I'm just over here making soil science memes, and you got to get all serious on me.
Sandy clay does exist, but it is very rare. Look at the size of the box on the triangle. Typically, it's only found in specific settings where you've had waterlain sediment with periodic flooding. The water has to move very quickly (to deposit only sand) and then have a period of stagnation to allow for the clay particles to settle out.
Because this is a rare occurrence in nature, the joke is that it doesn't exist
Each axis runs 0 to 100 clockwise. At any point in the triangle you represent a location 0 to 100 for any given axis. Remember that the axis are rotated relative to each other by 66 degrees, not the normal 90.
Edit: For example the top vertex represents 100 on the clay line but 0 for loam and silt. Whereas the top left corner of clay loam represents values of 40 clay, 45 sand and 15 silt