Our next diversion from (Q) models is this chapter of (R)(A) toroids. These are conglomerations of convex polyhedra that together form a ring, or multiple rings, often interconnected. One area of exploration here is generating models that are comprised of specified n-gons, and finding models of arbitrarily high genus.
Many of the initial models consist of rings that are arranged in a planar fashion, but some other combinations of rings that are of special interest are those that wrap around to create models of tetrahedral, octahedral and icosahedral symmetry. Many of these models are based on the discoveries of Kurt Schmucker that 8 octahedra form a ring with special properties relating it to the rhombic dodecahedron, and 8 dodecahedra form a similar ring with properties relating it to the rhombic triacontahedron. I would propose calling the models based on these discoveries Stewart/Schmucker toroids.
Disclaimer: These pages are dedicated to B.M. Stewart. They are intended to be used by readers of his book to better illustrate his ideas in three dimensions. His book has tons of information that I do not intend to represent here, and I highly encourage anyone interested in this subject to buy the book. If you like my illustrations, please let me know. And if you are interested in a particular Stewart Toroid being modeled, please let me know and I will do what I can.
Thanks also to Robert Webb for his very cool "Stella" program. I have used it extensively to generate VRML files for my site. It is a great tool for rapid exploration of augmentations and excavations of polyhedra (among other things).
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Alexander's Polyhedra, (c) 1998-2006, Alex Doskey