Tom Verhoeff's work also involves '3D Turtle Graphics' which is essentially 'Minkowski addition' in drag. I haven't been able to read Tom Verhoeff's paper on this subject (it's behind a pay wall), but I would imagine that he uses perfectly mitered joins (or gets them for free) through the use of 3D turtle graphics & Minkowski summing. At 11:04 AM 6/4/2013, George Hart wrote:
Henry,
If you are interested in minimizing the number of triangles in the surface, be aware that the sides of an n-gon prism are represented in the STL file as 2n triangles, which is identical in cost to an n-gon antiprism. So constraining your algorithm to prismatic struts does not help with the sides of the struts and can hurt if extra facets are needed to close up the surface around vertices.
If you are interested in minimizing the number of triangles in the boundary, see this earlier paper, which uses a duality-based approach that gives surprisingly small STL files for high-genus graph embeddings:
George Hart, "Solid-Segment Sculptures," Proceedings of Colloquium on Math and Arts, Maubeuge, France, 20-22 Sept. 2000, and in Mathematics and Art, Claude Brute ed., Springer-Verlag, 2002, pp. 17-28.
http://georgehart.com/solid-edge/solid-edge.html
For the "No-twist" theorem of mitered prismatic struts in a loop, see several papers by Tom Verhoeff in the Proceedings of the Bridges Conference from 2008-2011. He has also made some rotating animations of the type you suggest:
http://www.win.tue.nl/~wstomv/publications/
George http://georgehart.com/