Chapter 6 - Simplest (R)(A)(Q)(T) Toroids of genus p=2,3

  • Now that we have seen models with polar tunnels, it is time to see a few (R)(A)(Q)(T)(D) toroids with more entrances. Of special interest will be models of tetrahedral, octahedral and icosahedral symmetry.
    Model.Stel GenusProperties Pages with Diagram Pages with DescriptionNotes
    4Q3(S3)=hole .Stel0 (R)(A)(D)41 hole only
    K3 / 4Q3(S3) .Stel3 (R)(A)(Q)(T)(D)41, 45 =4Q3+6Y4 - tetrahedral symm
    K3 / Q3(S3)Q3 .Stel1 (R)(A)(Q)(T)(D)42 polar natural
    K3 / gQ3(S3)Q3 .Stel1 (R)(A)(Q)(T)(D)42 polar gyrated
    K3≈S3⊕8Q3⊕6Y4 .StelNA NA42 dissection
    K3 / 2Q3(S3) .Stel1 (R)(A)(Q)(T)(D)43 apolar
    K3 / 2Q3(Y4P3) .Stel1 (R)(A)(Q)(T)(D)43 apolar
    K3 / 2Q3(Y4gP3) .Stel1 (R)(A)(Q)(T)(D)43 apolar
    K3 / 2Q3(Y4P4) .Stel1 (R)(A)(Q)(T)(D)43 apolar
    K3 / 3Q3(S3) .Stel2 (R)(A)(Q)(T)(D)44  
    K3 / 3Q3(S3)=hinge .StelNA NA44 hinged view
    K3 / 4Q3(S3)=hinge .StelNA NA45 hinged view
    (3Q3⊕3Y4)⊕(3Q3⊕3Y4) .Stel4 (R)(A)(T)(D)46 F(5,3,4) <= 48
    K4 / 5P4(E4) .Stel4 (R)(A)(Q)(T)(D) 46, 94-97 
    (Q3⊕3Y4)3P3(Q3⊕3Y4) .Stel2 (R)(A)(T)(D) 46 
    (Q3⊕3Y4)3P3(3Q3⊕3Y4) .Stel3 (R)(A)(T)(D) 46 
    (3Q3⊕3Y4)3P3(3Q3⊕3Y4) .Stel4 (R)(A)(T)(D) 46 

    Prev - Chapter 5 - Simplest (R)(A)(Q)(T) Toroids of genus p=1
    Next - Chapter 7 - Exploration of (R)(A) Toroids
    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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