for the non-pedologists:
Sandy clay is a textural box on the soil triangle. It’s small and requires the absence of silt. The reason we joke about them not existing is because of the size of the box and how far apart the two grain sizes are. There are very few scenarios where sand and clay would be deposited and not silt.
Also what’s the deal with the weird shape of the Sandy Loam section? At the bottom center, there’s a point where you could start with loam, then remove clay and add silt to get sandy loam. It has the same amount of sand!
Part of it has to do with loam being a balance of clay, sand, and silt but not equal parts of each. Another part of it has to do with the outsized weight clay content has on the soil characteristics.
This is also why loamy sand and sand are angled as they are in the chart.