Chapter 5 - Simplest (R)(A)(Q)(T) Toroids of genus p=1

Finally we get to the models we are most interested in. (R)(A)(Q)(T)(D) toroids. The Quasiconvex property and the Tunneled property will lead us to some convex polyhedra that can be drilled by removing other polyhedra (excavations).

Model .Stel Genus Properties Pages with Diagram Pages with Description Notes T4 / gQ4P4Q4 .Stel 1 (R)(A)(Q)(T)(D) 29     Q32 / S3S3 .Stel 1 (R)(A)(Q)(T)(D) 4, 31, 136 3, 75, 77 "Tortuous tunnel" Q3P6Q3 / P6 .Stel 1 (R)(A)(Q)(T)(D) 32   convex hole Q3P6gQ3 / P6 .Stel 1 (R)(A)(Q)(T)(D) 32   convex hole Q42 / B4 .Stel 1 (R)(A)(Q)(T)(D) 33   convex hole K3 / Q3T3 .Stel 1 (R)(A)(Q)(T)(D) 34 42   K3 / gQ3T3=cheat .Stel 1 (R)(Q)(T)(D)   34 cheat - coplanar faces Q4P8 / P4Q4 .Stel 1 (R)(A)(Q)(T)(D) 35   orthogonal translation Q5P10 / P5Q5 .Stel 1 (R)(A)(Q)(T)(D) 35   orthogonal translation R5P10 / P5R5 .Stel 1 (R)(A)(Q)(T)(D) 35   orthogonal translation R5 / S5Q5 .Stel 1 (R)(A)(Q)(T)(D) 4, 36, 136   "Oriental hat" E4 / P4B4 .Stel 1 (R)(A)(Q)(T)(D) 37   unit elongation Q3P6Q3 / S3(P3)S3 .Stel 1 (R)(A)(Q)(T)(D) 37   unit elongation Q3P6Q3 / P3(S3)S3 .Stel 1 (R)(A)(Q)(T)(D) 37   unit elongation R5P10 / S5(P5)Q5 .Stel 1 (R)(A)(Q)(T)(D) 37   unit elongation R5P10 / P5(S5)Q5 .Stel 1 (R)(A)(Q)(T)(D) 37   unit elongation R5P10R5 / P10 .Stel 1 (R)(A)(Q)(T)(D) 38   convex hole R5P10gR5 / P10 .Stel 1 (R)(A)(Q)(T)(D) 38   convex hole Q4T4Q4 / B4(P4)B4 .Stel 1 (R)(A)(Q)(T)(D) 39     Q4T4Q4 / B4(B4)P4 .Stel 1 (R)(A)(Q)(T)(D) 39     T4 / Q4P4Q4 .Stel 1 (R)(A)(Q)(T)(D) 40   hole gyrated T4≈P4⊕6Q4⊕8Y3 .Stel NA NA 40   dissection Q4T4 / P4(B4)Q4 .Stel 1 (R)(A)(Q)(T)(D) 40   Q4-elongated Q4T4 / B4(P4)Q4 .Stel 1 (R)(A)(Q)(T)(D) 40   Q4-elongated Prev - Chapter 4 - (R)(A)(C) Deltahedra Next - Chapter 6 - Simplest (R)(A)(Q)(T) Toroids of genus p=2,3 Back to Adventures Among the Toroids - Index 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). Back to the main Polyhedron Page. Link to this page as http://Polyhedra.Doskey.com/Stewart05.html Alexander's Polyhedra, (c) 1998-2006, Alex Doskey