The tile industry has determined (largely through an NTCA study) that a 1/4x1/2x1/4-inch U-notch trowel may be large enough for 10- and 12-inch tiles provided the floor and tiles are flat enough. The current flatness standard of 1/4-inch in 10-feet is OK for 1-, 2-, 3-, 4-, 6-, 8-, and some 10-inch tiles, but is inadequate for tiles 12-inches or larger.
One of the biggest problems in the tile industry is that some installers believe that a certain size trowel must be used for a particular size of tile. This results in lousy adhesion, poor compressive strength, poor shear strength, freeze/thaw damage in cold exteriors, and as a bonus, the voids below such tiles are probably the most secure location for mold and mildew to thrive.
And when the job fails, the installer invariably whines: "But I used a 1/4-inch notched trowel!!!!!"
To avoid problems and lawsuits, installers should be more concerned about COVERAGE. ANSI A108 standards call for 95% uniform coverage in wet or exterior areas and 80% in other areas. Since I understand the benefits of providing 95% coverage over 80%, it is the coverage I shoot for regardless of the installation.
Selecting trowel notch sizes from a chart has its risks since the chart usually cannot tell you the condition of the surface you want to tile. Instead, best practices call for a brief test prior to tiling that involves the actual tile and an actual setting bed. Try out your best guess to see what the actual coverage is: spread the mortar, using the grip and angle that is most comfortable to you, press in one of the tiles, and then remove it to check for coverage. Obviously, use fresh tile for each test until you have determined what notch size to use for your application.
For example, I recently installed 18-inch stone tiles over a floor warming system covered with a troweled-on featheredge compound that was flat to within a 1/4-inch in 10-feet - the current industry standard. For these tiles, I had to use a 1/4x3/4x3/4-inch U-notch trowel to apply adhesive to the floor AND back-butter each tile. In addition, because the floor surface was marginal, and because the tiles themselves were rather poorly gauged, additional thinset mortar (a medium bed thinset) had to be applied to the backs of numerous tiles.
Contrast that installation with a current floor covered with 24-inch porcelain tiles made by Stonepeak. First, the concrete slab had to be covered with a self-leveling underlayment to bring its surface up to the 1/16-inch in 10-foot tolerance that I spec'd for this installation. Like the SLC floor, each of the tiles is incredibly flat with no air gaps showing when a straightedge was placed against it. After trowel testing, these larger tiles were installed using a 1/4x1/2x1/4-inch U-notch trowel to spread the mortar on the floor, and a regular flat trowel was used to hard-trowel the back of each tile with a thin (less than 1/16-inch) layer of latex modified thinset.