichromats. In Fig. 2 the same is shown, alongside the three types of dichromatic deficiencies.


Fig. 1. Color space in trichromats. source: Lighting Analysis   


Fig. 2. Triangles in trichromatic and dichromatic vision. source: Chartlr.