Stewart B4,3 and B4,4 polyhedra

thingiverse

In "Adventures Among the Toroids" by Professor Bonnie M. Stewart, I discovered unique polyhedra that he uses as examples of a specific type not discussed elsewhere in the book. They are known as B4,3 (with square sides removed) and B4,4 (triangle sides removed), also called octahemioctahedron and cubohemioctahedron. Both share a property of having four hexagonal faces that intersect, similar to the tetrahemihexahedron. However, unlike the latter, B4,3 is orientable while B4,4 is non-orientable. The models can be customized by choosing the polyhedron type, side length, fillet block size, and print orientation. For B4,3, a hollow side is recommended for printing without support, whereas B4,4 requires a solid side. Post-processing using tools like Netfabb or Meshlab may be necessary before slicing. The provided STL files are 30 mm in size, rotated to print without support and fixed in Netfabb Cloud.