Stewart B4,3 and B4,4 polyhedra

thingiverse

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. Instructions The models are customizable to choose which polyhedron is generated, the length of a side, the size of the fillet blocks and whether a hollow or solid side is down. I found that with this shape, the fillet blocks needed to be slightly larger than with the tetrahemihexahedron model; the default works for my printers. Note that as far as I can see the B4,3 model is printable without support only on a hollow side, and B4,4 only on a solid side. Both are likely to need fixup with Netfabb, Meshlab or the like before they can be sliced. The STL files are 30 mm on a side, rotated to print without support and fixed in Netfabb Cloud.