Stewart B4,3 and B4,4 polyhedra
I came across these polyhedra in Professor Bonnie M. Stewart's wonderful book, Adventures Among the Toroids. They aren't toroidal, and he uses them as examples of a particular type of polyhedron that he doesn't discuss elsewhere in the book; nevertheless, I thought they were worth modeling.
In Stewart's notation, the cuboctahedron is B4, and these two are B4,3 (with square sides removed) and B4,4 (triangle sides removed). They're otherwise known as an octahemioctahedron and a cubohemioctahedron. They share the property of having four hexagonal faces that cut each other, similar to the tetrahemihexahedron; like that shape, B4,4 is non-orientable. Interestingly, though, B4,3 is orientable. For both models it's easier to see the central hexagons if they're colored or painted after printing.
March 20 update - I added an option to choose the plain B4 so you can print a set of all three shapes, along with its STL.