These 4 tilings are the "normal" snubs, sometimes called the wythoffian snubs (even though they're not really very wythoffian). They can be formed by alternating omnitruncates and then resizing edge lengths until they're all equal. I don't think any of these are used in nonprismatic honeycombs, but if any were to be used, the 3 squattic-y ones would have a much better chance than the kihexattic one. Two of these have representations as semisnubs, giving them Bonus Symmetry. Snasquat and snathat have mirror symmetric pentagon verfs, rasisquat has a mirror symmetric pentagram verf, and snassa's verf is an evil nonconvex chiral hexagon (a kicapellogram for my noble enthusiasts).
These two are the only convex ones. The cyclotriggic omnisnub is just trat.
31: Snasquat - Snub square tiling. Its faces are triangles and squares. Symbols are s4s4o and s4s4s. This is alternated tosquat, and thus has representation as either a semisnub or an omnisnub, with the semisnub having reflection symmetry and only one type of square. I call s4s4o symmetry "iosquattic".
32: Snathat - Snub trihexagonal tiling. Its faces are two orbits of triangles and hexagons. Symbol is s3s6s. This is alternated grothat. As is obvious by looking at it, this is a diminishing of trat. All nonconvex hexattic snubs end up overlapping into exotic members of the trat regiment, so only this one manages to exist.
This case is a retrosnub. Only squattic symmetry allows a retrosnub, because the hexattic one is exotic.
33: Rasisquat - Retrosnub square tiling. Its faces are triangles and squares. Symbols are s4/3s4o and s4/3s4/3s. This is alternated quitsquat, and thus has representation as either a semisnub or an omnisnub, with the full semisnub symmetry being iosquattic with only one type of square. It's almost like it's the conjugate of snasquat or something!
34: Snassa - Snub squarisquariapeirogonal tiling. Its faces are triangles, two orbits of squares, and apeirogons. Symbol is s4s4/3s∞*a. This is alternated satsa. This is the only snub tiling with a nonlinear diagram, and thus the only one with a hexagonal verf. This is also the only squattic snub without bonus symmetry, and the only snub with apeirogons. Essentially, it's very strange. There's actually quite a large superregiment here with many wacky polygon arrangements, but it unfortunately doesn't manage to produce anything else.
Below shows how the snubs pair up as conjugates.
Conjuates:
The following are self-conjugate: snathat (trivially), and snassa
The following are conjugate pairs: snasquat-rasisquat
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