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 GenusProperties Pages with Diagram Pages with DescriptionNotes
    T4 / gQ4P4Q4 .Stel1 (R)(A)(Q)(T)(D)29  
    Q32 / S3S3 .Stel1 (R)(A)(Q)(T)(D)4, 31, 1363, 75, 77"Tortuous tunnel"
    Q3P6Q3 / P6 .Stel1 (R)(A)(Q)(T)(D)32 convex hole
    Q3P6gQ3 / P6 .Stel1 (R)(A)(Q)(T)(D)32 convex hole
    Q42 / B4 .Stel1 (R)(A)(Q)(T)(D)33 convex hole
    K3 / Q3T3 .Stel1 (R)(A)(Q)(T)(D)3442 
    K3 / gQ3T3=cheat .Stel1 (R)(Q)(T)(D) 34cheat - coplanar faces
    Q4P8 / P4Q4 .Stel1 (R)(A)(Q)(T)(D)35 orthogonal translation
    Q5P10 / P5Q5 .Stel1 (R)(A)(Q)(T)(D)35 orthogonal translation
    R5P10 / P5R5 .Stel1 (R)(A)(Q)(T)(D)35 orthogonal translation
    R5 / S5Q5 .Stel1 (R)(A)(Q)(T)(D)4, 36, 136 "Oriental hat"
    E4 / P4B4 .Stel1 (R)(A)(Q)(T)(D)37 unit elongation
    Q3P6Q3 / S3(P3)S3 .Stel1 (R)(A)(Q)(T)(D)37 unit elongation
    Q3P6Q3 / P3(S3)S3 .Stel1 (R)(A)(Q)(T)(D)37 unit elongation
    R5P10 / S5(P5)Q5 .Stel1 (R)(A)(Q)(T)(D)37 unit elongation
    R5P10 / P5(S5)Q5 .Stel1 (R)(A)(Q)(T)(D)37 unit elongation
    R5P10R5 / P10 .Stel1 (R)(A)(Q)(T)(D)38 convex hole
    R5P10gR5 / P10 .Stel1 (R)(A)(Q)(T)(D)38 convex hole
    Q4T4Q4 / B4(P4)B4 .Stel1 (R)(A)(Q)(T)(D)39  
    Q4T4Q4 / B4(B4)P4 .Stel1 (R)(A)(Q)(T)(D)39  
    T4 / Q4P4Q4 .Stel1 (R)(A)(Q)(T)(D)40 hole gyrated
    T4≈P4⊕6Q4⊕8Y3 .StelNA NA40 dissection
    Q4T4 / P4(B4)Q4 .Stel1 (R)(A)(Q)(T)(D)40 Q4-elongated
    Q4T4 / B4(P4)Q4 .Stel1 (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).


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